arXiv subjects

Ángel J. Murcia

Publications and source records attributed to Ángel J. Murcia.

At least 19 recordsLinked to original sources

arXiv2026

Thin shells in Lovelock and Quasi-topological gravities

We derive the junction conditions for spherically symmetric thin shells in Lovelock and Quasi-topological gravities along two independent routes: from the distributional form of the field equations, and from the boundary term that makes the variational problem well-posed in the non-null case. The former method is ambiguous as it stands, since the equations contain products of Heaviside step functions with a Dirac delta. We show that the singular parts of the field equations are exact differentials in the jumping variables, so that the Vol'pert chain rule for functions of bounded variation fixes these singular combinations uniquely and no products of two deltas survive for a single shell, finding that both routes then agree. The same rule yields the null junction conditions, for which no boundary term is available in Quasi-topological gravities, together with the mass conservation law of the shell. These results clarify recent questions concerning the existence of thin shells in these theories. In particular, we show that previous claims that the junction conditions force the shell mass to vary with radius are incorrect and arise from treating a trapezoidal approximation to the relevant distributional products as exact. Our results also provide a basis for the recent analyses of mass inflation in these theories.

gr-qc↗

arXiv2026

All theories of gravity with second-order traced field equations

We classify all diffeomorphism-invariant theories of gravity which possess traced field equations of motion of second order in derivatives. We also prove in the affirmative a conjecture regarding the form of theories constructed algebraically from the Riemann tensor with second-order traced field equations and classify all polynomial quasi-topological gravities with second-order traced field equations.

gr-qc↗

arXiv2026

Logarithmic correction to the entropy of near-extremal higher-curvature black holes

The spherically symmetric sector of broad classes of $D$-dimensional gravitational theories can be effectively described by general two-dimensional Horndeski theories. Exploiting this correspondence, we study the low-temperature dynamics of near-extremal black hole solutions of the parent theories by deriving a universal near-horizon effective description in terms of Jackiw--Teitelboim (JT) gravity. We explicitly show that the logarithmic quantum correction to the entropy, $S_{\rm JT}=\frac{3}{2}\log \left(T/T_{\rm breakdown} \right)$, previously derived for near-extremal black holes in Einstein gravity coupled to matter from the one-loop exact JT partition function, is universal across all models admitting an effective two-dimensional Horndeski description. We determine the general form of the scale at which this correction becomes dominant, $T_{\rm breakdown}$, in terms of the data of the $D$-dimensional theories. We illustrate our general results with charged black holes in Lovelock gravities and regular black holes in Quasitopological gravities.

hep-th↗

arXiv2026

Regular Black Holes in Nonlocal Quasitopological Gravity

We present infinite-derivative completions of Quasitopological gravities that are ghost-free, avoid strong coupling instabilities and admit exact, spherically symmetric vacuum regular-black-hole solutions satisfying a perturbative Birkhoff theorem.

gr-qc↗

arXiv2026

Cosmological higher-curvature gravities

We examine higher-curvature gravities whose FLRW configurations are specified by equations of motion which are of second order in derivatives, just like in Einstein gravity. We name these theories Cosmological Gravities and initiate a systematic exploration in dimensions $D \geq 3$. First, we derive an instance of Cosmological Gravity to all curvature orders and dimensions $D \geq 3$. Second, we study Cosmological Gravities admitting non-hairy generalizations of the Schwarzschild solution characterized by a single function whose equation of motion is, at most, of second order in derivatives. We present explicit instances of such theories for all curvature orders and dimensions $D \geq 4$. Finally, we investigate the equations of motion for cosmological perturbations in the context of generic Cosmological Gravities. Remarkably, we find that the linearized equations of motion for scalar cosmological perturbations in any Cosmological Gravity in $D\geq 3$ contain no more than two time derivatives. We explicitly corroborate this aspect by presenting the equations for the scalar perturbations in some four-dimensional Cosmological Gravities up to fifth order in the curvature.

gr-qc↗

arXiv2026

Buchdahl limits in theories with regular black holes

We study generalizations of Buchdahl's compactness limits for perfect-fluid star solutions of $D$-dimensional Einstein gravity coupled to higher-curvature corrections. We focus on Quasi-topological theories involving infinite towers of terms for which the unique vacuum spherically symmetric solutions correspond to regular black holes. We solve analytically the problem of constant-density stars and find that the space of solutions is bounded by: configurations with divergent central-pressure, corresponding to the most compact stars; configurations which possess zero central-pressure; and configurations for which the sizes of the stars coincide with the inner-horizon radii of the would-be regular black holes. In the more general case of perfect-fluid stars for which the mean density decreases with increasing radius, we show that, for each density profile, maximum compactness is reached when the metric becomes singular at the center. Under certain additional conditions, we find a novel Buchdahl limit for the maximum compactness of stars, attained by a specific constant-density profile. We show, in particular, that stars in these theories may be more compact than in Einstein gravity. While the vacuum solutions of these theories are such that all curvature invariants take mass-independent maximum finite values, we argue that there exist ordinary matter stars with finite central pressures for which such bounds can be violated -- namely, arbitrarily high curvatures can be reached -- unless additional constraints, such as the dominant energy condition, are imposed on the fluid.

gr-qc↗

arXiv2026

Regular Geometries from Singular Matter in Quasi-Topological Gravity

Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent scales. We study how this picture changes when the theory is coupled to matter. We find that minimally coupled matter spoils the scaling properties of the vacuum equations that lead to the validity of Markov's hypothesis, but the corresponding geometries often remain regular. We make this precise by developing a set of sufficient conditions on general static, spherically symmetric stress-tensors such that the corresponding solutions have bounded curvature. These conditions cover regular matter sectors but also singular matter profiles that are sufficiently singular in a sense we quantify. Our conclusions hold independently of the matter field equations and include configurations in which matter exhibits divergent energy density and pressure at finite radius or at Killing horizons, results that may have implications for mass inflation in these models. We then explore non-minimal couplings, focusing on theories with infinite towers of higher-curvature and electromagnetic terms in the action. In this class, Markov's hypothesis can be restored: we present theories admitting a universal upper bound on curvature, independent of the mass and charge. Overall, our results highlight subtleties in coupling quasi-topological gravity to matter and suggest Markov's hypothesis as a potential selection criterion for resummed gravity-matter effective theories.

gr-qc↗

arXiv2026

Higher-dimensional BKL dynamics in AdS black holes

Chaotic BKL dynamics provides a canonical description of the approach to spacelike singularities as a sequence of Kasner epochs grouped into eras. While this paradigm is well established for cosmological singularities, explicit realizations inside black holes have been scarce, despite renewed interest from holography. Here, we construct a broad class of asymptotically AdS black holes in $D\ge 4$ whose interiors exhibit bona fide BKL dynamics as the singularity is approached. In the near-singularity regime, the evolution reduces to billiard-like motion in a compact domain that forms a regular $(D-2)$-simplex. We derive closed-form bouncing rules for the Kasner exponents in arbitrary dimension and prove the ensuing chaotic dynamics. A key novelty for $D\ge 5$ is a richer internal organization of eras: inequivalent transitions between epochs lead to distinct Kasner seasons, yielding new patterns of epoch/era structure for both electric and gravitational walls. Finally, we investigate a holographic diagnostic, the thermal $a$-function, whose monotonic flow captures individual epochs and eras and can display near-walking behavior in suitable Kasner regimes.

hep-th↗

arXiv2025

Birkhoff implies Quasi-topological

Quasi-topological gravities (QTGs) are higher-curvature extensions of Einstein gravity in $D\geq 5$ spacetime dimensions. Throughout the years, different notions of QTGs constructed from analytic functions of polynomial curvature invariants have been introduced in the literature. In this paper, we show that all such definitions may be reduced to three distinct inequivalent notions: type I QTGs, for which the field equations evaluated on a single-function static and spherically symmetric ansatz are second order; type II QTGs, whose field equations on general static and spherically symmetric backgrounds are second order; and type III QTGs, for which the trace of the field equations on a general background is second order. We show that type II QTGs are a subset of type I QTGs and that type III QTGs are a subset of type II QTGs modulo pure Weyl invariants. Moreover, we prove that type II QTGs possess second-order equations on general spherical backgrounds. This allows us to prove that any theory satisfying a Birkhoff theorem is a type II QTG, and that the reverse implication also holds up to a zero-measure set of theories. For every theory satisfying Birkhoff's theorem, the most general spherically symmetric solution is a generalization of the Schwarzschild spacetime characterized by a single function which satisfies an algebraic equation.

gr-qc↗

arXiv2025

Novel duality-invariant theories of electrodynamics

We identify new families of duality-invariant theories of electrodynamics. We achieve this in two different ways. On the one hand, we present an algorithm to construct a one-parameter family of exactly duality-invariant theories from a single seed duality-invariant theory. If the seed theory is causal, the theories constructed from this method will also be causal when the parameter is non-negative. On the other hand, we find two additional novel families of duality-invariant theories which include a nonzero term independent of the electromagnetic field. The first of them generalizes Bialynicki-Birula electrodynamics, while the second family of theories features a well-defined Maxwell limit as the term independent of the gauge field strength is sent to zero.

hep-th↗

arXiv2025

Regular black hole formation in four-dimensional non-polynomial gravities

We construct four-dimensional gravity theories that resolve the Schwarzschild singularity and enable dynamical studies of nonsingular gravitational collapse. The construction employs a class of nonpolynomial curvature invariants that produce actions with (i) second-order equations of motion in spherical symmetry and (ii) a Birkhoff theorem, ensuring uniqueness of the spherically symmetric solution. Upon spherical reduction to two dimensions, these theories map to a particular subclass of Horndeski scalar-tensor models, which we use to explicitly verify the formation of regular black holes as the byproduct of the collapse of pressureless stars and thin-shells. We also show that linear perturbations on top of maximally symmetric backgrounds are governed by second-order equations.

gr-qc↗

arXiv2025

Regular black holes from Oppenheimer-Snyder collapse

It has been recently shown that regular black holes arise as the unique spherically symmetric solutions of broad families of generalizations of Einstein gravity involving infinite towers of higher-curvature corrections in $D\geq 5$ spacetime dimensions. In this paper we argue that such regular black holes arise as the byproduct of the gravitational collapse of pressureless dust stars. We show that, just like for Einstein gravity, the modified junction conditions for these models impose that the dust particles on the star surface follow geodesic trajectories on the corresponding black hole background. Generically, in these models the star collapses until it reaches a minimum size (and a maximum density) inside the inner horizon of the black hole it creates. Then, it bounces back and reappears through a white hole in a different universe, where it eventually reaches its original size and restarts the process. Along the way, we study FLRW cosmologies in the same theories that regularize black hole singularities. We find that the cosmological evolution is completely smooth, with the big bang and big crunch singularities predicted by Einstein gravity replaced by cosmological bounces.

gr-qc↗

arXiv2024

Regular black holes from thin-shell collapse

We establish that regular black holes can form from gravitational collapse. Our model builds on a recent construction that realized regular black holes as exact solutions to purely gravitational theories that incorporate an infinite tower of higher curvature corrections in any dimension $D \ge 5$ [arXiv:2403.04827]. We identify a two-dimensional Horndeski theory that captures the spherically symmetric dynamics of the theories in question and use this to prove a Birkhoff theorem and obtain the generalized Israel junction conditions. Armed with these tools, we consider the collapse of thin shells of pressureless matter, showing that this leads generically to the formation of regular black holes. The interior dynamics we uncover is intricate, consisting of shell bounces and white hole explosions into a new universe. The result is that regular black holes are the unique spherically symmetric solutions of the corresponding theories and also the endpoint of gravitational collapse of matter. Along the way, we establish evidence for a solution-independent upper bound on the curvature, suggestive of Markov's limiting curvature hypothesis.

gr-qc↗

arXiv2024

Dynamical Formation of Regular Black Holes

We study dynamical gravitational collapse in a theory with an infinite tower of higher-derivative corrections to the Einstein-Hilbert action and we show that, under very general conditions, it leads to the formation of regular black holes. Our results are facilitated by the use of a class of theories that possess second-order equations on spherically symmetric metrics, but which are general enough to provide a basis for the gravitational effective action. We analytically solve the collapse of a thin shell of dust and show that it inevitably experiences a bounce at small radius and that its motion can be extended to arbitrary proper time. The collapse of the shell always gives rise to a singularity-free, geodesically complete spacetime that contains horizons if the total mass is above a critical value. In that case, the shell bounces into a new universe through a white hole explosion. Our construction provides, to the best of our knowlege, the first fully dynamical description of formation of regular black holes, and it suggests that higher-derivative corrections may be the most natural way to resolve the singularities of Einstein's theory.

gr-qc↗

arXiv2024

Kasner eons with matter: holographic excursions to the black hole singularity

Recent work has shown that introducing higher-curvature terms to the Einstein-Hilbert action causes the approach to a space-like singularity to unfold as a sequence of Kasner eons. Each eon is dominated by emergent physics at an energy scale controlled by higher-curvature terms of a given order, transitioning to higher-order eons as the singularity is approached. The purpose of this paper is twofold. First, we demonstrate that the inclusion of matter dramatically modifies the physics of eons compared to the vacuum case. We illustrate this by considering a family of quasi-topological gravities of arbitrary order minimally coupled to a scalar field. Second, we investigate Kasner eons in the interior of black holes with field theory duals and analyze their imprints on holographic observables. We show that the behavior of the thermal $a$-function, two-point functions of heavy operators, and holographic complexity can capture distinct signatures of the eons, making them promising tools for diagnosing stringy effects near black hole singularities.

hep-th↗

arXiv2024

Waves and strings in an interacting conformal chiral 2-form theory in six dimensions

In six dimensions there exists a unique one-parameter family of non-linear conformal electrodynamics for a chiral 2-form gauge field which includes (in a free-field limit) the linear chiral 2-form theory and is related, by dimensional reduction, to the four-dimensional ModMax electrodynamics. In this work, we present the first exact solutions of this theory in presence of gravity. In particular, we will consider plane-wave, Robinson-Trautman, and self-dual dyonic string configurations, generalizing well-known solutions of this type in six-dimensional supergravities with linear chiral 2-form multiplets.

hep-th↗

arXiv2024

Generalized Siklos space-times

Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex function. We call the resulting geometry a generalized Siklos space-time. After deriving a number of identities for complex spaces, we specialize to Lorentz signature, where we show that the Killing function must be real and that the corresponding Dirac spinor is Majorana (as long as the space-time is not conformally flat), and we obtain the local form of the metric. We show that the purely gravitational degrees of freedom correspond to waves, whereas the matter sources generically correspond, via Einstein's field equations, to a sum of pure radiation and a space-like perfect fluid. Consequently, we conclude that the physically relevant case is obtained when the Killing function is homogeneous on the wave surfaces.

gr-qc↗

arXiv2024

The Heterotic-Ricci flow and its three-dimensional solitons

We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter $κ$, for a complete Riemannian metric and a three-form $H$ on a manifold $M$. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion $H$. When $κ= 0$ the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when $H=0$ and $κ>0$ the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form $H$. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.

math.DG↗