Black Hole Perturbation Research Articles

Holographic thermal correlators and quasinormal modes from semiclassical Virasoro blocks

Motivated by its relevance for thermal correlators in strongly coupled holographic CFTs, we refine and further develop a recent exact analytic approach to black hole perturbation problem, based on the semiclassical Virasoro blocks, or equivalently via AGT relation, the Nekrasov partition functions in the Nekrasov-Shatashvili limit. Focusing on asymptotically AdS5 black hole backgrounds, we derive new universal exact expressions for holographic thermal two-point functions, both for scalar operators and conserved currents. Relatedly, we also obtain exact quantization conditions of the associated quasinormal modes (QNMs). Our expressions for the holographic CFT4 closely resemble the well-known results for 2d thermal CFTs on ℝ1,1. This structural similarity stems from the locality of fusion transformation for Virasoro blocks. We provide numerical checks of our quantization conditions for QNMs. Additionally, we discuss the application of our results to understand specific physical properties of QNMs, including their near-extremal and asymptotic limits. The latter is related to a certain large-momentum regime of semiclassical Virasoro blocks dual to Seiberg-Witten prepotentials.

Gauge theory meets cosmology

We reconsider linear perturbations around general Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom involving only time reparametrizations, we write down classical background solutions analytically, for an arbitrary number of fluid components. We then show that the time evolution of scalar and tensor adiabatic perturbations are governed by Schrödinger-like differential equations of generalized Heun type. After recovering known analytic results for a single-component fluid, we discuss more general situations with two and three different fluid components, with special attention to the combination of radiation, matter and vacuum energy, which is supposed to describe the ΛCDM model. The evolution of linear perturbations of a flat ΛCDM universe is described by a two-transient model, where the transitions from radiation to matter and matter to vacuum energy are governed by a Heun equation and a Hypergeometric equation, respectively. We discuss an analytic approach to the study of the general case, involving generalized Heun equations, that makes use of (quantum) Seiberg-Witten curves for 𝒩 = 2 supersymmetric gauge theories and has proven to be very effective in the analysis of Black-Hole, fuzzball and ECO perturbations.

Novel approach to solving Schwarzschild black hole perturbation equations via physics informed neural networks

Novel approach to solving Schwarzschild black hole perturbation equations via physics informed neural networks

Connection formulae in the collision limit I: case studies in Lifshitz geometry

Abstract The connection formulae provide a systematic way to compute physical quantities, such as the quasinormal modes, Green functions, in blackhole perturbation theories. In this work, we test whether it is possible to consistently take the collision limit, which brings two or more regular singularities into an irregular one, of the connection formulae, and we provide some supportive evidence for it.

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Tidal Love numbers from EFT of black hole perturbations with timelike scalar profile

We study static tidal Love numbers (TLNs) of a static and spherically symmetric black hole for odd-parity metric perturbations.We describe black hole perturbations using the effective field theory (EFT), formulated on an arbitrary background with a timelike scalar profile in the context of scalar-tensor theories.In particular, we obtain a static solution for the generalized Regge-Wheeler equation order by order in a modified-gravity parameter and extract the TLNs uniquely by analytic continuation of the multipole index ℓ to non-integer values.For a stealth Schwarzschild black hole, the TLNs are vanishing as in the case of Schwarzschild solution in general relativity.We also study the case of Hayward black hole as an example of non-stealth background, where we find that the TLNs are non-zero (or there is a logarithmic running).This result suggests that our EFT allows for non-vanishing TLNs and can in principle leave a detectable imprint on gravitational waves from inspiralling binary systems, which opens a new window for testing gravity in the strong-field regime.

Gravitational waves on Kerr black holes: I. Reconstruction of linearized metric perturbations

Abstract The gravitational perturbations of a rotating Kerr black hole are notoriously complicated, even at the linear level. In 1973, Teukolsky showed that their physical degrees of freedom are encoded in two gauge-invariant Weyl curvature scalars that obey a separable wave equation. Determining these scalars is sufficient for many purposes, such as the computation of energy fluxes. However, some applications -- such as second-order perturbation theory -- require the reconstruction of metric perturbations. In principle, this problem was solved long ago, but in practice, the solution has never been worked out explicitly. Here, we do so by writing down the metric perturbation (in either ingoing or outgoing radiation gauge) that corresponds to a given mode of either Weyl scalar. Our formulas make no reference to the Hertz potential (an intermediate quantity that plays no fundamental role) and involve only the radial and angular Kerr modes, but not their derivatives, which can be altogether eliminated using the Teukolsky--Starobinsky identities. We expect these analytic results to prove useful in numerical studies and for extending black hole perturbation theory beyond the linear regime.

Even-parity black hole perturbations in minimal theory of bigravity

Even-parity black hole perturbations in minimal theory of bigravity

Scalar field perturbation of hairy black holes in EsGB theory

We investigate scalar field perturbations of the hairy black holes involved with spontaneous symmetry breaking of the global U(1) symmetry in Einstein-scalar-Gauss-Bonnet theory for asymptotically flat spacetimes. We consider the mechanism that black holes without hairs become unstable at the critical point of the coupling constant and undergo a phase transition to hairy black holes in the symmetry-broken phase driven by spontaneous symmetry breaking. This transition occurs near the black hole horizon due to the diminishing influence of the Gauss-Bonnet term at infinity. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function, incorporating the branch cut contribution. This allows us to analytically investigate the late-time behavior of the perturbation at both spatial and null infinity. We found that the late-time behavior only differs from the Schwarzschild black hole by a mass term. We then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. Our primary interest lies in utilizing QNMs to investigate the stability of the black hole solutions both the symmetric and symmetry-broken phases. Consistent with the prior study, our analysis shows that hairy black holes in the symmetric phase become unstable when the quadratic coupling constant exceeds a critical value for a fixed value of the quartic coupling constant. In contrast, hairy black holes in the symmetry-broken phase are always stable at the critical value. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking.

Even- and odd-parity stabilities of black holes in Einstein-Aether gravity

In Einstein-Aether theories with a timelike unit vector field, we study the linear stability of static and spherically symmetric black holes against both even- and odd-parity perturbations.For this purpose, we formulate a gauge-invariant black hole perturbation theory in the background Aether-orthogonal frame where the spacelike property of hypersurfaces orthogonal to the timelike Aether field is always maintained even inside the metric horizon. Using a short-wavelength approximation with large radial and angular momenta, we show that, in general, there are three dynamical degreesof freedom arising from the even-parity sector besides two propagating degrees of freedom present in the odd-parity sector. The propagation speeds of even-parity perturbations and their no-ghost conditions coincide with those of tensor, vector, and scalar perturbations on the Minkowski background, while the odd sector contains tensor and vector modes with the same propagation speeds as those in the even-parity sector (and hence as those on the Minkowski background).Thus, the consistent study of black hole perturbations in the Aether-orthogonal frame on static and spherically symmetric backgrounds does not add new small-scale stability conditions to those known for the Minkowski background in the literature.

Axial perturbations of hairy black holes in generalized scalar-tensor theories

Axial perturbations of hairy black holes in generalized scalar-tensor theories

Massless Dirac perturbations of black holes in f(Q) gravity: quasinormal modes and a weak deflection angle

This article considers a static and spherical black hole (BH) in f(Q) gravity. f(Q) gravity is the extension of symmetric teleparallel general relativity, where both curvature and torsion are vanishing and gravity is described by nonmetricity. In this study, we investigate the possible implications of quasinormal mode (QNM) modified Hawking spectra and deflection angles generated by the model. The Wentzel–Kramers–Brillouin method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter (Q 0). Based on the QNM computation, we can ensure that the BH is stable against massless Dirac perturbations and as Q 0 increases the oscillatory frequency of the mode decreases. We then discuss the weak deflection angle in the weak field limit approximation. We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it. We find that the Q 0 parameter reduces the deflection angle.

Can a radiation gauge be horizon-locking?

In this short Note, I answer the titular question: yes, a radiation gauge can be horizon-locking. Radiation gauges are very common in black hole perturbation theory. It’s also very convenient if a gauge choice is horizon-locking, i.e. the location of the horizon is not moved by a linear metric perturbation. Therefore it is doubly convenient that a radiation gauge can be horizon-locking, when some simple criteria are satisfied. Though the calculation is straightforward, it seemed useful enough to warrant writing this Note. Finally I show an example: the ℓ vector of the Hartle–Hawking tetrad in Kerr satisfies all the conditions for ingoing radiation gauge to keep the future horizon fixed.

Superradiant instability of charged extremal black holes in Einstein-Born-Infeld gravity

We study charged scalar perturbations of charged extremal black holes in Einstein-Born-Infeld theory. Our numerical results indicate that these black holes all suffer from superradiant instability by the unstable quasi-bound states, regardless how small the coupling constant is. We therefore provide a new example that the superradiant stability of the Reissner-Nordström black hole is a fine-tuned result, as in the case when it is embedded in the STU supergravity model. The work is also motivated by the weak gravity conjecture since at the linear coupling constant level, the theory belongs to a subsect of four-derivative corrections in the effective field theory. Our results appear to support the notion that the black holes do decay when gravity is weaker by the correction, but the decaying halftime requires nonlinear effects and cannot be seen at the level of linear coupling constant. The full nonlinear effects also indicate that the black holes can decay even when gravity is stronger.

Massive scalar field perturbations of black holes immersed in Chaplygin-like dark fluid

We consider massive scalar field perturbations in the background of black holes immersed in Chaplygin-like dark fluid (CDF), and we analyze the photon sphere modes, the de Sitter modes as well as the near extremal modes and discuss their dominance, by using the pseudospectral Chebyshev method and the third order Wentzel-Kramers-Brillouin approximation. We also discuss the impact of the parameter representing the intensity of the CDF on the families of quasinormal modes. Mainly, we find that the propagation of a massive scalar field is stable in this background, and it is characterized by quasinormal frequencies with a smaller oscillation frequency and a longer decay time compared to the propagation of the same massive scalar field within the Schwarzschild-de Sitter background.

Analytically separating the source of the Teukolsky equation

Recent gravitational wave detections from black hole mergers have underscored the critical role black hole perturbation theory and the Teukolsky equation play in understanding the behavior of black holes. The separable nature of the Teukolsky equation has long been leveraged to study the vacuum linear Teukolsky equation; however, as theory and measurements advance, solving the sourced Teukolsky equation is becoming a frontier of research. In particular, second-order calculations, such as in quasinormal mode and self-force problems, have extended sources. This paper presents a novel method for analytically separating the Teukolsky equation’s source, aimed to improve efficiency. Separating the source is a nontrivial problem due to the angular and radial mixing of generic quantities in Kerr spacetime. We provide a proof-of-concept demonstration of our method and show that it is accurate, separating the Teukolsky source produced by the stress-energy tensor of an ideal gas cloud surrounding a Kerr black hole. The detailed application of our method is provided in an accompanying notebook. Our approach opens up a new avenue for accurate black hole perturbation theory calculations with sources in both the time and frequency domain. Published by the American Physical Society 2024

Inverse problem in energy-dependent potentials using semiclassical methods

Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semiclassical Wentzel-Kramers-Brillouin (WKB) method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials. Published by the American Physical Society 2024

Love numbers and Love symmetries for p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes

The static Love numbers of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} (“Love”) symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with p-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-0 scalar and spin-2 tensor-type tidal perturbations of the higher-dimensional Reissner-Nordström black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of General Relativity. Interestingly, these near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} structures acquire extensions to Witt algebras. Our setup allows to also study the p-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone.

Effective field theory of black hole perturbations in vector-tensor gravity

We formulate the effective field theory (EFT) of vector-tensor gravity for perturbations around an arbitrary background with a timelike vector profile, which can be applied to study black hole perturbations. The vector profile spontaneously breaks both the time diffeomorphism and the U(1) symmetry, leaving their combination and the spatial diffeomorphism as the residual symmetries in the unitary gauge. We derive two sets of consistency relations which guarantee the residual symmetries of the EFT. Also, we provide the dictionary between our EFT coefficients and those of generalized Proca (GP) theories, which enables us to identify a simple subclass of the EFT that includes the GP theories as a special case. For this subclass, we consider the stealth Schwarzschild(-de Sitter) background solution with a constant temporal component of the vector field and study the decoupling limit of the longitudinal mode of the vector field, explicitly showing that the strong coupling problem arises due to vanishing sound speeds. This is in sharp contrast to the case of gauged ghost condensate, in which perturbations are weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura terms. This implies that, in order to consistently describe this type of stealth solutions within the EFT, the scordatura terms must necessarily be taken into account in addition to those already included in the simple subclass.

Spectral method for metric perturbations of black holes: Kerr background case in general relativity

Spectral method for metric perturbations of black holes: Kerr background case in general relativity