We introduce basic mathematical techniques, followed by an exploration of three distinct topics: the Callan-Giddings-Harvey-Strominger (CGHS) model in 1+1-dimensional spacetime, the formation of astrophysical jets in Schwarzschild-like black holes, and collisions and confinement phenomena in the third-order Lovelock gravity. In the CGHS model, we investigate the collision of ghost fields within the dilaton background geometry, observing the formation and dissolution of wormholes by inserting and removing the ghost fields, respectively. This process mimics a cosmological-scale analogue of Feynman diagrams. Next, we study the non-zero expectation values of bumblebee fields due to Lorentz symmetry breaking. This alteration in the energy-momentum tensor necessitates the inclusion of a potential vacuum, resulting in a shift of the vacuum solution towards Schwarzchild-like black holes with a scaling factor $l$. This scaling factor facilitates discussions on the collision of null sources, leading to the formation of impulsive null shells and satisfying the type-D condition. When $l$ approaches zero, jet-like formations vanish, transforming the problem into one involving colliding gravitational waves, which is isometric to the Schwarzschild geometry. Moreover, our method can be applied to any resembling Schwarzschild-like metrics. We aim to enhance our model by incorporating additional physical factors such as extra polarizations or EM fields. Finally, our examination extends to the 4-dimensional third-order Lovelock gravity, observing that particles possess finite energy and be confined within the metric time interval extending from - to + infinity. Moreover, this finding does not admit flat rotation curves. Additionally, when collisions occur within the background of this metric, intriguingly, we observe impulsive Weyl curvatures along the null boundaries subsequent to the collision.

Gravitational lensing has empowered telescopes to discover astronomical objects that are otherwise out of reach without being highly magnified by foreground structures. While we expect gravitational waves (GWs) from compact binary coalescences to also experience lensing, the phenomenology of highly magnified GWs has not been fully exploited. In this letter, we fill this gap and explore the observational signatures of these highly magnified GWs. We find that these signatures are robust against modeling details and can be used as smoking-gun evidence to confirm the detection of lensing of GWs without any electromagnetic observation. Additionally, diffraction becomes important in some cases, which limits the maximum possible magnification and gives waveform signatures of lensing that can only be observed by GW detectors. Even with current-generation observatories, we are already sensitive to these highly magnified GWs and can use them to probe the high-redshift Universe beyond the usual horizon.

In this work we study the Friedmann-Lema\^{i}tre-Robertson-Walker cosmologies with arbitrary spatial curvature for the symmetric teleparallel theories of gravity, giving the first presentation of their coincident gauge form. Our approach explicitly starts with the cosmological Killing vectors and constructs the coincident gauge coordinates adapted to these Killing vectors. We then obtain three distinct spatially flat branches and a single spatially curved branch. Contrary to some previous claims, we show that all branches of connection in the covariant approach can be studied in this gauge-fixed formalism, which offers certain conceptual advantages. Interestingly, we find that the flat and negative spatially curved solutions in $f(Q)$ gravity can be seen as equivalent to the metric teleparallel $f(T)$ theories, demonstrating a deeper connection between these theories. This is accomplished by studying the connection equation of motion, which can be interpreted as a consistency condition in the gauge-fixed approach. Finally, we discuss the role of diffeomorphism invariance and local Lorentz invariance in these geometric modifications of gravity.

Neutron stars are powerful probes into the extremes of physics. In this chapter, we will discuss how observations of neutron stars, either in isolation or in binaries, can be leveraged to test general relativity and constrain competing theories of gravity.

Quantum cosmology aims at elucidating the beginning of our Universe. Back in early 80's, Vilenkin and Hartle-Hawking put forward the "tunneling from nothing'' and "no boundary'' proposals. Recently there has been renewed interest in this subject from the viewpoint of defining the oscillating path integral for Lorentzian quantum gravity using the Picard-Lefschetz theory. Aiming at going beyond the mini-superspace and saddle-point approximations, we perform Monte Carlo calculations using the generalized Lefschetz thimble method to overcome the sign problem. In particular, we confirm that either Vilenkin or Hartle-Hawking saddle point becomes relevant if one uses the Robin boundary condition depending on its parameter. We also clarify some fundamental issues in quantum cosmology, such as an issue related to the integration domain of the lapse function and an issue related to reading off the real geometry from the complex geometry obtained at the saddle point.

Considering the Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) metric and the Einstein scalar field system as an underlying gravitational model to construct fractional cosmological models has interesting implications in both classical and quantum regimes. Regarding the former, we just review the most fundamental approach to establishing an extended cosmological model. We demonstrate that employing new methodologies allows us to obtain exact solutions. Despite the corresponding standard models, we cannot use any arbitrary scalar potentials; instead, it is determined from solving three independent fractional field equations. This article concludes with an overview of a fractional quantum/semi-classical model that provides an inflationary scenario.

By employing modified Chaplygin fluid prescription for the dark energy, we construct slowly rotating isotropic and anisotropic dark energy stars. The slow rotation is incorporated via general relativistic Hartle-Thorne formalism; whereas the anisotropy is introduced through Bowers-Liang prescription. We consider both the monopole and quadrupole deformations and present a complete analysis of rotating dark energy stars. By numerically solving the rotating stellar structure equations in presence of anisotropy, we analyse and quantify various properties of dark energy stars such as mass ($M$), radius, mass deformation, angular momentum ($J$), moment of inertia, and quadrupole moment ($Q$), for three different equation of state parameters. We find that anisotropic slow rotation results in significant deformation of stellar mass and thereby affects other global properties studied. For the values of angular frequencies considered, the effect of anisotropy on the stellar structure is found to be more prominent than that due to rotation. The dimensionless quadrupole moment $QM/J^2$ measuring deviation from a Kerr metric black hole was obtained for anisotropic dark energy stars. We observe that dark energy stars with higher anisotropic strength tend to approach the Kerr solution more closely. We report that our results have considerable agreement with various astrophysical observational measurements.

In this paper, we present the solution for a Schwarzschild black-hole immersed in an electric or magnetic background field within the framework of Entangled Relativity. Previous solutions in Entangled Relativity required black-holes to be charged for the matter field to be defined everywhere. This is because the theory precludes the existence of vacuum solutions, thereby satisfying Einstein's definition of Mach's Principle. The current black-hole solutions represent the first exact and neutral black-hole solutions of Entangled Relativity discovered to date. The Schwarzschild black-hole of General Relativity emerges as a limit of these solutions when the background field approaches zero, whereas the Melvin solution of General Relativity does not emerge as a limit when the black hole's size approaches zero. This finding suggests that astrophysical black-holes in Entangled Relativity are indistinguishable from those in General Relativity, given the generally weak interstellar density of matter fields.

Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree of geometrical content. In recent years, Geometric Algebra appeared claiming to be a unifying language for physics and mathematics with a high level of geometrical content. Its strength is based on the unification of the inner and outer product into a single geometric operation, and its easy interpretation. Given their similarities, in this article we compare both formalisms side-by-side to narrow the gap between them in literature. We present a direct translation including differential identities, integration theorems and various algebraic identities. As an illustrative example, we present the case of classical electrodynamics in both formalism and finish with their description of GR.

Scalar fields which are favorite among the possible candidates for the dark energy usually have degenerate minima at $\pm \phi_{min}$. In the presented work, we discuss a two Higgs doublet model with the non-degenerate vacuum named inert uplifted double well type two-Higgs doublet model (UDW-2HDM) for the dark energy. It is shown that when the both Higgs doublets lie in their respective true minima then one Higgs doublet can cause the current accelerated expansion of the Universe.

Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is assumed that on large scales the Universe is homogeneous and isotropic. These fundamental principles should be tested. In this thesis, we explore the implications of breaking them. In order to understand possible modifications to gravity on cosmological scales, we extend the formalism of parameterised post-Newtonian cosmology, an approach for building cosmological tests of gravity that are consistent with tests on astrophysical scales. We demonstrate how this approach can be used to construct theory-independent equations for the cosmic expansion and its first-order perturbations. Then, we apply the framework to observations of the anisotropies in the cosmic microwave background. We use these to place novel cosmological constraints on the evolution of the post-Newtonian parameters. We investigate the consequences of inhomogeneity and isotropy by developing a new approach to studying anisotropy in the Universe, wherein we consider how an anisotropic cosmology might emerge on large scales as a result of averaging over inhomogeneous structures, and demonstrate how the emergent model is affected by backreaction. We perform a detailed study of light propagation in a wide class of inhomogeneous and anisotropic spacetimes, exploring the conditions under which the Hubble diagram can be accurately predicted by an anisotropic model constructed using explicit averaging, even in the presence of large inhomogeneities. We show that observables calculated in a suitable averaged description closely reproduce the true Hubble diagram on large scales, as long as the spacetime possesses a well-defined homogeneity scale.

The emergence of the Ultra-Diffuse Galaxies in recent years has posed a severe challenge to the galaxy formation models as well as the Extended Theories of Gravity. The existence of both dark matter lacking and dark matter dominated systems within the same family of astrophysical objects indeed requires the gravity models to be versatile enough to describe very different gravitational regimes. In this work, we study a non-local extension of the theory of General Relativity that has drawn increasing attention in recent years due to its capability to account for the late time cosmic acceleration without introducing any dark energy fluid. We leverage the kinematic data of three Ultra-Diffuse Galaxies: NGC 1052-DF2 and NGC 1052-DF4, which are dark matter lacking, and Dragonfly 44, which exhibits a highly dominant dark matter component. Our analysis shows that the non-local corrections to the Newtonian potential do not affect the kinematic predictions, hence no spoiling effects emerge when the Non-local Gravity model serves as a dark energy model. We additionally provide the minimum value that the characteristic non-local radii can reach at these mass scales.

We present new families of solutions of D-dimensional Einstein-Maxwell theory depending on one variable for all space-time signatures. The solutions found can be thought of as generalized Melvin solutions including fluxtubes, domain walls and cosmological space-times. Explicit examples are given in four and five space-time dimensions.

Addressing the general physical question whether spacetime singularities inside black holes exist, we investigate the problem in the context of an analogue system, a flowing laboratory liquid, for which the governing equations are at least in principle known to all relevant scales, and in all regions of the effective spacetime. We suggest to probe the physical phenomena taking place close to a Penrose-type singularity in the interior of a $2+1$D analogue black hole arising from a polytropic, inviscid, irrotational, and axisymmetric steady flow, and propose to this end an experimental setup in a Bose-Einstein condensate. Our study provides concrete evidence, for a well understood dynamical system, that the Einstein equations are not necessary for a singularity to form, demonstrating that Penrose-type spacetime singularities can potentially also exist in non-Einsteinian theories of gravity. Finally, we demonstrate how the singularity is physically avoided in our proposed laboratory setup, and that our analysis can be generalized to three-dimensional flows ($3+1$D analogues).

We calculate the holographic complexity of a family of hyperbolic black holes in an Einstein-Maxwell-dilaton (EMD) system by applying the complexity=action (CA) conjecture. While people previously studied spherical black holes in the same system, we show that hyperbolic black holes have intriguing features. We confirm that the complexity expression mainly depends on the spacetime causal structure despite the rich thermodynamics. The nontrivial neutral limit that exists only for hyperbolic black holes enables us to analytically obtain the complexity growth rate during phase transitions. We find that the dilaton accelerates the growth rate of complexity, and the Lloyd bound can be violated. This is in contrast to the spherical case where the dilation slows the complexity growth rate down, and the Lloyd bound is always satisfied. As a special case, we study the holographic complexity growth rate of the neutral hairy black holes and find that the Lloyd bound is always violated.

We construct the $z=0$ galaxy stellar mass function (GSMF) by combining the GSMF at stellar masses $M_* \lesssim 10^{11.3} M_\odot$ from the census study of Leja et al. (2020) and the GSMF of massive galaxies at $M_* \gtrsim 10^{11.5} M_\odot$ from the volume-limited MASSIVE galaxy survey. To obtain a robust estimate of $M_*$ for local massive galaxies, we use MASSIVE galaxies with $M_*$ measured from detailed dynamical modeling or stellar population synthesis modeling (incorporating a bottom-heavy initial mass function) with high-quality spatially-resolved spectroscopy. These two independent sets of $M_*$ agree to within ${\sim}7$%. Our new $z=0$ GSMF has a higher amplitude at $M_* \gtrsim 10^{11.5} M_\odot$ than previous studies, alleviating prior concerns of a lack of mass growth in massive galaxies between $z\sim 1$ and 0. We derive a local black hole mass function (BHMF) from this GSMF and the scaling relation of SMBH and galaxy masses. The inferred abundance of local SMBHs above $\sim 10^{10}M_\odot$ is consistent with the number of currently known systems. The predicted amplitude of the nanohertz stochastic gravitational wave background is also consistent with the levels reported by Pulsar Timing Array teams. Our $z = 0$ GSMF therefore leads to concordant results in the high-mass regime of the local galaxy and SMBH populations and the gravitational wave amplitude from merging SMBHs. An exception is our BHMF yields a $z=0$ SMBH mass density that is notably higher than the value estimated from quasars at higher redshifts.

We construct $\mathbb{Z}_N$ orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is that the gauge symmetry must be broken by a Wilson line to ensure modular invariance. We completely classify the patterns of symmetry breaking. We show that the tachyonic contributions in all cases can be analytically continued, with a finite answer in the domain $0<N \leq 1$, relevant for calculating entanglement entropy across the Rindler horizon. We discuss the physical implications of our results.

In this paper we construct a dissipative quintessential cosmic inflation. For this purpose, we add a multiplicative dissipative term in the standard quintessence field Lagrangian. We consider the specific form of dissipation as the time integral including the Hubble parameter and an arbitrary function that describes the dissipative properties of the quintessential scalar field. Inflation parameters and observables are calculated under slow-roll approximations and a detailed calculation of the cosmological perturbations is performed in this setup. We consider different forms of potentials and calculate the scalar spectral index and tensor-to-scalar ratio for a constant as well as variable dissipation function. To check the reliability of this model, a numerical analysis on the model parameters space is done in confrontation with recent observational data. By comparing the results with observational joint datasets at 68% and 95% confidence levels, we obtain some constraints on the model parameters space, specially the dissipation factor with e-folds numbers N = 55 and N = 60. As some specific results, we show that the power-law potential with a constant dissipation factor and N = 60 is mildly consistent with observational data in some restricted domains of the model parameter space with very small and negative dissipation factor and a negligible tensor-toscalar ratio. But this case with N = 55 is consistent with observation considerably. For power-law potential and variable dissipation factor as $Q = {\alpha}\phi^n$, the consistency with observation is also considerable with a reliable tensor-to-scalar ratio. The quadratic and quartic potentials with variable dissipation function as $Q = {\alpha}\phi^n$ are consistent with Planck2018 TT, TE, EE+lowE+lensing data at the 68% and 95% levels of confidence for some intervals of the parameter n.

We study symmetry reductions in the context of Euclidean Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in certain gauge theories is a common tool for obtaining explicit soliton solutions. Although pure Chern-Simons theories do not admit solitonic solutions, symmetry reduction still leads to interesting results. We establish relations at the semiclassical regime between pure Chern-Simons theories on $S^3$ and the reduced Quantum Field Theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding $BF$-theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instantons and show that under certain circumstances, the reduced action can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions have a fermionic nature at the level of the partition function.

The degree of Gaussianity of a field offers insights into its cosmological nature, and its statistical properties serve as indicators of its Gaussianity. In this work, we examine the signatures of Gaussianity in a gravitational wave background (GWB) by analyzing the cumulants of the one- and two-point functions of the relevant observable, using pulsar timing array (PTA) simulations as a proof-of-principle. This appeals to the ongoing debate about the source of the spatially-correlated common-spectrum process observed in PTAs, which is likely associated with a nanohertz stochastic GWB. We investigate the distribution of the sample statistics of the one-point function in the presence of a Gaussian GWB. Our results indicate that, within PTAs, one-point statistics are impractical for constraining the Gaussianity of the nanohertz GWB due to dominant pulsar noises. However, our analysis of two-point statistics shows promise, suggesting that it may be possible to constrain the Gaussianity of the nanohertz GWB using PTA data. We also emphasize that the Gaussian signatures identified in the one- and two-point functions in this work are expected to be applicable to any gravitational wave background.

Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann-Lemaitre-Robertson-Walker (FLRW) background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 (CF4) sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaitre-Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

Nonlinear simulations of neutron star mergers are complicated by the need to represent turbulent dynamics. As we cannot (yet) perform simulations that resolve accurately both the gravitational-wave scale and the smallest scales at which magneto/hydrodynamic turbulence plays a role, we need to rely on approximations. Addressing this problem in the context of large-eddy models, we outline a coherent Lagrangian filtering framework that allows us to explore the many issues that arise, linking conceptual problems to practical implementations and the interpretation of the results. We develop understanding crucial for quantifying unavoidable uncertainties in current and future numerical relativity simulations and consider the implications for neutron-star parameter estimation and constraints on the equation of state of matter under extreme conditions.

In the first part of this thesis, we make use of representation theory of groups and algebras to perform an irreducible decomposition of tensors in the context of metric-affine gravity. In particular, we consider the action of the orthogonal group O(1, d$-1$) on the Riemann tensor associated with an affine connection defined on a d-dimensional pseudo-Riemannian manifold. This connection, with torsion and non-metricity, is the characteristic ingredient of metric-affine theories of gravity. In the second part of this thesis, we construct the projection operators used for the aforementioned decomposition. They are realized in terms of the symmetric group algebra $\mathbb{C}\mathfrak{S}_n$ and of the Brauer algebra B$_n$(d) which are related respectively to the action of GL(d,$\mathbb{C}$) (and its real form GL(d,$\mathbb{R}$)) and to the action of O(d,$\mathbb{C}$) (and its real form O(1 , d$-1$)) on tensors via the Schur-Weyl duality. First of all, we give an alternative approach to the known formulas for the central idempotents of $\mathbb{C}\mathfrak{S}_n$. These elements provide a unique reducible decomposition, known as the isotypic decomposition. For our purposes, this decomposition is remarkably handy to arrive at the sought after irreducible decomposition with respect to GL(d,$\mathbb{R}$). Then, we construct the elements in B$_n$(d) which realize the isotypic decomposition of a tensor under the action of O(d,$\mathbb{C}$). This decomposition is irreducible under O(d,$\mathbb{C}$) when applied to an irreducible GL(d,$\mathbb{C}$) tensor of order $5$ or less. As a by product of the construction, we give a solution to the problem of decomposing an arbitrary tensor into its traceless part, doubly traceless part and so on. These results led to the development of several Mathematica packages linked to the \textit{xAct} bundle for tensor calculus in field theory.

The recent observation of the GW230529 event indicates that black hole-neutron star binaries can contain low-mass black holes. Since lower mass systems are more favourable for tidal disruption, such events are promising candidates for multi-messenger observations. In this study, we employ five finite-temperature, composition-dependent matter equations of state and present results from ten 3D general relativistic hydrodynamic simulations for the mass ratios $q = 2.6$ and $5$. Two of these simulations target the chirp mass and effective spin parameter of the GW230529 event, while the remaining eight contain slightly higher-mass black holes, including both spinning ($a_{BH} = 0.7$) and non-spinning ($a_{BH} = 0$) models. We discuss the impact of the equation of state, spin, and mass ratio on black hole-neutron star mergers by examining both gravitational-wave and ejected matter properties. For the low-mass ratio model we do not see fast-moving ejecta for the softest equation of state model, but the stiffer model produces on the order of $10^{-6}M_\odot$ of fast-moving ejecta, expected to contribute to an electromagnetic counterpart. Notably, the high-mass ratio model produces nearly the same amount of total dynamical ejecta, but yields $52$ times more fast-moving ejecta than the low-mass ratio system. In addition, we observe that the black-hole spin tends to decrease the amount of fast-moving ejecta while increasing significantly the total ejected mass. Finally, we note that the disc mass tends to increase as the neutron star compactness decreases.

The recent DESI Baryon Acoustic Oscillation measurements have led to tight upper limits on the neutrino mass sum, potentially in tension with oscillation constraints requiring $\sum m_{\nu} \gtrsim 0.06\,{\text{eV}}$. Under the physically motivated assumption of positive $\sum m_{\nu}$, we study the extent to which these limits are tightened by adding other available cosmological probes, and robustly quantify the preference for the normal mass ordering over the inverted one, as well as the tension between cosmological and terrestrial data. Combining DESI data with Cosmic Microwave Background measurements and several late-time background probes, the tightest $2\sigma$ limit we find without including a local $H_0$ prior is $\sum m_{\nu}<0.05\,{\text{eV}}$. This leads to a strong preference for the normal ordering, with Bayes factor relative to the inverted one of $46.5$. Depending on the dataset combination and tension metric adopted, we quantify the tension between cosmological and terrestrial observations as ranging between $2.5\sigma$ and $5\sigma$. These results are strenghtened when allowing for a time-varying dark energy component with equation of state lying in the physically motivated non-phantom regime, $w(z) \geq -1$, highlighting an interesting synergy between the nature of dark energy and laboratory probes of the mass ordering. If these tensions persist and cannot be attributed to systematics, either or both standard neutrino (particle) physics or the underlying cosmological model will have to be questioned.

The Weyl double copy is a relationship between classical solutions in gauge and gravity theories, and has previously been applied to vacuum solutions in both General Relativity and its generalisations. There have also been suggestions that the Weyl double copy should extend to solutions with non-trivial sources. In this paper, we provide a systematic derivation of sourced Weyl double copy formulae, using spinorial methods previously established for ${\cal N}=0$ supergravity. As a cross-check, we rederive the same formulae using a tensorial approach, which then allows us to extend our arguments to sources containing arbitrary powers of the inverse radial coordinate. We also generalise our results to include the Kerr-Newman black hole, clarifying previous alternative double copy formulae presented in the literature. Our results extend the validity of the Weyl double copy, and may be useful for further astrophysical applications of this correspondence.

We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class as Liouville quantum gravity. The diffeomorphism-invariant observable that allows us to compare the averaged curvature of highly quantum-fluctuating geometries with that of classical spaces is the so-called curvature profile. A Monte Carlo analysis on three geometric ensembles, which are physically equivalent but differ by the inclusion of local degeneracies, leads to new insights on the influence of finite-size effects. After eliminating them, we find strong evidence that the curvature profile of 2D Euclidean quantum gravity is best matched by that of a classical round four-sphere, rather than the five-sphere found in previous work. Our analysis suggests the existence of a well-defined quantum Ricci curvature in the scaling limit.

The 21-cm forest is a sensitive probe for the early heating process and small-scale structures during the epoch of reionization (EoR), to be realized with the upcoming Square Kilometre Array (SKA). Its detection relies on the availability of radio-bright background sources, among which the radio-loud quasars are very promising, but their abundance during the EoR is still poorly constrained due to limited observations. Here, we use a physics-driven model to forecast future radio-loud quasar observations. We fit the parameters of the model using observational data of high-redshift quasars. Assuming Eddington accretion, the model yields an average lifetime of $t_{\rm q} \sim 10^{5.3}$yr for quasars at $z\sim6$, consistent with recent results obtained from quasar proximity zone pre-study. We show that if the radio-loud fraction of quasars evolves with redshift, it will significantly reduce the abundance of observable radio-loud quasars in the SKA era, making 21-cm forest studies challenging. With a constant radio-loud fraction, our model suggests that a one-year sky survey conducted with SKA-LOW has the capability to detect approximately 20 radio-loud quasars at $z\sim 9$, with sufficient sensitivity to resolve individual 21-cm forest lines.

We present a new exact solution for a general non-BPS black ring in the bosonic sector of five-dimensional minimal supergravity. This obtained solution carries four independent conserved charges: the mass, two angular momenta, an electric charge, and an additional dipole charge related to other charges. By employing the Ehlers-Harrison transformation, we derive this solution by transforming a five-dimensional vacuum solution into a charged solution in the theory. Previously, our work produced a vacuum doubly rotating black ring solution possessing a Dirac-Misner string singularity by using the Ehlers transformation. In this study, we use the singular black ring as the seed for the Harrison transformation. The resultant solution exhibits regularity, free from curvature singularities, conical singularities, orbifold singularities, Dirac-Misner string singularities, and closed timelike curves both on and outside the horizon. We show that within a specific parameter range, the black ring presents two branches for the same mass, two angular momenta and electric charge but these are distinguished by a dipole charge, which exhibits discontinuous non-uniqueness. Furthermore, this newly obtained black ring seamlessly connects to various physically significant solutions, such as the Pomeransky-Sen'kov black ring, the extremal black ring, the supersymmetric black ring, and the charged singly-spinning black ring.

We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl conformal geometry in $d$ dimensions to obtain a Weyl gauge invariant theory. For $d=4$, in a leading order expansion the DBI action becomes the general Weyl quadratic gravity action associated to this geometry, that has the same gauge symmetry; this is broken spontaneously and Einstein-Hilbert gravity is recovered in the broken phase, with $\Lambda>0$. The series expansion of the DBI action also contains additional non-polynomial terms that can be generated at quantum level in Weyl quadratic gravity in $d=4$, by a regularisation that respects this gauge symmetry. Such a regularisation is automatically provided by the DBI action in $d$ dimensions. If the Weyl gauge boson of dilatations is `pure gauge', the DBI action recovers in the leading order the conformal gravity action plus a locally Weyl invariant dilaton action. All fields are of geometric origin, with no added matter or compensating Weyl scalars, etc. The calculation is done in a Weyl {\it gauge covariant} and {\it metric} formulation of Weyl conformal geometry in $d$ dimensions.

An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(\pi \mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM is the generator of the time evolution of a diamond observer, and its dynamical behavior leads to the predicted thermal nature. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials.

In this paper, we generalize the correspondence between large $D$ gravity and low $D$ string theory to the most general case, including its T-dual solutions. It is well-known that the large $D$ limit of the Schwarzschild-Tangherlini black hole in gravity becomes a two-dimensional near-horizon geometry. Similarly, the large $D$ limit of its T-dual solution, obtained by the Buscher rules, namely the string black hole with a naked singularity, reduces to a two-dimensional near-singularity geometry. Both of these geometries are described by the two-dimensional low-energy effective action of string theory and are related to each other by scale-factor duality. Secondly, we demonstrate that these near-horizon/singuglarity geometries, including complete $\alpha^{\prime}$ corrections, can be described by the two-dimensional Hohm-Zwiebach action. This approach allows for the derivation of non-perturbative and non-singular solutions. Furthermore, the Hohm-Zwiebach action provides a systematic way to investigate the $\alpha^{\prime}$-corrected near-horizon/singularity geometries of different kinds of black holes, which are difficult to achieve through the Wess-Zumino-Witten (WZW) model method.

Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond, governed by one of the conformal quantum mechanics (CQM) symmetry generators: the noncompact hyperbolic operator $S$. In this paper, we show that the unbounded nature of $S$ endows it with a quantum instability, which is a generalization of a similar property exhibited by the inverted harmonic oscillator potential. Our analysis is semiclassical, including a detailed phase-space study of the classical dynamics of $S$ and its dual operator $R$, and a general semiclassical framework yielding basic instability and thermality properties that play a crucial role in the quantum behavior of the theory. For an observer with a finite lifetime $\mathcal{T}$, the detected temperature $T_D = 2 \hbar/(\pi \mathcal{T})$ is associated with a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate.