In this paper, we obtain pointwise decay estimates in time for massive Vlasov fields on the exterior of Schwarzschild spacetime. We consider massive Vlasov fields supported on the closure of the largest domain of the mass-shell where timelike geodesics either cross $\mathcal{H}^+$, or escape to infinity. For this class of Vlasov fields, we prove that the components of the energy-momentum tensor decay like $v^{-\frac{1}{3}}$ in the bounded region $\{r\leq R\}$, and like $u^{-\frac{1}{3}}r^{-2}$ in the far-away region $\{r\geq R\}$, where $R>2M$ is sufficiently large. Here, $(u,v)$ denotes the standard Eddington--Finkelstein double null coordinate pair.

We compute the quadrupolar gravitoelectric tidal Love numbers of spherical configurations made of anisotropic matter. Anisotropies are introduced within the vanishing complexity factor, while interior solutions are obtained adopting the Extended Chaplygin gas equation-of-state. A comparison with a more conventional approach is made as well.

In space-based gravitational wave observatories such as Taiji, LISA, and TianQin, data gaps are inevitable due to mission design, implementation, and the long duration of observations. These data gaps degrade data quality and cause spectral leakage during Fourier transformations. Since ringdown signals are a key scientific objective for these observatories, it is crucial to assess the impact of data gaps on ringdown signal observations. This study employs LISA's science requirement of maintaining a duty cycle of at least 75% to evaluate the worst-case impact of data gaps, and uses massive black hole binary catalogs to assess the average effects. Our findings indicate that, on average, data gaps increase parameter estimation errors by approximately 2.1 times for the (2,2) mode and by about 1.6 times for the (3,3) mode. Joint observation is commonly employed to alleviate the impact of data gaps. Similarly, we have evaluated the effects of joint observation with two configurations, Taiji-LISA and Taiji-TianQin, which demonstrate notable mitigation of the effects of data gaps. This work provides a quantitative assessment of data gaps on ringdown signals and highlights the significance of joint observation.

In this contribution we explore the consequences of including additional sources to the original Casimir energy Stress-Energy Tensor. In particular, we will discuss the effects of an additional electromagnetic field, the modification induced by non-zero temperature effects on the energy density obtained by a Casimir device and finally the effect obtained by including a massless scalar field. For each of these examples, we have introduced an auxiliary stress tensor which we have interpreted as a thermal tensor. Consequences on the size of the throat are also discussed. We will show that these additional extra fields do not destroy the traversability of the wormhole.

Extended gravitational models have gained large attention in the last couple of decades. In this work, we examine the solution space of vacuum, static, and spherically symmetric spacetimes within $F(R)$ theories, introducing novel methods that reduce the vacuum equations to a single second-order equation. For the first time, we derive analytic expressions for the metric functions in terms of the arbitrary functional $F(R)$, providing detailed insight into how the gravitational action impacts the structure of spacetime. We analyze conditions under which solutions are asymptotically flat, regular at the core, and contain an event horizon, obtaining explicit expressions for entropy, temperature, and specific heat in terms of $F(R)$. By using a single metric degree of freedom, we identify the most general solution and examine its (un)physical properties, showing that resolving singularities is not possible within this restricted framework in vacuum. For the general case involving two metric functions, we use several approximation schemes to explore corrections to Schwarzschild-(anti)de Sitter spacetimes, finding that $F(R)$ extensions to General Relativity induce instabilities that are not negligible. Finally, through an analysis of axial perturbations, we derived a general expression for the potential of quasinormal modes of a black hole as a function of the arbitrary Lagrangian.

We assess the prospects for detecting gravitational wave echoes arising due to the quantum nature of black hole horizons with LISA. In a recent proposal, Bekenstein's black hole area quantization is connected to a discrete absorption spectrum for black holes in the context of gravitational radiation. Consequently, for incoming radiation at the black hole horizon, not all frequencies are absorbed, raising the possibility that the unabsorbed radiation is reflected, producing an echo-like signal closely following the binary coalescence waveform. In this work, we further develop this proposal by introducing a robust, phenomenologically motivated model for black hole reflectivity. Using this model, we calculate the resulting echoes for an ensemble of Numerical Relativity waveforms and examine their detectability with the LISA space-based interferometer. Our analysis demonstrates promising detection prospects and shows that, upon detection, LISA provides a direct probe of the Bekenstein-Hawking entropy. In addition, we find that the information extractable from LISA data offers valuable constraints on a wide range of quantum gravity theories.

We study the performances of a world-wide network made by a European third-generation gravitational-wave (GW) detector, together with a 40-km Cosmic Explorer detector in the US, considering three scenarios for the European detector: (1) Einstein Telescope (ET) in its 10-km triangle configuration; (2) ET in its configuration featuring two 15-km L-shaped detectors in different sites, still taken to have all other ET characteristics (underground, and with each detector made of a high-frequency interferometer and a cryogenic low-frequency interferometer); (3) A single L-shaped underground interferometer with the ET amplitude spectral density, either with 15~km or with 20~km arm length. Overall, we find that, if a 2L configuration should be retained for ET, the network made by a single-L European underground detector together with CE-40km could already provide a very interesting intermediate step toward the construction of a full 2L+CE network, and is in any case superior to a 10-km triangle not inserted in an international network.

The origin of the binary black hole mergers observed by LIGO-Virgo-KAGRA (LVK) remains an open question. We calculate the merger rate from primordial black holes (PBHs) within the density spike around supermassive black holes (SMBHs) at the center of galaxies. We show that the merger rate within the spike is comparable to that within the wider dark matter halo. We also calculate the extreme mass ratio inspiral (EMRI) signal from PBHs hosted within the density spike spiralling into their host SMBHs due to GW emission. We predict that LISA may detect $\sim10^4$ of these EMRIs with signal-to-noise ratio of 5 within a 4-year observation run, if all dark matter is made up of PBHs. Uncertainties in our rates come from the uncertain mass fraction of PBHs within the dark matter spike, relative to the host central SMBHs, which defines the parameter space LISA can constrain.

Spatially homogeneous thermal equilibria of self-gravitating gas, being impossible otherwise, are nevertheless allowed in an expanding background accounting for Universe's expansion. Furthermore, a fixed density at the boundary of a perturbation is a natural boundary condition keeping the mass finite inside without the need to invoke any unphysical walls.These facts allow us to develop a consistent gravitational thermodynamics of isothermal spheres inside an expanding Universe. In the canonical and grand canonical ensembles we identify an instability for both homogeneous and inhomogeneous equilibria. We discuss a potential astrophysical application. If such an instability is triggered on baryonic gas at high redshift $z > 137$ when the primary baryonic component, namely atomic hydrogen, was still thermally locked to the Cosmic Microwave Background radiation, then the corresponding destabilized gaseous clouds have baryonic mass $\geq 0.8\cdot 10^5 {\rm M}_\odot$ and radius $\geq 15{\rm pc}$.

The evolution of quantum states influenced by semiclassical gravity is distinct from that in quantum gravity theory due to the presence of a state-dependent gravitational potential. This state-dependent potential introduces nonlinearity into the state evolution, of which the theory is named Schroedinger-Newton (SN) theory. The formalism for understanding the continuous quantum measurement process on the quantum state in the context of semiclassical gravity theory has been previously discussed using the Schr\"odinger picture in Paper I [1]. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols that targeted testing the quantum nature of gravity. This Heisenberg picture formalism of the SN theory has the advantage of helping the investigation of the covariance matrices of the outgoing light fields in these protocols and further the entanglement features. We found that the classical gravity between the quantum trajectories of two mirrors under continuous quantum measurement in the SN theory can induce an apparent entanglement of the outgoing light field (though there is no quantum entanglement of the mirrors), which could serve as a false alarm for those experiments designed for probing the quantum gravity induced entanglement.

We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method of differential equations. We explicitly express the internally massive, externally conformally coupled correlator as a power series with respect to a small mass parameter, where the various terms in the series are given by multiple polylogarithms.

We advance the study of pure de Sitter supergravity by introducing a finite formulation of unimodular supergravity via the super-St\"uckelberg mechanism. Building on previous works, we construct a complete four-dimensional action of spontaneously broken ${\cal N}\!\!=\!\!1$ supergravity to all orders, which allows for de Sitter solutions. The introduction of finite supergravity transformations extends the super-St\"uckelberg procedure beyond the second order, offering a recursive solution to all orders in the goldstino sector. This work bridges the earlier perturbative approaches and the complete finite theory, opening new possibilities for de Sitter vacua in supergravity models and eventually string theory.