Papers

We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.

Traversable wormholes in general relativity require non-standard matter sources, making the identification of physically motivated equations of state particularly important. We investigate wormholes supported by a polytropic equation of state, considering homogeneous and inhomogeneous configurations within a unified framework. We derive the corresponding solutions and analyze the effects of the polytropic parameters on the geometry and energy conditions. In the homogeneous case, the polytropic construction yields a consistent wormhole interior whose geometry and matter content are governed by the constant polytropic parameters. For the inhomogeneous case, we obtain a general analytical expression showing that the geometry is completely determined by the radial polytropic coefficient $\omega(r)$. For positive $\omega(r)$, the requirement for physically meaningful solutions naturally restricts the polytropic exponent to odd integer values. Using a power-law profile, we construct explicit classes of solutions exhibiting distinct parameter regimes and finite radial support. Interestingly enough, for an exponent $\alpha=2\gamma-3$, a generalized absurdly benign traversable wormhole-like configuration emerges naturally. Although the flare-out condition implies null-energy-condition violation at the throat, the inhomogeneous framework allows its radial distribution to be controlled. Our results establish a systematic connection between polytropic matter and wormhole geometry, providing a flexible framework for constructing compact wormholes with localized exotic matter.

Relativistic capture and tidal disruption around a spinning black hole depend on both the magnitude and direction of the star's angular momentum, yet loss-cone models often assume fixed orbital inclinations by ignoring the associated diffusion. We show that this is not justified: for isotropic two-body relaxation near a small loss threshold, angular-momentum magnitude $L$ and inclination $x = L_{z}/L$ diffuse on comparable timescales, $t_{E} \gg t_{L} \sim t_{x}$. For Kerr capture, retaining inclination diffusion significantly amplifies the prograde–retrograde contrast while leaving the total inclination-integrated flux nearly unchanged. An almost correct integrated flux can hide a badly wrong angular distribution. The three-dimensional diffusion problem nevertheless retains enough angular structure to permit analytic treatment. By representing pericenter removal as a continuous sink, we obtain a closed-form loss flux solution for a nearly linear Kerr tidal-disruption boundary, finding close agreement with phase-resolved calculations. Inclination-dependent loss therefore requires inclination-resolved diffusion even when integrated rates appear robust.

A warped extra dimension in a five-dimensional (5D) anti-de Sitter (AdS) background was introduced in 1999 by Lisa Randall and Raman Sundrum to solve the gauge hierarchy problem in particle physics. As a bonus, a holographic interpretation in terms of four-dimensional (4D) conformal field theories (CFTs) was found. Interestingly enough, another 5D background, linear dilaton (LD), was found to have a holographic interpretation in terms of Little String Theory. In this review, we will show how a set of 5D backgrounds, parametrized in terms of a real parameter $\nu$, generalizes both theories and gives rise, in particular, to AdS for $\nu=0$ and to LD for $\nu=1$. Furthermore, working in the 5D theory, we will consider applications of the LD background to: (i) particle physics, so that the 5D Planck scale can be lowered to sub-Planckian values, and (ii) Brane World Cosmology (BWC), based on the appearance of an extra vacuum characterized by a 5D black hole. In all cases, we find a gapped continuum for bulk propagating fields, which makes a connection with unparticles. In the case of BWC, we also point out the existence of a pressureless holographic fluid that could play the role of dark matter (DM), with feeble (gravitational) interactions with the Standard Model (SM), decoupled from the thermal SM bath, and generated by a freeze-in mechanism after inflation. We also point out the additional possibility of identifying DM with a long-lived, feebly interacting massive graviton, as an isolated resonance generated by radiative corrections to the continuum graviton propagator self-energy.

We investigate the unitarity of quantum evolution relative to an internal time defined by a local observer's clock. The observer is modeled as a relativistic particle carrying both a clock and a matter-field detector, analyzed first on a fixed curved background and subsequently within a fully diffeomorphism-invariant theory of dynamical gravity. In the former case, we find that evolution with respect to the internal clock time is generally nonunitary, implying a violation of the Einstein equivalence principle at the quantum level. In contrast, in the latter case, diffeomorphism invariance allows us to adopt observer-centric coordinates without loss of generality. On the resulting partially-reduced phase space, one of the diffeomorphism generators becomes linear in the clock Hamiltonian, generating a relational evolution that is consistent with the remaining diffeomorphism constraints. Assuming that an effective quantum field theory exists to be consistent with the diffeomorphism invariance, these features ensure unitary evolution relative to the internal clock, thereby preserving the equivalence principle even in the quantum regime. Our results highlight the fundamental role of diffeomorphism invariance in shaping relational unitary evolution from the perspective of a local observer.

We investigate traversable wormhole solutions in five-dimensional Einstein-Chern-Simons (EChS) gravity, a gauge-theoretic extension of General Relativity that introduces a higher-curvature correction parametrized by the combination $\alpha l^2$, where $\alpha$ is a dimensionless coupling and $l$ is a length scale. Working with the Morris-Thorne metric and an anisotropic fluid, we derive exact expressions for the energy density, radial pressure, and lateral pressure at the wormhole throat. We show that the radial Null Energy Condition (NEC) is satisfied at the throat if and only if $\alpha l^2\leq-r_0^2$, being saturated at $\alpha l^2=-r_0^2$ and strictly satisfied for $\alpha l^2<-r_0^2$, independently of the shape function. In the latter regime, the energy density is strictly positive and the full NEC, Weak, Strong, and Dominant Energy Conditions can be simultaneously satisfied. These results are established analytically for arbitrary shape functions and illustrated concretely for the power-law family $b(r)=r_0(r_0/r)^n$, $\Phi=0$, for which all four standard energy conditions are satisfied at the throat for all $n>0$ when the EChS coupling is sufficiently negative. We further show that the radial pressure is negative and geometrically fixed at the throat, independently of $\alpha$, $b(r)$, and $\Phi(r)$. Using the Volume Integral Quantifier (VIQ), we establish that the EChS correction reduces the magnitude of the negative integrated NEC contribution relative to GR, and derive an exact closed-form critical coupling $\alpha l^2_{\rm crit}$ at which the VIQ vanishes. The hierarchy $\alpha l^2_{\rm crit}<-r_0^2<0$ shows that NEC satisfaction at the throat and a non-negative global VIQ are compatible but distinct conditions, both achievable within EChS gravity. All results reduce continuously to those of GR in the limit $l\to0$, confirming the consistency of the framework.

The process-matrix formalism describes quantum processes without assuming a fixed global causal order, but the physical meaning of indefinite causal order remains open. We address this question within histories theory, where temporal ordering and dynamical evolution are distinct structures. We show that the decoherence functional admits coherent superpositions of dynamics. In measurement settings, under suitable factorization conditions, these generate process matrices. Thus, we identify process-matrix indefinite causal order as an operationally restricted realization of the more general phenomenon of superposition of dynamics. Histories theory also admits a distinct kinematical notion of indefinite order, in which the ordering of physical events is itself a history observable. The resulting distinction between event order and intervention order clarifies the relation between indefinite causal order, quantum dynamics, and spacetime structure.

Hawking's area theorem states that the total event-horizon area of classical black holes can never decrease. Gravitational-wave tests of this law have so far focused on individual loud mergers, thus probing only a sparse subset of binary parameter space. Here we perform the first population-level test. We exploit the decomposition of the coalescing black holes in the latest gravitational-wave catalogue into a low-spin subpopulation of stellar-collapse origin and a high-spin subpopulation assembled through hierarchical mergers of the former. If the high-spin black holes are merger remnants, the area theorem requires their horizon areas to exceed the total pre-merger areas of the low-spin binaries. Using parameter estimation restricted to the inspiral of 241 events, so that no merger-ringdown information enters the inference, we find that both peaks of the horizon-area distribution of second-generation black holes lie above their first-generation counterparts. The displacement is significant at each peak ($2.1$–$3.7\sigma$), and when we tie the two subpopulations with a single common shift, an area decrease is excluded decisively ($\gtrsim5.0\sigma$). The second law of black-hole mechanics thus holds statistically across the quasicircular, moderately spinning mergers that dominate current catalogues, which in turn underpins the robustness of our classification of stellar-collapse and hierarchical-merger black holes.

Grounded in the covariant phase space approach of the Iyer-Wald formalism, we propose a quasi-local Hamiltonian for generalized Kerr-Schild (GKS) black holes. Evaluated for spherically symmetric spacetimes over a flat Minkowski background, our formulation recovers the Misner-Sharp mass. Because this framework relies solely on the GKS structure, it provides a straightforward extension of the Misner-Sharp mass to rotating geometries. We further extend our analysis to asymptotically anti-de Sitter (AdS) black holes, where a renormalization procedure to subtract the background AdS energy naturally emerges. By employing this technique, we establish a geometric quasi-local formulation of Kerr-AdS thermodynamics.

Quantum permutations, or magic unitaries, have in recent years been explored in the context of identifying `genuinely quantum' isometries of graphs. Here, we import this tool in physics, showing that quantum permutations yield a generalisation of quantum reference frames in a discrete setting that is reminiscent of the passage from special to general relativity. We show that the typical quantum reference frames framework corresponds to quantum permutations classified as `classical' in the mathematical literature, and which we demonstrate are quantum controlled transformations (superpositions of classical coordinate maps). Genuinely quantum permutations (i) allow to construct non–commuting quantum reference frames (ii) correspond to local, as opposed to global, superpositions of transformations. Strikingly, we find that the non-commutativity of quantum fields, when used as reference systems, is exactly what implies that the change of frame is achieved through a genuine quantum permutation. We illustrate the above with several examples in both first and second quantization formalism, which demonstrate (a) simultaneous control on non–commuting variables, (b) the existence of bipartite states that can be localized with a genuine quantum permutation and cannot be localized with the usual quantum reference frame transformations (without introducing additional degrees of freedom), (c) extension of the Ising model symmetries to genuinely quantum permutations, and (d) extension of the symmetries of a scalar field action on curved spacetime to genuinely quantum permutations. While we have in mind applications in quantum gravity, we expect our formalism to be of interest in a wide range of topics in quantum information.

We investigate how a surrounding dark-matter halo imprints itself on the QNM spectrum of a static, spherically symmetric black hole, considering two physically distinct density profiles: the Dehnen (1,4,5/2) and DC14 profiles. Both follow double-power-law forms, while the shape parameters of the DC14 profile are calibrated to galaxy-formation simulations and vary with the stellar-to-halo mass ratio $X=\log_{10}(M_*/M_{\rm halo})$, which controls the inner density structure of the halo. For both profiles, we compute the halo contribution to the metric function and the resulting effective potential governing axial gravitational ($s=2$) perturbations, and extract the fundamental QNM frequencies for the $\ell=2$ multipole. Our results show that the halo scale radius $r_s$ has the largest influence on the QNM spectrum among the halo parameters explored, reshaping the effective potential barrier near the light ring and shifting both the real and imaginary parts of the QNM frequencies. The density normalization, by contrast, plays a comparatively minor role for the Dehnen profile but is more consequential for DC14, reflecting the different inner structures associated with its varying $X$ values. The Prony-extracted frequencies show excellent agreement with the sixth-order WKB results, with relative differences remaining below $0.04\%$ across the parameter ranges considered. To our knowledge, this constitutes the first QNM analysis of a black hole embedded in a DC14 dark-matter halo. These results demonstrate the sensitivity of the QNM spectrum to the surrounding dark-matter environment and provide a consistent numerical framework for studying such environmental effects.

We study the exceptional line (EL) in the quasinormal modes (QNMs) of Reissner-Nordström-de Sitter black hole surrounded by a static thin shell of matter. For a conformally scalar perturbation, we derive the QNM condition by matching the interior and exterior solutions across the shell and show that higher overtones are particularly sensitive to variations of the shell and background parameters. A mode permutation between two QNMs reveals an exceptional point (EP). After extending the parameter space, this degeneracy forms a continuous EL. We show that the spectral response near the line is intrinsically directional. For a perturbation in parameter space $\epsilon\widehat{\mathbf u}$, the QNM splitting is $|\omega_+-\omega_-| =C_{\widehat{\mathbf u}}\sqrt{\epsilon}+o(\sqrt{\epsilon})$, with $C_{\widehat{\mathbf u}}=(\widehat{\mathbf u}^{T}\mathbf{K}\widehat{\mathbf u})^{1/4}$ and $\mathbf{K}$ is so-called spectral sensitivity anisotropy matrix. The tangent direction of EL is a null direction of $\mathbf{K}$, so that the leading square-root splitting vanishes along the exceptional line, whereas the two principal directions in the normal plane exhibit different sensitivities. Furthermore, the square-root branch structure makes conventional linear QNM parametrizations singular near an EL. We therefore construct an EL adapted parametrization which incorporates both the local geometry of the line and the nonanalytic QNM splitting.

Extending the work presented in a workshop “From Quarks to Neutron Stars: Insights from kHz gravitational waves”, we discuss some limiting cases of the moment of inertia, tidal deformability, and spin-induced quadrupole moment for relativistic stars. First, conjecturing that a hierarchy of the length scale is the key to proposed universality among these second-order moments, we revisit the relation for incompressible relativistic stars (known as Schwarzschild's interior solution) as a candidate of the possible stiff limit. Second, we present the limiting form for the weak-field limit. In particular, we demonstrate how relativistic computations of tidal deformation are related to the traditional Newtonian counterpart, which might not have been presented explicitly in the literature.

We establish the perturbative stability of the fuzzy-sphere black-hole horizon in the large-$N$ matrix quantum mechanics of \cite{Chu:2024qil}. Large-$N$ counting shows that the leading quantum correction to the fluctuation spectrum is the planar bosonic one-loop contribution, while higher-loop bosonic effects and the leading fermionic one-loop contribution are parametrically suppressed. The classical spectrum contains a tachyonic $(1,2)$ mode and a marginal $(2,3)$ mode; we show that both acquire positive quantum curvature and are stabilized. For the general spectrum, we find that a factorization structure of the Hessian controls the leading quantum curvature and renders it non-negative. Quantum effects dominate the stabilization of generic low-angular-momentum modes, whereas classical curvature dominates at high angular momentum. The two effects become comparable in the crossover regime $L \sim \sqrt{N}$, where both must be retained. Under smoothness and non-saturation assumptions supported by finite-$N$ numerical tests, positivity of the quantum fluctuation spectrum is thus established for sufficiently large but finite $N$. This local curvature stability is compatible with non-perturbative monopole tunneling. Intriguingly, the same $L\sim\sqrt{N}$ mesoscopic angular momentum range also dominates the tunneling process, suggesting a distinguished IR–UV crossover regime in the quantum dynamics of the black-hole horizon.

We study the gravitational collapse of a homogeneous dust sphere in higher-dimensional spacetime, with the loop quantum gravity correction entered through a modified Friedmann equation. Its most striking feature is an endpoint: at a finite horizon radius the temperature vanishes and evaporation stops, leaving a remnant. Reading \(\alpha\) as an effective charge, we find behavior reminiscent of the Weak Gravity Conjecture (WGC), although no \(U(1)\) gauge field is present in the model. Solving the degeneracy conditions with the untruncated metric function, rather than with a mass expansion that is not uniform near the endpoint, we obtain closed-form expressions for the remnant radius and mass in \(D=4,5,6,7\). The unscaled ratio \(\alpha/M_{\text{remnant}}^2\) is constant only in four dimensions and grows as \(\alpha^{4-D}\) elsewhere, but it carries dimension \(L^{8-2D}\), so that growth is an artifact of the units. The dimensionless combination \(\tilde{\mathcal{R}} = (\alpha/M^2) r_0^{2D-8}\) settles instead on a finite \(\alpha\)-independent number in every dimension, decreasing from \(27/64\) in four dimensions to \(13824/(15625\pi^4)\) in seven. We also deform the quantum parameter, \(\alpha \to \alpha + \varepsilon\), and evaluate \(-T(\partial S/\partial \varepsilon)_M\) in the remnant limit. Because \((\partial M/\partial r)_\alpha\) vanishes there, the fixed-entropy derivative reduces exactly to a fixed-radius one, and the resulting combination \(\mathcal{U}\) is finite in each dimension but depends on \(\varepsilon\) except for \(D=5\). What is invariant is the product \(\mathcal{R}\,\mathcal{U}\,M_{\text{remnant}} = (D-3)/2\), which we verify numerically. Lastly, we study Bondi accretion onto the quantum-corrected black hole and obtain the Eddington luminosity for each dimension.

We construct a charged Oppenheimer-Snyder-like collapse model in scale-dependent gravity by matching a spatially flat FLRW interior to a charged scale-dependent exterior across a timelike thin shell. The electric charge is confined to the stellar surface, preserving interior homogeneity and isotropy. The exterior geometry is supported by a phenomenological Bianchi-consistent effective source, while the shell dynamics follow from the Israel-Maxwell junction conditions. A barotropic surface equation of state closes the shell system, with a charged-dust shell as the minimal realization. For a negative scale-dependent parameter, $\tilde{\omega}<0$, the exterior contains a finite-radius boundary $x_s$ defined by $D(x_s)=0$. Charge separates the solutions into three regimes. For $0\le q^2<x_s$, the lapse develops a negative pole at a curvature singularity, the physical exterior contains one outer horizon, and a representative monotonic collapse crosses this horizon before reaching $x_s$; no future-directed locally outgoing radial null branch emerges from the singular boundary. At $q^2=x_s$, simultaneous zeros of the numerator and denominator cancel the curvature pole, although the prescribed running coupling remains singular. For $q^2>x_s$, the curvature singularity persists with a positive pole and locally outgoing radial null branches exist. Depending on the physical extremality condition $x_e>x_s$, the exterior may contain two simple horizons, one degenerate horizon, or no horizon. These results show that charge qualitatively changes the singular and horizon structure of scale-dependent collapse and provide model-level evidence for horizon shielding in the negative-pole regime.

Black-hole quasinormal modes (QNMs) may coalesce at exceptional points (EPs) in the frequency spectrum. We study EPs and their phenomenology for gravitational perturbations of a Schwarzschild black hole whose Regge-Wheeler potential is perturbed by a localized delta-function of amplitude $\epsilon$ at radius $r_0$. For real $\epsilon$, we find infinite families of discrete EPs. Each family approaches a distinct unperturbed QNM overtone frequency as $r_0$ grows large. Under perturbation at fixed $r_0$, we find that neighboring QNM overtones migrate in the complex plane to meet at these EPs, with the higher overtone moving further. We derive large-$r_0$ asymptotics, finding that EPs have (asymptotically) equal spacing in the tortoise coordinate, and that EP amplitudes $\epsilon$ can be exceedingly small, decaying exponentially according to a rule governed by the complex frequency of the unperturbed QNM. Using quadratic approximations around EPs and high-precision numerical methods, we investigate a range of phenomena in the model: square-root splittings, avoided crossings and hyperbolae, hysteresis and geometric phases generated by encircling an EP, adiabatic invariants, deformed Cassini ovals and cusp-like trajectories, as well as the lemniscate geometry of the excitation factors. We then replace the delta-function perturbation by a finite-width Gaussian, verify the persistence of the EP structure, and show that varying the width extends isolated EPs into exceptional lines in parameter space. Finally, we study the response to initial data and find that, although a weak perturbation can substantially reconfigure the QNM spectrum, the corresponding time-domain response remains perturbative. This contrast is captured by a re-interpretation of the tale of The Princess and the Pea.

The angular structure and temporal variability of neutrino emission from binary neutron star mergers are characterized using fully general-relativistic simulations with energy-integrated M1 neutrino transport across a representative set of equations of state, total masses, and mass ratios. The angle-dependent neutrino energy flux is extracted on a spherical surface outside the remnant and decomposed into spherical harmonics to quantify its multipolar content and evolution. Following the initial post-merger transient, the neutrino radiation flux approaches an axisymmetric configuration dominated by a strong quadrupolar component, producing persistent polar flux enhancement and equatorial suppression due to torus shadowing. The dipolar contribution remains subdominant, indicating the absence of sustained one-sided emission. The degree of anisotropy increases with mass asymmetry and for softer equations of state, reflecting the compactness and morphology of the remnant–disk system. Superimposed on this time-averaged geometry, coherent azimuthal modulations associated with the $m=1$ mode are identified. Fourier analysis reveals a characteristic frequency of $\sim 0.6$–$0.7$ kHz, consistent with differential rotation in the remnant and inner disk layers, indicating a dynamical coupling between rotational structure and neutrino emission variability. Finally, we quantify how the same quadrupole-dominated radiation geometry induces a latitude-dependent equilibrium electron fraction. The polar material is driven close to the neutrino-equilibrium target, whereas equatorial material remains systematically more neutron-rich and below equilibrium.

In this paper, we examine the stellar properties of quark stars containing dark matter, focusing on both non-rotating and slowly rotating configurations. By employing a two-fluid framework, we formulate the generalized Tolman–Oppenheimer–Volkoff equations, treating dark matter and ordinary matter as independent perfect fluids that interact solely through gravitational forces. We model ordinary matter using the color-flavor-locked and the MIT bag model equation of state, while for dark matter, we apply a self-interacting bosonic condensate along with fermionic equation of state. By considering a dark matter fraction of $f_\x=5\%$ and varying the bag constant for ordinary matter, we investigate how dark matter accumulation affects global stellar features such as maximum gravitational mass, radius, and dimensionless tidal deformability. Further, we extend our analysis to first-order rotational effects, calculating the frame-dragging equation and the influence of moments of inertia on the two-fluid system. We also explore universal relations, particularly the connection between rotation and tidal effects, to understand how the inclusion of dark matter affects the relationship between rotational and the tidal deformability. Our findings indicate that a dark matter fraction of $f_\x=5\%$ can lead to notable deviations from the traditional single-fluid quark star characteristics in stellar radius, gravitational mass and tidal deformability. Moreover, the response to rotational and tidal forces remains consistent even in the inclusion of the dark matter component. Finally, we compare our theoretical results with current observational data from GW events and the NICER mission, thereby demonstrating that our developed two-fluid models are consistent with these observations.

Area metric theories have been proposed as effective descriptions in a number of quantum gravity approaches: as continuum limit of effective spin foams, as an effective description for string theory and in the context of holography. Area metric actions allow for non-topological parity violating terms, which opens the possibility of observationally determining the Barbero-Immirzi parameter. We consider the shift symmetric version of linearized area metric theory in Lorentzian signature, which arises in particular from spin foams and modified Plebanski theory, and avoids ghost and tachyonic instabilities in the graviton sector. We discuss the gravitational wave like solutions of this theory and through an analysis of the coupling to electro-magnetism, deduce the signals in gravitational wave detectors. Using polarized light in such interferometers allows in principle to measure area metric induced birefringence. For the non-length excitations that accompany a gravitational wave this birefringence turns out to be independent of the Barbero-Immirzi parameter; the parameter is instead encoded in the polarization structure of the massive non-length waves, where it rotates the axes of the induced birefringence. Assuming Planck massive non-length excitations in the area metric the resulting signals are however extremely weak.

In this paper, we investigate the behavior of a vector field subject to a Lorentz-violating quartic potential on a fixed Schwarzschild background. We analyze the equilibrium configuration of the field and its linear perturbations. We show that the equilibrium solution and spherically symmetric perturbations are governed by a quadratic function whose properties determine their qualitative behavior. By requiring the background field to be real and finite, we derive bounds on the allowed parameters and identify critical cases in which the monopole perturbations become enhanced. We further derive asymptotic expressions for multipole perturbations near the event horizon and at spatial infinity.

Extreme-mass-ratio inspirals (EMRIs) provide sensitive probes of the astrophysical environments surrounding massive black holes. We investigate the inference of dark-matter (DM) spikes with eccentric EMRI gravitational waves within the analytic-kludge waveform framework, including DM-induced dynamical friction and accretion in the secular orbital evolution. We perform Bayesian parameter estimation using Markov-chain Monte Carlo sampling, complemented by Fisher-matrix analyses. We find that steeper DM spikes produce stronger accumulated waveform modifications and substantially improve the measurement of the spike slope $\alpha_{\rm DM}$. More importantly, the constraints exhibit a nonmonotonic dependence on orbital eccentricity. At moderate eccentricity, higher harmonics help break the degeneracy between $e_{\rm LSO}$ and $\alpha_{\rm DM}$, whereas this correlation can persist or the parameter recovery can deteriorate for highly eccentric systems. These results demonstrate that the harmonic structure of eccentric EMRIs can provide valuable information for probing DM distributions around massive black holes with future LISA observations.

Recent studies strongly suggest that the $\Lambda$CDM model may no longer serve as the definitive standard model in cosmology, given the increasing tensions between different cosmological observables. Some researchers have described this situation as a "crisis in cosmology." The $\Lambda$CDM model relies on two fundamental assumptions: the isotropy of the universe (supported by observational evidence) and the Copernican principle (a philosophical postulate). Together, these assumptions lead to the well-known Cosmological Principle, with the homogeneity of the universe emerging as a direct consequence. In this thesis, I review the cosmological consequences of relaxing some of these assumptions, exploring inhomogeneous and anisotropic universe models, as well as tilted cosmologies, which consider observers in motion relative to the Hubble flow. We examine methods to study these effects using existing cosmological data. First, we explore a variety of models that describe inhomogeneous and anisotropic universes, including different metric theories, perturbative analyses, averaging effects, tilted scenarios, and cosmographic approaches. We then apply this theoretical framework to analyze SNIA data and the local peculiar velocity field, aiming to constrain key parameters.

The current paper reports an investigation on the cosmological and thermodynamic behaviour of an $f(Q,T)$ modified-gravity framework in which the gravitational Lagrangian is written as $f(Q,T)=f(Q)+\lambda T$, with $Q$ denoting the non-metricity scalar and $T$ the trace of the energy-momentum tensor. The modified Friedmann equations are formulated in terms of an effective Dark Energy sector, and the corresponding equation of state and squared speed of sound are examined for a phenomenological polynomial form of $f(Q)$. A power-law background is constrained using 32 Cosmic Chronometer measurements. The resulting background is then used to study the effective Dark Energy dynamics and its classical stability in the redshift range considered. In this study, we further construct a generalized Ricci-Gauss-Bonnet holographic Dark Energy model with logarithmic entropy corrections based on the Nojiri-Odintsov prescription and establish a correspondence between its energy density and the effective Dark Energy density of the $f(Q,T)$ framework. The full function $f(Q,T)$ is then given by adding the trace contribution $\lambda T$. Finally, the thermodynamic behaviour of the reconstructed model is studied at the apparent horizon with the Nojiri-Odintsov entropy motivated by Phys. Rev. D 105, 044042 (2022) and the Gibbs relation. The entropy evolution obtained from the compact background description is also found to be consistent with that obtained from the reconstructed effective-fluid formulation, with only small numerical residuals. These results provide a consistent framework for examining the connection between generalized holographic dark energy, reconstructed $f(Q,T)$ gravity, and cosmic thermodynamics.

The key focus of this research work is the analysis of a non-singular cosmic bounce in the context of $\mathcal{F}(Q)$ gravity, with $Q$ representing the non-metricity scalar. We consider the gravitational Lagrangian $\mathcal{F}(Q)=Q+\psi Q^n$ in the presence of a modified Chaplygin-type matter source with a flat Friedmann-Robertson-Walker spacetime and a perfect matter distribution. In order to proceed, we adopt two approaches: a reconstruction approach using scale-factor ansatz and analysis of a two-dimensional autonomous dynamical system. Our results imply that the geometry coupling parameter $\psi$ plays an important role and causes geometrical repulsion for violating the null energy condition. A numerical scan of the $(\rho_0,\psi)$ parameter space suggests that there is a critical energy density for the bounce to take place, below which the universe evolves towards the standard singular cosmological solution. Moreover, the effective equation of state slowly evolves towards the de Sitter value ($\omega_{eff}\rightarrow -1$) and the squared sound speed is bounded by the stability and causality condition ($0\leq C_s^2\leq1$). It is found that $\mathcal{F}(Q)$ gravity provides a coherent geometric picture of the non-singular bouncing universe in accordance with the cosmic accelerated expansion.

We perform a cosmographic analysis of Type Ia supernovae using the Pantheon+&SH0ES, DES-SNY5 and Union3 compilations. We consider different redshift intervals, analyzed through a third-order Taylor expansion and a Padé $(1,2)$ approximation of the luminosity distance. First, we first infer the cosmographic parameters directly from the observed supernova redshifts. Afterwards, we extend the analysis by including a dipole correction associated with the local peculiar velocity field, constraining both its amplitude and direction. For Pantheon+&SH0ES, the Cepheid calibration allows a direct determination of the Hubble constant, whereas for DES-SNY5 and Union3 we fix $H_0$ to set the absolute distance scale. By progressively increasing the maximum redshift of the sample, we study how the inferred cosmographic parameters depend on the adopted redshift interval. We find that the Hubble constant obtained from Pantheon+&SH0ES remains consistent with previous determinations for both cosmographic parameterizations. Instead, the agreement of the deceleration $q_0$ and jerk $j_0$ parameters with the $\Lambda$CDM values depends on the adopted compilation and improves mainly for Pantheon+&SH0ES as the redshift interval is enlarged. Moreover, the reconstructed dipole parameters remain stable across the redshift intervals considered, with velocity amplitudes of order $300\,\mathrm{km\,s^{-1}}$, for all three supernova samples. Finally, fixing the dipole parameters with the cosmic microwave background values leads to a slight shift from the fiducial $\Lambda$CDM values of the deceleration $q_0$ and jerk $j_0$ parameters.

In this work, we investigate Hawking radiation and second order quantum corrected thermodynamics of a Vaidya-Bonnor black hole surrounded by quintessence. Within the Hamilton-Jacobi tunneling formalism, analytical expressions for the event horizons, tunneling probability, and Hawking temperature are derived by treating the quintessence field as a perturbative contribution. The classical thermodynamic quantities, including entropy, heat capacity, enthalpy, Helmholtz free energy, and Gibbs free energy, are then obtained and analyzed. Quantum thermal fluctuations are incorporated through logarithmic and inverse-entropy corrections to the Bekenstein-Hawking entropy, leading to second-order corrected thermodynamic quantities. Their effects on thermal stability and phase transitions are examined in detail. Furthermore, analytical expressions for the quantum-corrected remnant radius and remnant mass are derived, showing that the combined effects of quintessence and quantum corrections can prevent complete black hole evaporation and lead to the formation of a stable remnant. Our results show that both quintessence and higher-order quantum corrections enhance thermodynamdymic stability and significantly favor the formation of stable black hole remnants.

Some dynamical spacetime solutions that describe ultra-compact objects are analysed. We show that by turning a static spacetime that describes a one-way wormhole into a dynamical time-dependent one, a singularity might arise in general. Several well-known wormhole solutions are studied, which are shown to become singular when promoted to a time-dependent wormhole. However, we show that one can construct a dynamical wormhole free of singularities. The corresponding Lagrangian that holds such dynamical spacetimes is also reconstructed, based on a two-scalar-field model free of ghosts. Energy conditions are also analysed, which might remain satisfied for a dynamical -singular- wormhole. Finally, the evolution of the optical appearance of such dynamical objects is simulated and compared to static solutions. Some interesting features emerge that point to a way to measure the time evolution of dynamical objects by looking at the photon ring structure around the object.

We study the conformal scattering of massless scalar waves in Minkowski spacetime. The conformal scattering problem is formulated as a Goursat (characteristic initial-value) problem of the physical wave equation in compactified double-null coordinates, including the neighborhood of spatial infinity $i^0$. As null infinities $\mathcal{I}^\pm$ lie on the domain boundary by construction, asymptotic radiation is directly accessible. We consider three physical scenarios: free wave propagation, scattering off a Pöschl–Teller (PT) potential, and the semi-linear $|\phi|^{n-1}\phi$ wave equation. For multipole numbers $\ell =0,1$, an explicit stencil, averaging along the spatial direction, yields globally second-order convergent results. For $\ell \ge 2$, an implicit stencil averaging along the temporal direction is required for numerical stability. Although the singular $i^0$ reduces the convergence of the radiation data on $\mathcal{I}^+$ to first order, Richardson extrapolation enhances the effective convergence rate to approximately $1.5$. For PT scattering, our method accurately computes scattering quantities, notably the phase shifts induced by the potential. In the semi-linear case, our method captures the physical signatures of a self-defocusing Kerr nonlinearity, including self-phase modulation and spectral broadening. The compactified double-null framework proves to be simple and efficient, suggesting a promising approach to the global evolution of conformal scattering.

The effective-one-body (EOB) framework, originally formulated within the post-Newtonian (PN) expansion, is central to modeling and interpreting gravitational-wave signals. Recent developments have incorporated the post-Minkowskian (PM) expansion into EOB theory. In this work, we focus on the bound state dynamics in the PM approximation up to the third order and construct the core ingredients of EOB: the effective metric. We examine two correspondence strategies, one based on the radial action variable and the other on the precession angle. We demonstrate that the radial action variable provides a consistent correspondence, which is further verified by the correspondence based on the precession angle. Building on these results, we adopt an isotropic gauge with a Schwarzschild-like parametrization to fix the remaining freedom. Within this parametrization, the effective metric coefficients are determined at 3PM order. Our results provide a consistent effective metric for the bound state dynamics.