An exact rotating geometry need not define a black hole in equilibrium when its surface gravity varies across the horizon. We construct an asymptotically flat, non-Kerr subfamily of the aligned null solutions of generalized Proca theory whose outer horizon is exactly Killing and isothermal to second order in rotation. The horizon conditions constrain the vector hair, and integrability of the normalized horizon charge fixes the remaining second-order amplitude. Computing the complete gravitational and nonminimal vector surface charges, we obtain the asymptotically normalized mass and total angular momentum, and derive a logarithmic Hamiltonian entropy. The first law holds in both independent directions of the resulting two-parameter solution space. We express the mass as a function of entropy and angular momentum, recover the geometric thermodynamic potentials, and establish a scale-corrected Smarr relation that retains the dimensionful coupling. The exact metric defines the geometry, while equilibrium thermodynamics is consistently restricted to second order in spin. less

We demonstrate that the swirling universe can be recovered through a coordinated horizon-degeneration and scaling procedure applied to the Kerr C-metric. The construction exploits the horizon structure of accelerating, rotating black holes, which allows their inner and outer horizons to coalesce while simultaneously approaching the acceleration horizon. By magnifying the near-acceleration-horizon region faster than the black hole horizons approach it, the pair of accelerating, rotating black holes is pushed to an infinite proper distance, while a finite gravitomagnetic twist survives. The resulting geometry reproduces precisely the swirling universe, providing a physical interpretation of its intrinsic rotation as the gravitational remnant of rotating black holes sent to infinity. less

Hydrodynamic modeling of viscous neutron stars requires a choice of theory of relativistic hydrodynamics. That distinct formulations contain the same physical content in the long-wavelength limit is referred to as ``hydrodynamic universality.'' It has been recently shown that hydrodynamic universality can break down in radial neutron star oscillations: causality and finite-size effects restrict access to the long-wavelength universal hydrodynamic regime in sufficiently viscous stars. We show that this breakdown occurs for a broad range of causal hydrodynamic frames in Bemfica--Disconzi--Noronha--Kovtun (BDNK) theory. Increasing viscosity collectively pushes this class of causal frames away from the BDNK regime of validity, eventually forcing all to lie outside it at bulk viscosities in the range $ζ\sim10^{30}$--$10^{31}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. This breakdown of universality is accompanied by material changes in the oscillation mode structure: non-hydrodynamic modes become damped on timescales comparable to those of hydrodynamic modes, the first overtone can become longer lived than the fundamental mode, and unphysical instabilities with sub-millisecond timescales can emerge. Even in regimes where universality has broken down, we find that the inviscid threshold of gravitational collapse remains unchanged in BDNK theory. These results provide evidence that first-order theories of relativistic hydrodynamics may be insufficient for modeling sufficiently viscous neutron stars. less

A confident detection of orbital eccentricity in gravitational-wave signals from black hole-neutron star systems would be a strong indicator of their dynamical formation origin. While eccentric waveform models have recently been developed, their validity for analyzing black hole--neutron star signals has yet to be tested against numerical-relativity simulations. Building upon our previous study of quasicircular black hole--neutron star mergers, we perform simulations of a subset of these systems with orbital eccentricities around five times larger than those inferred for GW200105_162426. Additionally, we perform simulations with magnetized matter to assess whether trapped $g$-mode oscillations persist in strongly magnetized disks. Regarding the emitted gravitational-wave signal, we find that the effective one-body waveform model SEOBNRv5EHM shows reasonable agreement unless tidal contributions become important, and the inspiral-only post-Newtonian models pyEFPE/pyEFPEHM show larger disagreement in the late inspiral. For the equal-mass system, which has the largest effective tidal deformability, eccentric tidal corrections have a small but noticeable impact on the phase, $\sim0.1$ rad. We find an almost negligible impact of eccentricity on the properties of the remnant black hole, and differences of up to a factor of two in the remnant disk mass. Trapped $g$ modes in the accretion disks have the same frequency regardless of the eccentricity, confirming that they depend mainly on the properties of the remnant black hole. We find that when accretion disks are strongly magnetized, they become less dense and have less pronounced structure, and that the trapped $g$ modes previously identified in the unmagnetized cases are efficiently damped. less

How precisely must a photon's impact parameter be tuned for it to complete $n$ windings around a nearly extremal Kerr black hole before escaping, and how does the same near extremal scaling control the focusing of neighboring rays? For equatorial prograde returns we find, with $κ=\sqrt{1-a^2/M^2}$ and $X=nκ$, $ε_n=\sqrt{3}\,κ/(e^{2πX}-1) +O(κ^2|\lnκ|)$. This single law connects the extremal inverse-winding hierarchy to subextremal exponential accumulation. Perturbing the return family quasi-equatorially, we derive a second scaling law for the polar Jacobi phase, $Ψ_θ=2\ln[\sinh(πX)/κ]+C_s+o(1)$, and show that its focusing points cross from geometric spacing in winding number to asymptotically uniform spacing $Δ\mathcal N\simeq(2κ)^{-1}$. Numerical integrations of the exact Kerr radial dynamics and linear polar equation verify both scaling collapses. Thus near extremal Kerr exhibits parametrically distinct winding and polar-focusing scales, rather than a discontinuous jump between extremal and subextremal lensing hierarchies. less

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+ε$, we also obtain explicit Laurent expansions through $O(ε)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams. less

The spin-induced quadrupole moment (SIQM) of a compact object provides a direct null test of the Kerr hypothesis. Most existing gravitational-wave tests of SIQM assume quasi-circular binaries, although dynamical formation channels can produce measurable eccentricity that may persist in the sensitive band of third-generation (3G) detectors. We extend the symmetric SIQM test to eccentric, aligned-spin binaries using a post-Newtonian spinning-eccentric phasing model, and forecast its measurability with Cosmic Explorer (CE) and Einstein Telescope (ET). Single-event Fisher-matrix forecasts show that the impact of eccentricity on SIQM measurement precision depends on the binary parameters and detector configuration, rather than uniformly degrading the measurement. A population study with a truncated eccentric expansion indicates that ET's additional low-frequency eccentric cycles tighten $Δκ_s$ by roughly a factor of two relative to CE (median $0.11$ to $0.12$ versus $0.20$ to $0.23$); the absolute values are indicative only. We further show that quasi-circular template banks can lose significant effectualness for moderately eccentric signals, motivating the development of eccentric-spin template families. Accounting for eccentricity is therefore important both for SIQM measurements and for avoiding systematic losses in searches, and it strengthens tests of the nature of compact objects with 3G gravitational-wave detectors. less

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner--Nordström black holes remarkably vanish, the tidal response of a generic Kerr--Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein--Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging. less

In this work, using nonlinear electrodynamics (NLED) as a source in the field equations of extended scalar-tensor-Gauss-Bonnet (E-STGB) gravity, a novel type of static and spherically symmetric spacetime is found. We show that this novel type of spacetime can be used to explain the rotation curves and gravitational lensing of spiral galaxies. The NLED model used to derive our solution, in the weak and strong field limits, reduces to Maxwell electrodynamics. Furthermore, for a wide range of parameter values where our solution describes the gravitational field of a spiral galaxy, the NLED model satisfies the null and weak energy conditions. Hence, our results suggest that the extended scalar-tensor-Gauss-Bonnet gravity minimally coupled to nonlinear electrodynamics (E-STGB-NLED) provides a viable alternative to explain flat rotation curves of spiral galaxies without invoking dark matter. less

The discrete geometry on an $n$-dimensional simplicial manifold are studied, in order to incorporate torsion into Regge calculus. In each simplex, the edge vectors are assigned to the edges to encode the information of their lengths and directions. In addition, the holonomies along the curves across the interfaces of two adjacent simplices are represented by the internal gauge group elements. The torsion manifests itself as the difference between an edge vector on an interface belonging to one simplex and the parallel transported edge vector, via the holonomy, of the same edge but belonging to the adjacent simplex. The simplicial Einstein--Cartan actions are then constructed as functions of the edge vectors and holonomies in three and four dimensions with Euclidean and Lorentzian signatures, respectively. It is shown that they return to the corresponding Regge actions for the torsion-free cases. The variations of the 4-dimensional discrete action with respect to the edge vectors and holonomies, respectively, give two equations of motion. It is shown that the former is consistent with the corresponding equation in the continuum theory, and the torsion-free holonomies satisfy the latter equation as in the continuous case. Thus, the resulting theory on the simplicial manifold can be regarded as a discrete analogue of Einstein--Cartan theory. less