Building on the earlier work by Araki and Tanii, Aschieri et al., and Buratti et al., we demonstrate that every model for self-dual nonlinear electrodynamics in four dimensions has a $\mathsf{U}(1)$ duality-invariant extension to $4p>4$ dimensions, and construct new self-dual nonlinear theories for a gauge ($2p-1$)-form. We present a family of models for self-dual nonlinear ($2p-1$)-form electrodynamics in which the trace of the energy-momentum tensor determines the flow with respect to a duality-invariant deformation parameter. Finally, we propose the interesting problem of computing the so-called induced action in the case that self-dual ($2p-1$)-form electrodynamics is coupled to dilaton and axion fields, and the compact duality group $\mathsf{U}(1)$ is enhanced to the noncompact group $\mathsf{SL}(2,\mathbb{R})$.

Rovibrational transitions in the hydrogen and antihydrogen molecular ions ${\mathrm{H}}_2^{+}$ and ${\overline{\mathrm{H}}}_2^{-}$ offer the possibility of testing Lorentz and $CPT$ symmetry to extremely high precision, in principle attaining $O({10}^{-17})$. In this paper, the third in a series, we give a comprehensive derivation of the rovibrational spectrum of ${\mathrm{H}}_2^{+}$ and ${\overline{\mathrm{H}}}_2^{-}$ in the standard model extension (SME), an effective quantum field theory incorporating Lorentz and $CPT$ violation. New developments described here include a complete analysis of the molecular dynamics from first principles in terms of the spherical tensor representation of the SME couplings, the systematic extension of our previous results to the nonminimal SME, a full description of the quantum number dependence of the rovibrational energy levels in the spherical tensor formalism with both high and low background magnetic fields, and an extended discussion of sidereal and annual variations of transition frequencies arising from both rotations and Lorentz boosts. The resulting sensitivity of the rovibrational spectrum to an extended range of SME couplings, together with the ability to isolate their individual effects using the quantum number dependence of the transition frequencies, enhances the opportunities to detect Lorentz and $CPT$ symmetry breaking through rovibrational spectroscopy of ${\mathrm{H}}_2^{+}$ and ${\overline{\mathrm{H}}}_2^{-}$.

We provide strong evidence for spontaneous breaking of spacetime parity persisting to arbitrarily high temperatures in a local, unitary, ultraviolet-complete quantum field theory in $2+1$ dimensions. The theory is defined by a renormalization group trajectory, triggered by a relevant deformation of a conformal field theory, consisting of a critical biconical vector model and a free massless Dirac fermion. This deformation couples the fermion to the scalar sector, generating a renormalization group flow that terminates at a nontrivial infrared fixed point described by a conformal Gross-Neveu-Yukawa model and a decoupled critical vector model. By construction, the quantum field theory is parity invariant at zero temperature. However, we show that at sufficiently high temperatures, parity symmetry is spontaneously broken and remains so even in the infinite-temperature limit. Our analysis relies on both, perturbative renormalization group techniques in $4-\epsilon$ dimensions and functional renormalization group techniques directly in $2+1$ dimensions.

We present a unified framework for the discussion of black hole thermodynamics of $d$-dimensional static black holes with spherical or compact hyperbolic horizon topology satisfying $g_{tt}{g}_{rr}=-1$ in Schwarzschild gauge. To that end, we consider any such black hole as a solution to an integrable two-dimensional effective dilaton theory and thereby as a vacuum solution to a generalized notion of $d$-dimensional quasitopological gravity. We show that the generating function determining $f(r)=-g_{tt}$ in the integrated equation of motion provides the thermodynamic mass in a generalized first law with entropy computed as the Wald entropy. The framework presented here can be applied to singular and regular black holes with flat or anti–de Sitter asymptotics.

Fermion-boson stars are compact equilibrium configurations composed of ordinary fermionic matter and a bosonic dark component interacting only through gravity. Such systems provide a natural framework for exploring deviations from standard neutron-star models, including the possible accumulation of dark matter inside neutron stars, and may be relevant for compact objects near the low-mass black hole gap. We construct static and uniformly rotating fermion-boson stars within the framework of $R$-squared $f(R)$ gravity, characterized by the functional form $f(R)=R+a{R}^2$, where $a$ is a positive parameter governing the effective mass scale from the scalar degree of freedom. The fermionic sector is modeled as a perfect fluid described by a tabulated equation of state at zero temperature, while the bosonic component is represented by a self-interacting complex bosonic field. Our results show that the scalar degree of freedom modifies the spatial distribution of both the bosonic field and the fermionic pressure, enlarges the domain of admissible equilibrium solutions, and increases the maximum supported masses relative to general relativity. Our models remain compatible with current astrophysical and gravitational-wave constraints, suggesting that fermion-boson stars in $R$-squared gravity offer a promising framework to investigate the combined effects of dark bosonic matter, rotation, and strong-field modifications of gravity in compact objects.

Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, and curvature singularities. These structures are usually identified by different geometric or causal criteria. We show that, for the Kerr-Newman black hole, the membrane-paradigm pressure of a stretched horizon admits an analytically continued scalar representative whose fully factorized form has zeros, poles, and singular factors aligned with these standard Kerr-Newman loci. Its zeros occur at the outer and inner horizons, its poles occur at the outer and inner stationary-limit surfaces, its higher-order divergence contains the ring-singularity factor, and its large-$r$ behavior records the asymptotic decay of the scalar. The construction is not proposed as a new invariant characterization of the spacetime, nor as a physical extension of the membrane fluid into the black hole interior. Rather, it gives a compact membrane-pressure-based diagnostic whose analytic structure reorganizes several familiar surfaces of the Kerr-Newman geometry. We also note a secondary, purely algebraic analogy with generalized multicomponent van der Waals-type equations of state.

We study the five-dimensional Schwarzschild-Tangherlini solution, with particular attention to its geodesic structure and massless scalar perturbations. In the probe limit, we present two applications. First, we compute the scattering angle for unbound geodesics showing both post-Newtonian and post-Minkowskian type expansions, and succeeding in resumming the resulting series in terms of hypergeometric functions. Second, we derive the Lyapunov exponent for deviations from a critical circular orbit, which is relevant to the eikonal estimation of quasinormal modes. We then investigate the dynamics of massless scalar ($s=0$) perturbations, for which the radial equation becomes a reduced confluent Heun equation. In this $d=5$ Schwarzschild-Tangherlini case we develop an original extension of the standard Mano-Suzuki-Takasugi formalism and validate the construction by computing the renormalized angular-momentum parameter $\nu$, whose value agrees with an independent determination based on the quantum Seiberg-Witten formalism. Finally, we analyze the energy flux from circular orbits, obtaining post-Newtonian results through 2.5PN order.

Next-generation gravitational-wave detectors will require significant improvements in current theoretical waveform models, particularly in the case of asymmetric-mass binaries. Here we provide one such improvement by calculating fully relativistic finite-size effects for small mass ratios—primarily, fluxes of energy—including quadratic-in-secondary-spin terms, spin-induced quadrupole terms, and tidally induced quadrupole terms, for quasicircular inspirals of a small companion into a Kerr black hole. We formulate these calculations within a multiscale waveform-generation framework in self-force theory, which could be used, with an energy-balance law we derive, to develop self-contained waveform models for asymmetric binaries involving stars orbiting black holes. Our results could additionally be used to improve other families of waveform models across all mass ratios. We present results both as complete numerical data sets on a Chebyshev grid and as analytical post-Newtonian expansions (to sixth PN order relative to the leading term in each contribution to the flux).

We numerically study perturbations of spatially homogeneous and orthogonal solutions to the Einstein-Euler equations with positive cosmological constant and linear equation of state $p=K\rho$ for $K\in (\frac{1}{3},1)$. Recent numerical and analytic work has demonstrated that the fluid density gradient in these perturbed spacetimes can form steep gradients and blow up as future timelike infinity is approached, a phenomenon now known as the “Rendall instability.” In this article, we study the onset of this instability outside of one spatial dimension for the first time. Our results provide compelling evidence that the Rendall instability causes a forward ultraviolet cascade and $H^s$ norm inflation in the energy density of the fluid from small $U(1)$-symmetric perturbations. This is, to the best of our knowledge, the first example of small data norm inflation for solutions of the field equations with a positive cosmological constant.

In this work, we show that if the bumblebee field in the Einstein-bumblebee theory is given by its vacuum expectation value ($B_{\mu }=b_{\mu }$) and it is not dynamical (${\partial }_{\mu }{B}_{\nu }-{\partial }_{\nu }{B}_{\mu }=0$), then these conditions uniquely provide a generating technique, allowing us to construct exact solutions to bumblebee gravity from the vacuum solutions by adding a term $\sim b_{\mu }{b}_{\nu }$ to the metric tensor (thus proving the uniqueness of the method, presented in Poulis and Soares [Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value, Eur. Phys. J. C 82, 613 (2022)]). Also, we show that the bumblebee field within this technique is proportional to the tangential vector of the (timelike or spacelike) geodesic curve in the background vacuum spacetime, and can be easily found knowing the solution to the Hamilton-Jacobi equation. Moreover, we prove that this technique can be extended to the case of any nonzero cosmological constant and the presence of the electromagnetic field. We apply this generating technique and obtain the bumblebee extension of the Kerr-Newman-Taub-NUT-(anti–)de Sitter spacetime. We show that this extension is not unique, as it depends on the exact geodesic curve one chooses to associate a bumblebee field with. Also, we show that for some choices of parameters, the bumblebee field and the metric functions may become complex, and to avoid this, we find the conditions under which the bumblebee field remains globally real.

A key question in early Universe cosmology is whether inflation can be successfully seeded by a generic, localized fluctuation in the inflaton field that probes the inflationary part of the potential. Past simulations have mainly considered periodic spacetimes representing either a closed universe of a specific size or a typical patch of a larger one, and as a result have needed to impose restrictive conditions on the extrinsic and intrinsic curvatures, which are arguably not generic. In this work we consider initial fluctuations in asymptotically flat spacetimes, allowing more general profiles of the intrinsic and extrinsic curvature. Our findings confirm and generalise the result of Goldwirth and Piran that a fluctuation with proper size several times the inflationary scale $1/\sqrt{G{\rho }_{\mathrm{infl}}}$ is required for successful inflation. We also discuss inherent restrictions on the initial data, and how imposing a periodic length close to the inflationary scale may bias results.

The quasinormal modes of black holes (BHs) in the large-angular-momentum limit can be computed within the eikonal approximation. This approximation is often extrapolated to low angular momentum to obtain a rough estimate of the dominant ringdown modes. Although approximate, this approach is particularly convenient in theories beyond general relativity with intricate dynamics, or for phenomenological metrics that lack an underlying fundamental theory. Here we explore a complementary approximate strategy: we compute exactly the quasinormal modes of a test scalar field propagating on the BH background and use their deviations from the general-relativity predictions as a proxy for the corresponding corrections to the gravitational quasinormal modes. For Kerr-Newman and Einstein-scalar–Gauss-Bonnet BHs, we show that this method reproduces the exact corrections (including the coupling among different degrees of freedom) within tens of percentages, an accuracy that is adequate as long as ringdown measurements remain at the percentage level. Furthermore, this method is typically comparable to, or more accurate than, the eikonal approximation. We then apply the same strategy to phenomenological metrics commonly employed in tests of gravity using BH imaging. By computing scalar quasinormal modes in a large family of these metrics for the first time, we find that current ringdown constraints are comparable to, and in some cases more stringent than, those derived from BH shadow observations, while also providing complementary bounds on sectors that would otherwise be inaccessible.

A common feature of regular black-hole spacetimes is the presence of an inner Cauchy horizon. The analogy to the Reissner-Nordström solution then suggests that these geometries suffer from a mass-inflation effect, rendering the Cauchy horizon unstable. Recently, it was shown that this analogy fails for certain classes of regular black holes, including the Hayward solution, where the late-time behavior of the mass function no longer grows exponentially but follows a power law. In this work, we extend these results in a twofold way. First, we determine the basin of attraction for the power-law attractor, showing that the tamed growth of the mass function is generic. Second, we extend the systematic analysis to the Bardeen and Dymnikova geometries, the Ghosh-Culetu black hole, and a spacetime arising from a nonsingular collapse model newly proposed in the context of asymptotically safe quantum gravity. Remarkably, in the latter solution, the Misner-Sharp mass at the Cauchy horizon remains of the same order of magnitude of the mass of the black hole, since its growth is just logarithmic.

We show that chainlike transients in head-on collisions of radially excited boson stars are controlled by the binary collision time, not by radial excitation alone. For selected configurations with radial excitation number $n=2$ and repulsive quartic self-interaction coupling $\lambda =400$, isolated evolutions define transient breathing windows that serve as reference clocks. Numerical-relativity simulations show that visible chains form only when the collision time is compatible with the isolated breathing clock. A separation scan shifts the collision time relative to the same clock, providing direct evidence for the timing-window mechanism. An additional fixed-separation check at $\lambda =500$ shows the same event ordering, indicating that the observed pattern is not unique to the fiducial self-interaction strength.

We study quantum gravitational effects inside hyperbolic black holes with both outer and inner horizons by solving the Wheeler-DeWitt (WDW) equation in the minisuperspace approximation. The WDW equation contains a tachyonic region where the effective potential becomes negative. We develop a numerical method that consistently evolves the wave function across this region and obtain stable solutions throughout the entire minisuperspace. For small values of the parameter $\kappa$, which controls the strength of quantum gravitational effects, the wave packet propagates along the classical trajectory with only mild quantum spreading. As $\kappa$ increases, enhanced quantum effects lead to significant spreading of the wave packet during its propagation. Nevertheless, when the initial state is localized near the outer horizon, the wave packet becomes localized again in the vicinity of the inner horizon. We refer to this recovery of localization as a refocusing phenomenon. This result suggests that if the geometry is classical near the outer horizon, it becomes classical again near the inner horizon. Within the minisuperspace approximation, inner-horizon formation is not obstructed by quantum gravitational effects.

We investigate extreme-mass-ratio inspirals in which a stellar-mass compact object orbits a supermassive bosonic dark matter star, modeled as a boson star, using fully relativistic perturbative methods. Unlike inspirals around electro-vacuum black holes, these systems can shed scalar matter through dynamical friction which significantly alters the inspiral dynamics. We show that this additional dissipation can induce a chirplike gravitational-wave signal closely resembling that of black hole binaries, allowing boson stars to act as gravitational-wave chirp mimickers even when they are not ultracompact. The inspiral evolution and resulting waveform depend sensitively on the compactness of the central boson star: highly compact configurations trigger dipolar scalar radiation, leading to a rapid plunge, whereas less compact stars yield smoother inspirals dominated by gravitational and quadrupolar scalar waves. To support waveform modeling, we derive semianalytical prescriptions for the gravitational and scalar energy fluxes that remain accurate deep into the relativistic regime. Our findings indicate that future space-based detectors such as the Laser Interferometer Space Antenna could distinguish these mimicker signals from true black hole inspirals through measurable phase dephasings induced by scalar dissipation.

We study braneworld cosmology in quasitopological gravity (QTG) with an infinite tower of higher-curvature terms, focusing on the case in which the bulk admits regular black hole solutions. We derive the ${\mathbb{Z}}_2$-symmetric junction conditions for a Friedmann–Lemaître–Robertson–Walker brane moving in a static, spherically symmetric bulk geometry, and obtain the corresponding modified Friedmann equations for the scale factor. We prove that, in the small scale factor regime, the brane generically approaches a de Sitter phase characterized solely by the length scale $\sqrt{\alpha }$ of the higher-derivative terms, while the standard Einstein-gravity braneworld dynamics is recovered in the low-energy regime. We further provide a universal estimate for the number of e-folds of the de Sitter phase in terms of the ratio between the black hole scale and the scale of new physics $r_g/\sqrt{\alpha }$. The inflationary regime is fully independent of the brane matter content and hence avoids the problem of trans-Planckian matter densities. Numerical integrations for explicit regular bulk solutions (Dymnikova-like and Hayward black holes) confirm these estimates and illustrate how the bulk black hole sector controls the onset and termination of inflation. This framework leverages the powerful properties of QTGs, defined only in $D\ge 5$, to study consequences for a four-dimensional universe.

Spacetimes with an ergoregion that is not connected to a horizon are linearly unstable. While the linear regime has been studied in a number of settings, little is known about the nonlinear evolution of this ergoregion instability. Here, we investigate this by numerically evolving the unstable growth of a massless vector field in a rapidly spinning boson star in full general relativity. We find that the backreaction of the instability causes the star to become more gravitationally bound, accelerating the growth, and eventually leading to black hole formation. During the nonlinear growth phase, small scale features develop in the unstable mode and emit radiation as nonlinear gravitational interactions mediate a direct turbulent cascade. The gravitational wave signal exhibits bursts, akin to so-called gravitational wave echoes, with increasing amplitude towards black hole formation.

We consider spherically symmetric Yang-Mills equations with gauge group $SO(d)$ in $d+1$-dimensional Minkowski spacetime. For any given odd $d\ge 11$, we establish existence and uniqueness (modulo reflection symmetry) of exactly $N$ smooth self-similar solutions, where $N$ is the number of zeros of an explicit polynomial $P_m(z)$ of degree $m=(d-5)/2$ in the interval $0<z<1$. The number $N$ can be determined algorithmically by an explicit computation. Our extensive computations for large odd dimensions suggest that $N=3$ for all odd $d\ge 11$. Two of these self-similar solutions admit closed-form expressions: one has been known previously, while the other appears to be new. Our result points toward a relatively simple landscape of possible blowup scenarios for high-dimensional Yang-Mills equations. Beyond its purely mathematical interest, this rigidity of self-similar blowup may also be relevant from a physical perspective, as it constrains the possible ultraviolet dynamics of non-Abelian gauge fields in higher-dimensional Yang–Mills theories arising in string-inspired extra-dimensional setups and in holographic models.

We extend the worldline quantum field theory formalism to include a direct diagrammatic method of computing the total flux of angular momentum from a black hole scattering event in the post-Minkowskian regime. Remarkably, except for subtle zero-frequency gravitons, the diagrammatic and integrational challenge is in a one-to-one correspondence with the analogous calculation of the black hole impulses—and the well-developed worldline quantum field theory (WQFT) methodologies for the impulse may thus be directly imported to this problem. Zero-frequency gravitons appear in this calculation as a “static” integration region in addition to the “dynamical” region usually encountered for the impulse. We show that a large class of static contributions can be organized systematically by introducing $n$-point functions referred to as “static correlators.” They reduce to a simple one-loop integral family which we compute explicitly using integration-by-parts relations and the method of differential equations. In passing, our analysis shows that static contributions disappear in space-time dimensions $D>4$. As a concrete application of our new method, we compute explicitly the $\mathcal{O}(G^3)$ total flux of angular momentum reproducing known results. Further, we apply the same method to electromagnetism where we compute the analogous $\mathcal{O}({\alpha }^3)$ result.