arXiv subjects

Pablo A. Cano

Publications and source records attributed to Pablo A. Cano.

At least 37 records · Page 2Linked to original sources

arXiv2024

Teukolsky equation for near-extremal black holes beyond general relativity: near-horizon analysis

We study gravitational perturbations on the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. We find a decoupled modified Teukolsky equation that rules the gravitational perturbations and that separates into an angular and a radial equation. The angular equation leads to a deformation of the spin-weighted spheroidal harmonics, while the radial equation takes the same form as in Kerr except for a modification of the angular separation constants. We provide a detailed analysis of the corrections to these angular separation constants and find analytic results for axisymmetric modes as well as in the eikonal limit. As an application, we reproduce recent results that show that extremal Kerr black holes in higher-derivative gravity become singular under certain deformations and extend them by including parity-breaking corrections, which we show lead to the same effect. Finally, we obtain constraints on the form of the full modified Teukolsky radial equation by demanding that it has the right near-horizon limit. These results serve as an stepping stone towards the study of quasinormal modes of near-extremal black holes in higher-derivative extensions of GR.

gr-qc↗

arXiv2024

Higher-derivative corrections to the Kerr quasinormal mode spectrum

We provide the most complete analysis so far of quasinormal modes of rotating black holes in a general higher-derivative extension of Einstein's theory. By finding the corrections to the Teukolsky equation and expressing them in a simple form, we are able to apply a generalized continued fraction method that allows us to find the quasinormal mode frequencies including overtones. We obtain the leading-order corrections to the Kerr quasinormal mode frequencies of all the $(l,m,n)$ modes with $l=2,3,4$, $-l\le m\le l$ and $n=0,1,2$, and express them as a function of the black hole spin $χ$ using polynomial fits. We estimate that our results remain accurate up to spins between $χ\sim 0.7$ and $χ\sim 0.95$, depending on the mode. We report that overtones are overall more sensitive to corrections, which is expected from recent literature on this topic. We also discuss the limit of validity of the linear corrections to the quasinormal mode frequencies by estimating the size of nonlinear effects in the higher-derivative couplings. All our results are publicly available in an online repository.

gr-qc↗

arXiv2024

Kasner eons in Lovelock black holes

In the vicinity of space-like singularities, general relativity predicts that the metric behaves, at each point, as a Kasner space which undergoes a series of "Kasner epochs" and "eras" characterized by certain transition rules. The period during which this process takes place defines a "Kasner eon", which comes to an end when higher-curvature or quantum effects become relevant. When higher-curvature densities are included in the action, spacetime can undergo transitions into additional Kasner eons. During each eon, the metric behaves locally as a Kasner solution to the higher-curvature density controlling the dynamics. In this paper we identify the presence of Kasner eons in the interior of static and spherically symmetric Lovelock gravity black holes. We determine the conditions under which eons occur and study the Kasner metrics which characterize them, as well as the transitions between them. We show that the null energy condition implies a monotonicity property for the effective Kasner exponent at the end of the Einsteinian eon. We also characterize the Kasner solutions of more general higher-curvature theories of gravity. In particular, we observe that the Einstein gravity condition that the sum of the Kasner exponents adds up to one, $\sum_{i=1}^{D-1}p_i=1$, admits a universal generalization in the form of a family of Kasner metrics satisfying $\sum_{i=1}^{D-1}p_i=2n -1$ which exists for any order-$n$ higher-curvature density and in general dimensions.

hep-th↗

arXiv2024

Isospectrality in Effective Field Theory Extensions of General Relativity

Two universal predictions of general relativity are the propagation of gravitational waves of large momentum along null geodesics and the isospectrality of quasinormal modes in many families of black holes. In extensions of general relativity, these properties are typically lost: quasinormal modes are no longer isospectral and gravitational wave propagation is no longer geodesic and it exhibits birefringence -- polarization-dependent speed. We study these effects in an effective-field-theory extension of general relativity with up to eight-derivative terms and show that there is a unique Lagrangian that has a non-birefringent dispersion relation for gravitational waves and isospectral quasinormal modes in the eikonal limit. We argue that both properties are related through a generalized correspondence between eikonal quasinormal modes and unstable photon-sphere orbits. These properties define a special class of theories that we denote as isospectral effective field theories. We note that the lowest-order isospectral correction to general relativity coincides with the quartic-curvature correction arising from type II string theory, suggesting that isospectrality might be a key feature of quantum gravity.

hep-th↗

arXiv2024

Kasner Epochs, Eras and Eons

As shown in the classic work of Belinski, Khalatnikov and Lifshitz, the approach to a generic space-like singularity in general relativity consists of a sequence of eras and epochs in which the metric is locally Kasner, connected by brief transitions. When quantum gravity effects are included, we argue that a new type of transition arises, giving rise to Kasner eons: periods which are dominated by emergent physics at each energy scale. We comment on the different ways in which the Einsteinian eon may come to an end and show explicitly how additional Kasner eons arise in the interior of a black hole solution due to higher-derivative corrections.

gr-qc↗

arXiv2024

Nonlocal Massive Gravity from Einstein Gravity

We present a top-down construction of a three-dimensional non-local theory of massive gravity. This "Non-Local Massive Gravity" (NLMG) is obtained as the gravitational theory induced by Einstein gravity on a brane inserted in Anti-de Sitter space modified by an overall minus sign. The theory involves an infinite series of increasingly complicated higher-derivative corrections to the Einstein-Hilbert action, with the quadratic term coinciding with New Massive Gravity. We obtain an analytic formula for the quadratic action of NLMG and show that its linearized spectrum consists of an infinite tower of positive-energy massive spin-2 modes. We compute the Newtonian potential and show that the introduction of the infinite series of terms makes it behave as $\sim 1/r$ at short distances, as opposed to the logarithmic behavior encountered when the series is truncated at any finite order. We use this and input from brane-world holography to argue that the theory may contain asymptotically flat black hole solutions.

hep-th↗

arXiv2024

Inconsistency of modified gravity in cosmology

We show that there is a fundamental flaw in the application of modified gravity theories in cosmology, taking $f(R)$ gravity as a paradigmatic example. This theory contains a scalar degree of freedom that couples to the matter stress-energy tensor but not to gravitational energy. However, when applied to cosmology this theory is unable to distinguish between gravitational and non-gravitational energy. Hence the cosmological version of the theory does not coincide with its own macroscopic average, and we show that this leads to order-one discrepancies. We argue that the same inconsistency is common to many other modified gravity theories with extra degrees of freedom. Our results put into question whether these theories can make sense as the cosmological average of a fundamental theory, hence challenging their physical significance.

gr-qc↗

arXiv2024

Regular Black Holes From Pure Gravity

We show via an explicit construction how an infinite tower of higher-curvature corrections generically leads to a resolution of the Schwarzschild singularity in any spacetime dimension $D \ge 5$. The theories we consider have two key properties that ensure the results are general and robust: (1) they provide a basis for (vacuum) gravitational effective field theory in five and higher-dimensions, (2) for each value of the mass, they have a unique static spherically symmetric solution. We present several exact solutions of the theories that include the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones. Unlike previous constructions, these regular black holes arise as vacuum solutions, as we include no matter fields whatsoever in our analysis. We show how the black hole thermodynamics can be studied in a completely universal and unambiguous way for all solutions.

gr-qc↗

arXiv2023

Boson stars with nonlinear sigma models

Boson stars arise as solutions of a massive complex scalar field coupled to gravity. A variety of scalar potentials, giving rise to different types of boson stars, have been studied in the literature. Here we study instead the effect of promoting the kinetic term of the scalar field to a nonlinear sigma model -- an extension that is naturally motivated by UV completions of gravity like string theory. We consider the $\mathrm{O}(3)$ and $\mathrm{SL}(2,\mathbb{R})$ sigma models with minimally interacting potentials and obtain their boson star solutions. We study the maximum mass and compactness of the solutions as a function of the curvature of the sigma model and compare the results to the prototypical case of mini boson stars, which are recovered in the case of vanishing curvature. The effect of the curvature turns out to be dramatic. While $\mathrm{O}(3)$ stars are massive and can reach a size as compact as $R\sim 3.3 GM$, $\mathrm{SL}(2,\mathbb{R})$ stars are much more diffuse and only astrophysically viable if the bosons are ultralight. These results show that the scalar kinetic term is at least as important as the potential in determining the properties of boson stars.

gr-qc↗

arXiv2023

Quasinormal modes of rotating black holes in higher-derivative gravity

We compute the spectrum of linearized gravitational excitations of black holes with substantial angular momentum in the presence of higher-derivative corrections to general relativity. We do so perturbatively to leading order in the higher-derivative couplings and up to order fourteen in the black hole angular momentum. This allows us to accurately predict quasinormal mode frequencies of black holes with spins up to about $70\%$ of the extremal value. For some higher-derivative corrections, we find that sizable rotation enhances the frequency shifts by almost an order of magnitude relative to the static case.

gr-qc↗

arXiv2023

Aspects of higher-curvature gravities with covariant derivatives

We study various aspects of higher-curvature theories of gravity built from contractions of the metric, the Riemann tensor and the covariant derivative, $\mathcal{L}(g^{ab},R_{abcd},\nabla_a)$. We characterise the linearized spectrum of these theories and compute the modified Newton potential in the general case. Then, we present the first examples of Generalized Quasi-topological (GQT) gravities involving covariant derivatives of the Riemann tensor. We argue that they always have second-order equations on maximally symmetric backgrounds. Focusing on four spacetime dimensions, we find new densities of that type involving eight and ten derivatives of the metric. In the latter case, we find new modifications of the Schwarzschild black hole. These display thermodynamic properties which depart from the ones of polynomial GQT black holes. In particular, the relation between the temperature and the mass of small black holes, $T\sim M^{1/3}$, which universally holds for general polynomial GQT modifications of Einstein gravity, gets modified in the presence of the new density with covariant derivatives to $T\sim M^{3}$. Finally, we consider brane-world gravities induced by Einstein gravity in the AdS bulk. We show that the effective quadratic action for the brane-world theory involving arbitrary high-order terms in the action can be written explicitly in a closed form in terms of Bessel functions. We use this result to compute the propagator of metric perturbations on the brane and its pole structure in various dimensions, always finding infinite towers of ghost modes, as well as tachyons and more exotic modes in some cases.

hep-th↗

arXiv2023

The universal Teukolsky equations and black hole perturbations in higher-derivative gravity

We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete computational strategy to obtain these decoupled equations in general higher-derivative theories. We apply this to six-derivative gravity to compute the shifts in the quasinormal mode frequencies with respect to those of Kerr black holes in general relativity. At linear order in the angular momentum we reproduce earlier results obtained with a metric perturbation approach. In contrast with this earlier work, however, the method given here applies also to post-merger black holes with significant spin, which are of particular observational interest.

gr-qc↗

arXiv2023

Accuracy of the slow-rotation approximation for black holes in modified gravity in light of astrophysical observables

Near-future, space-based, radio- and gravitational-wave interferometry missions will enable us to rigorously test whether the Kerr solution of general relativity accurately describes astrophysical black holes, or if it requires some kind of modification. At the same time, recent work has greatly improved our understanding of theories of gravity that modify the Einstein-Hilbert action with terms quadratic in the curvature, allowing us to calculate black hole solutions to (essentially) arbitrary order in a slow-rotation expansion. Observational constraints of such quadratic gravity theories require the calculation of observables that are robust against the expansion order of the black hole solution used. We carry out such a study here and determine the accuracy with respect to expansion order of ten observables associated with the spacetime outside a rotating black hole in two quadratic theories of gravity, dynamical-Chern-Simons and scalar-Gauss-Bonnet gravity. We find that for all but the most rapidly rotating black holes, only about the first eight terms in the spin expansion are necessary to achieve an accuracy that is better than the statistical uncertainties of current and future missions.

gr-qc↗

arXiv2023

On the stability of Einsteinian Cubic Gravity black holes in EFT

In this note we revisit the analysis performed in arXiv:2305.07217 of odd-parity perturbations around static and spherically symmetric black holes in Einsteinian Cubic Gravity (ECG). We show that the additional propagating modes always have masses much above the cutoff of the theory. Therefore, contrary to what is claimed in that paper, the ECG black holes remain stable within the effective field theory regime. We consider the same analysis for a general cubic theory, showing that the ECG results are not special in this regard. We use the occasion to make some clarifications on the role, uses and limitations of ECG and its generalizations.

hep-th↗

arXiv2023

The extremal Kerr entropy in higher-derivative gravities

We investigate higher derivative corrections to the extremal Kerr black hole in the context of heterotic string theory with $α'$ corrections and of a cubic-curvature extension of general relativity. By analyzing the near-horizon extremal geometry of these black holes, we are able to compute the Iyer-Wald entropy as well as the angular momentum via generalized Komar integrals. In the case of the stringy corrections, we obtain the physically relevant relation $S(J)$ at order $α'^2$. On the other hand, the cubic theories, which are chosen as Einsteinian cubic gravity plus a new odd-parity density with analogous features, possess special integrability properties that enable us to obtain exact results in the higher-derivative couplings. This allows us to find the relation $S(J)$ at arbitrary orders in the couplings and even to study it in a non-perturbative way. We also extend our analysis to the case of the extremal Kerr-(A)dS black hole.

hep-th↗

arXiv2023

Black Hole Multipoles in Higher-Derivative Gravity

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass $M_{n}$ and current $S_{n}$ multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles $S_{2n}\neq 0$ and $M_{2n+1}\neq 0$ that break equatorial symmetry, and the parity-preserving corrections that only modify $S_{2n+1}$ and $M_{2n}$. Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments.

gr-qc↗

arXiv2022

Electromagnetic Generalized Quasi-topological gravities in $(2 + 1)$ dimensions

The construction of Quasi-topological gravities in three-dimensions requires coupling a scalar field to the metric. As shown in arXiv:2104.10172, the resulting "Electromagnetic" Quasi-topological (EQT) theories admit charged black hole solutions characterized by a single-function for the metric, $-g_{tt}=g^{-1}_{rr}\equiv f(r)$, and a simple azimuthal form for the scalar. Such black holes, whose metric can be determined fully analytically, generalize the BTZ solution in various ways, including singularity-free black holes without any fine-tuning of couplings or parameters. In this paper we extend the family of EQT theories to general curvature orders. We show that, beyond linear order, $f(r)$ satisfies a second-order differential equation rather than an algebraic one, making the corresponding theories belong to the Electromagnetic Generalized Quasi-topological (EGQT) class. We prove that at each curvature order, the most general EGQT density is given by a single term which contributes nontrivially to the equation of $f(r)$ plus densities which do not contribute at all to such equation. The proof relies on the counting of the exact number of independent order-$n$ densities of the form $\mathcal{L}(R_{ab},\partial_a ϕ)$, which we carry out. We study some general aspects of the new families of EGQT black-hole solutions, including their thermodynamic properties and the fulfillment of the first law, and explicitly construct a few of them numerically.

gr-qc↗

arXiv2022

Non-extremal, $α'$-corrected black holes in 5-dimensional Heterotic Superstring Theory

We compute the first-order $α'$ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter $α'$ plays the role of thermodynamical variable.

hep-th↗