Black holes are the natural arena for exploring the interplay between gravity and thermodynamics. Although the association between black hole mechanics and black hole thermodynamics is well established, the comprehensive geometric formulation of thermodynamic variables deserves further investigation. In this work, both Newman-Penrose (NP) and Geroch-Held-Penrose (GHP) formalisms are considered within the framework of horizon thermodynamics. We show that the NP formalism reformulates the horizon condition as the Penrose-Rindler equation. In this context, a Smarr-like formula for stationary black holes is recovered from the Penrose-Rindler equation reinterpreted as a horizon equilibrium of pressures, which includes a pressure associated with the horizon rotation. A complete geometric reformulation of this reinterpretation of the Penrose-Rindler equation evaluated at the horizon is developed within the GHP formalism. The GHP approach further inspires the introduction of the horizon-averaged matter pressure and its conjugate volume, thereby enabling a quasilocal realization of the Smarr-like formula for stationary black holes. This geometric formulation clarifies the connection between horizon dynamics and thermodynamics and offers a unified setting for extending black hole thermodynamics beyond spherical symmetry.

In this study, we extend Leaver’s continued fraction method to evaluate black hole quasinormal modes (QNMs) in systems where the effective potential exhibits a discontinuity. In addition to the low-lying modes, we particularly focus on high overtones, which are physically pertinent due to the substantial deformation of the QNM spectrum triggered by spectral instability. In our algorithm, we expand the wave function at the point of discontinuity, instead of the black hole horizon, and incorporate the Israel-Lanczos-Sen junction conditions. We apply this algorithm to compute the QNMs of the modified Regge-Wheeler potential up to 2000 modes with high precision. For the low-lying modes, the numerical results show excellent agreement with those obtained using the matrix and Prony methods. The high overtones are significantly deformed, owing to the presence of echoes due to the discontinuity. This deformation in the asymptotic QNM spectrum reveals universal features that are largely independent of the specific form of the discontinuity in the potential, seemingly coinciding with those observed in the modified Pöschl-Teller effective potential. We speculate on whether the collective effect of the high overtones has an observational impact on gravitational-wave signals.

Exploring gravitational theories beyond general relativity (GR) with black hole (BH) spectroscopy requires accurate and flexible methods for computing their quasinormal mode (QNM) spectrum. A popular method of choice is the higher-order Wentzel-Kramers-Brillouin (WKB) approximation, mostly applied to nonrotating BHs. While previous studies demonstrated that the higher-order WKB method can also be used for Kerr BHs in GR, there has been little work on rotating BHs in modified theories of gravity. In this work, we revive the idea by extending WKB calculations of the Kerr QNM spectrum to higher order and assessing its accuracy against continued-fraction tabulated data. We then apply the WKB approximation beyond GR, comparing it against both linearized and continued fraction calculations in the parametrized beyond-Teukolsky formalism and in higher-derivative gravity theories. We find that the frequencies computed by the WKB method in theories beyond GR have better accuracy than the measurement errors for GW250114, the event with the highest ringdown signal-to-noise ratio observed to date.

Gravitational waves from comparable-mass binary-black-hole mergers are often described in terms of three stages: inspiral, merger, and ringdown. Post-Newtonian and black-hole perturbation theories are used to model the inspiral and ringdown parts of the waveform, respectively, while the merger phase has been modeled most accurately using numerical relativity (NR). Nevertheless, there have been several approaches used to model the merger phase using analytical methods. In this paper, we adapt a hybrid approximation method that applies post-Newtonian and black-hole perturbation theories at the same times in different spatial regions of a binary-black-hole waveform (and which are matched at a boundary region with prescribed dynamics). Prior work with the hybrid method used leading post-Newtonian theory and the perturbation theory of nonrotating black holes, which led to errors during the late inspiral and disagreement with the dominant quasinormal-mode frequency extracted from NR simulations during the ringdown. To obtain a better match with NR waveforms of binary-black-hole mergers, we made several phenomenological modifications to the hybrid method. Specifically, to better capture the inspiral dynamics, we use the effective-one-body method for modeling the trajectory of the boundary between the two spatial regions. The waveform is determined by evolving a Regge-Wheeler-Zerilli-type equation for an effective black-hole perturbation theory problem with a modified Poschl-Teller potential. By tuning the potential to match the dominant quasinormal-mode frequency of the remnant black hole and also optimizing the boundary data on the matching region, we could match NR waveforms from nonspinning, comparable-mass binary black holes with mass ratios between one and eight, with a relative error of the order of ${10}^{-3}$.

We review late-time cosmic acceleration after DESI Data Release 2 (DR2), emphasizing the interplay between Type Ia supernovae (SNe Ia), anisotropic baryon acoustic oscillation (BAO), cosmic microwave background (CMB) calibration, and perturbation-sensitive probes (redshift-space distortions and weak lensing). DESI DR2 delivers percent-level BAO distance ratios over $0\lesssim z\lesssim 2.5$, including a $\mathrm{Ly}\alpha$-forest anchor at $z_{\mathrm{eff}}=2.33$. In CMB-calibrated combinations, flat $\mathrm{\Lambda }\mathrm{CDM}$ exhibits a mild parameter mismatch, while allowing evolving dark energy (e.g., Chevallier-Polarski-Linder $w_0–w_a$) can improve the fit; the preference is dataset-dependent and is particularly sensitive to redshift-dependent SN calibration/selection residuals at the $\mathrm{few}\times {10}^{-2}\mathrm{mag}$ level. To sharpen likelihood-level interpretation, we provide two diagnostics: (i) a BAO-shape observable independent of the drag-epoch sound horizon $r_d$, namely the Alcock-Paczynski (AP) combination $F_{\mathrm{AP}}(z)\equiv D_{\mathrm{M}}(z)/D_{\mathrm{H}}(z)$, constructed directly from published $(D_{\mathrm{M}}/r_d,D_{\mathrm{H}}/r_d)$ with covariance propagation; (ii) a linear-response map from SN Hubble-diagram systematics $\delta \mu (z)$ to induced biases in $(w_0,w_a)$, yielding an explicit calibration requirement for DESI-era claims of evolving $w(z)$. We synthesize parametric and nonparametric reconstructions of $w(z)$ and ${\rho }_{\mathrm{DE}}(z)$ and map the resulting phenomenology to microphysical dark-energy and modified-gravity models subject to perturbation stability and gravitational-wave propagation constraints.

We explore the notion that cosmological models that modify the late-time expansion history cannot simultaneously fit the SH0ES Collaboration’s measurements of the Hubble constant, Dark Energy Spectroscopic Instrument baryon acoustic oscillations data, and type Ia supernova distances. Adopting a few simple phenomenological models, we quantitatively demonstrate that a satisfactory fit with a model with late-time expansion history can only be achieved if one of the following is true: (1) there is a sharp step in the absolute magnitude of type Ia supernovae at very low redshift, $z\sim 0.01$, or (2) the distance duality relation, $d_L(z)=(1+z{)}^2{d}_A(z)$, is broken. Both solutions are trivial in that they effectively decouple the calibrated type Ia supernovae measurements from other data, and this qualitatively agrees with previous work built on studying specific dark-energy models. We also identify a less effective class of late-time solutions with a transition at $z\simeq 0.15$ that lead to a more modest improvement in fit to the data than models with a very low-$z$ transition. Our conclusions are largely unchanged when we include surface brightness fluctuation distance measurements, with their current systematic uncertainties, to our analysis. We finally illustrate our findings by studying a physical model which, when equipped with the ability to smoothly change the absolute magnitude of type Ia supernovae, partially resolves the Hubble tension.

We present an analytical expression that gives both the matter and tracer (halo or galaxy) power spectrum with 1-loop corrections that include the neutrino effects on the mode-coupling kernels. We use the FFTLog algorithm to accelerate calculating the higher-order corrections to the power spectrum. We then use our power spectrum and bispectrum models to pursue two main goals. First, we examine the impact of neutrino mass on cosmological parameter estimation from both the power spectrum and bispectrum in real space. We create 1-loop power spectrum and bispectrum templates in real-space and fit to the quijote simulation suite at redshift $z=0$, including the cross-covariance between the power spectrum and the bispectrum. We show the neutrino signature kernels estimate the same cosmological parameters as the model with the standard perturbation theory (SPT) kernels, even for DESI Year 5 volume, except for the galaxy bias parameters inferred from the bispectrum. Second, we investigate to what extent the bispectrum can improve parameter constraints. We perform a Fisher forecast using the power spectrum, the tree-level bispectrum, and a joint analysis that includes the cross-covariance between them. We show that including the bispectrum can substantially reduce the error bars on key parameters. For the neutrino mass in particular, the uncertainty is reduced by $\sim 20\%$. We notify that our forecast is very optimistic for DESI, as DESI is at a higher redshift.

Machine learning can accelerate cosmological inferences that involve many sequential evaluations of computationally expensive data vectors. Previous works in this series have examined how machine learning architectures impact emulator accuracy and training time for optical shear and galaxy clustering two-point function. In this final manuscript, we explore neural network performance when emulating cosmic microwave background (CMB) temperature and polarization power spectra. We maximize the volume of applicability in the parameter space of our emulators within the standard $\mathrm{\Lambda }$-cold-dark-matter model while ensuring that errors are below cosmic variance. Relative to standard multi-layer perceptron architectures, we find that the dot-product-attention mechanism reduces the number of outliers among testing cosmologies, defined as the fraction of testing points with $\mathrm{\Delta }{\chi }^2>0.2$ relative to camb outputs, for a wide range of training set sizes. Such precision enables attention-based emulators to be directly applied to real data without requiring any additional correction via importance sampling. Combined with pre-processing techniques and optimized activation and loss functions, attention-based models can meet the precision criteria set by current and future CMB and lensing experiments. For each of Planck, Simons Observatory, CMB-S4, and CMB-HD, we find the fraction of outlier points to be less than 10% with around $2\times {10}^5$ to $4\times {10}^5$ training data vectors. We further explore the applications of these methods to supernova distance, weak lensing, and galaxy clustering, as well as alternative architectures and pre-processing techniques.

Decoherence and einselection explain many features of the emergence classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into constituent system and environment subsystems. In this work, given a fixed Hamiltonian we show that there can exist several factorizations (or tensor product structures) of a global Hilbert space that admit a quasiclassical description of subsystems in the sense that certain states (the “pointer states”) are robust to entanglement. We derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features. Our approach enables us to derive the division into quasiclassical subsystems and demonstrates that decohering subsystems do not necessarily align with our classical notion of locality. These results have interesting ramifications for the interpretation of quantum mechanics and, more practically, may be useful in algorithmically characterizing decoherence free subspaces.

Neutron stars (NSs) provide a unique laboratory to probe dark matter (DM) through its gravitational imprint on stellar evolution. We use a two-fluid framework with nonannihilating, asymmetric DM, both fermionic and bosonic, that interacts with ordinary matter solely through gravity. Within this framework, we track protoneutron stars across their thermal and compositional evolution via quasistatic modeling over the Kelvin-Helmholtz cooling timescale. We uncover a distinct thermal signature: DM cores deepen the gravitational potential, compressing and heating the baryonic matter, while extended DM halos provide external support, leading to cooling of the stellar matter. In contrast, hyperons and other exotic baryons soften the equation of state similar to DM cores but reduce, rather than increase, the temperature. DM thus alters both temperature and particle distribution profiles in ways that provide a clear diagnostic of its presence. DM cores also enhance compactness and shift hyperon onset, with the strongest effects during deleptonization and neutrino-transparent phases due to reduced neutrino pressure contributions. Consequently, this early thermal evolution, observable through supernova neutrino light curves and young pulsar cooling curves, offers a direct, testable probe of DM in NSs.

We investigate the rotational properties of strange quark stars using two representative quark matter (QM) equations of state (EOS): the vector MIT bag model and the density-dependent quark mass (DDQM) model. Through general-relativistic calculations of uniformly rotating sequences, we analyze their mass-radius relations, moments of inertia, quadrupole moments, surface redshifts, Keplerian frequencies, and energy components. A central result of this work is the full decomposition of the stellar energy budget in rotating strange stars, separating gravitational, internal, rotational, and binding energy contributions. Rotation amplifies the intrinsic EOS differences: the MIT model supports more massive ($M_{\max }\gtrsim 3.3M_{\odot }$) compact stars with larger moments of inertia and greater resistance to deformation, while the DDQM model produces larger radii, less massive stars limited by low Keplerian frequencies. Combined measurements of mass, radius, moment of inertia, surface redshift, and spin frequency can thus break the EOS degeneracy; massive, rapidly rotating pulsars favor MIT-like EOS, whereas larger moment of inertia in canonical stars point to a DDQM-like model. Moreover, by contrasting the rotational properties of quark stars with those of hadronic neutron stars, we identify distinctive multimessenger signatures of strange stars. These rotational observables, soon to be tightly constrained by Neutron Star Interior Composition Explorer and next-generation gravitational-wave detectors, offer a means to test the existence and composition of QM in compact stars.

Recent observations of supermassive black holes (SMBHs) at high redshifts pose challenges to standard seeding mechanisms. Among competing models, the collapse of self-interacting dark matter (SIDM) halos provide a plausible explanation for early SMBH formation. While previous studies on modeling the gravothermal collapse of SIDM halos have primarily focused on nonrelativistic evolution under the assumption of hydrostatic equilibrium, we advance this framework by relaxing the equilibrium assumption and additionally incorporating general-relativistic effects. To this end, we introduce the Misner-Sharp formalism to the SIDM context for the first time. Our model reproduces the standard hydrostatic models in the early long-mean-free-path (LMFP) regime but displays interesting distinct behavior in the late short-mean-free-path (SMFP) regime, where an intense outward heat flux drives a rapid expansion of the outer envelope, removing mass from the core, and significantly decelerating the collapse. Our general relativistic treatment enables us to follow halo evolution to the final stage when the apparent horizon forms. Our simulation yields a seed black hole mass of approximately $3\times {10}^{-8}$ of the halo mass at horizon formation, suggesting that additional mechanisms such as baryonic effects are critical for seeding black holes that are sufficiently massive to account for SMBHs in the early Universe.

We investigate the constraints on the neutron star equation of state (EOS) and nuclear properties achievable with third-generation gravitational wave detectors using the Fisher information matrix approach within the relativistic mean field theory. Assuming an optimistic binary neutron star merger rate, we generate simulated inspiral gravitational wave (GW) signals corresponding to one year of observation. From these simulated data, we compute the covariance matrix and posterior distributions for nuclear properties and EOS. Our results show that the EOS can be tightly constrained, particularly in the density range between one and four times nuclear saturation density. However, owing to the scarcity of low-mass neutron stars in the GW sample, the EOS at subsaturation densities remains poorly constrained. This, in turn, leads to weaker constraints on neutron star radii, as the radii are sensitive to the low-density EOS. Additionally, we present the expected correlations among nuclear parameters in general and plots of the inferred symmetry energy in particular, which represent degeneracies in their influence on the EOS and make them difficult to be constrained through GW observations alone. These highlight inherent limitations of inspiral GW signals in probing dense matter properties. Therefore, precise radius measurements, postmerger GW observations, and supplementary constraints from terrestrial nuclear experiments remain essential for a comprehensive understanding of dense matter.

Both observational and theoretical studies indicate that the central engine of a gamma-ray burst (GRB) is intrinsically time-variable, implying jet inhomogeneity. A jet with an inhomogeneous Lorentz factor distribution develops internal shocks both below and above the photosphere, relaxing toward homologous expansion. Below the photosphere, neutrons, whose mean free paths are much longer than those of charged particles, play an essential role in the dissipation process. Using neutron-inclusive shell simulations with initial conditions based on the collapsar scenario, we link the statistical inhomogeneity of the jet at the breakout of the progenitor to the dissipation that occurs inside and outside the photosphere, and calculate the GeV-TeV neutrino counterpart originated from inelastic neutron-proton interactions consistently with the prompt gamma-ray emission. We find that the peak energy of the GeV-TeV neutrinos is in 10–30 GeV irrespective of the baryon loading factor of the jet, with the high-energy tail extending into the TeV range as the amplitude of the time variability becomes stronger. When gamma-ray emission is efficient as in typical GRBs (i.e., the bolometric gamma-ray radiation efficiency with respect to the total engine-injected jet power is $\lesssim 100\%$), the radiative efficiency of GeV-TeV neutrinos remains 0.1%–10%. By contrast, when the gamma-ray radiation efficiency is relatively low ($\lesssim 10\%$) for jets where a large fraction of the energy is dissipated below the photosphere, the neutrino efficiency can increase up to 20%. This suggests that GRBs with relatively low gamma-ray luminosities, as well as x-ray-rich transients, can be promising targets for ongoing and future GeV-TeV neutrino transient searches.

Recent studies have shown that hadronic multiplicity in deep inelastic scattering can be associated with entanglement entropy. However, such definitions are intrinsically longitudinal and do not capture the full phase–space structure of the proton. In this work, we investigate the proton Wehrl entropy constructed from the gluon Husimi distribution, which provides a positive phase-space description within the present definitions and model calculations. Within this framework, we employ a gluon light-front spectator model based on soft-wall anti–de Sitter (AdS)/QCD-inspired wave functions, with free parameters constrained by global fits obtained by the NNPDF collaboration, allowing us to compute both parton distribution functions and Wigner distributions. The Husimi distribution is obtained via Gaussian smearing of the Wigner distribution with width given by the saturation scale in the Golec-Biernat-Wüsthoff model. We show that from a normalized Husimi distribution one can decompose the Wehrl entropy into an entanglement entropy term and a residual term associated with transverse degrees of freedom. Numerical results for the proton entanglement entropy are shown and compared with data obtained by the CMS collaboration, while the Wehrl entropy is presented for different values of the virtuality.

We extend the previously developed generally covariant formalism to include diffusion of conserved charges. We construct a partition function with chemical potential, and calculate the dynamics of the diffusion matrix in terms of the Ward identity enforcing charge conservation and linear response. We comment on the differences between diffusion of conserved scalar charges and full viscous hydrodynamics, and outline possible physical applications.

We examine the applicability of relativistic hydrodynamics far from equilibrium by constructing formal solutions of the Boltzmann moment equations in the relaxation time approximation. These solutions naturally decompose into a divergent gradient series and exponentially decaying nonperturbative modes that encode initial conditions. The nonperturbative contributions are essential for understanding causality, the divergence of the gradient series, and the unexpected effectiveness of relativistic hydrodynamics far from equilibrium. In the $0+1\mathrm{D}$ Bjorken scenario, we demonstrate that the exact evolution of nonequilibrium terms shares the same structural form as the gradient expansion, differing only through modified transport coefficients that reflect both initial data and free-streaming dynamics. Extending to $3+1\mathrm{D}$, we find that hydrodynamics remains effective not because the system is close to equilibrium, but because it interpolates smoothly between free streaming and collective behavior. This perspective offers a possible explanation for the remarkable success of hydrodynamics in modeling quark-gluon plasma evolution.

Entanglement is a hallmark of quantum theory, yet it alone does not capture the full extent of quantum complexity: some highly entangled states can still be classically simulated. Nonclassical behavior also requires magic, the non-Clifford component that enables universal quantum computation. Here, we investigate whether the interplay between entanglement and magic-state resources constrains the structure of fundamental interactions. We study gluon-gluon and graviton-graviton scattering at tree level. We focus on the high-energy limit, where mass-dependent terms are negligible, and conformal symmetry is preserved. In this regime, all particles behave as massless degrees of freedom, allowing us to isolate their transverse helicities as two-qubit states. We explicitly break gauge and general covariance by modifying the quartic vertices and analyzing the resulting generation of entanglement and magic. We find that imposing maximal entanglement (MaxEnt) alone does not uniquely recover gauge-invariant and diffeomorphism-invariant interactions, but adding the condition of minimal, but nonzero, magic-state generation singles it out. Our results indicate that nature favors MaxEnt and low magic: maximal quantum correlations with limited non-Cliffordness, sufficient for universal quantum computing but close to classical simulability. This dual informational principle may underlie the emergence of gauge invariance in fundamental physics.

We present the interpolating conformal algebra between the instant form dynamics (IFD) and the light-front dynamics (LFD) in ($1+1$) dimensions, along with a $4\times 4$ interpolating projective spacetime matrix representation. While there are six generators in the ($1+1$)-dimensional conformal algebra, the number of kinematic and dynamic generators dramatically changes in LFD, maximizing (minimizing) the number of kinematic (dynamic) generators to four (two) with respect to two (four) kinematic (dynamic) generators in IFD, as well as in any other forms of dynamics between IFD and LFD. It confirms and signifies the utility of LFD, saving substantial dynamical efforts in solving the ($1+1$)-dimensional quantum field theories. We also present $2\times 2$ Pauli matrix representation of ($1+0$) and ($0+1$) conformal groups and creation/annihilation operators of quantum simple harmonic oscillator representations of ($1+0$)-dimensional conformal groups.