Non-extremal Black Holes Research Articles

Gravitational waves of nonextremal Kerr black holes from conformal symmetry

In the low-energy limit, the near region of a generic Kerr black hole has been conjectured to be holographically dual to a two-dimensional conformal field theory. In this paper, we consider a test object orbiting in the near region of a nonextremal Kerr black hole. We first couple it to a massless scalar field. The resulting scalar radiation at the horizon is computed from the perspectives of gravity and dual conformal field theory. Considering the influence of nonzero temperature, the agreement of both computations is found. Then, we generalize the analysis to the gravitational radiation and find agreement again. The agreement supports the conjectured holography and provides a potential theoretical tool for gravitational wave computations. Published by the American Physical Society 2024

Mass Inflation without Cauchy Horizons.

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are present for dynamical geometries describing accreting black holes with slowly evolving inner trapping horizons, even in the absence of Cauchy horizons. The explicit evaluation of the adiabatic conditions behind these exponential buildups shows that this phenomenon is universally present for physically reasonable accreting conditions. This noneternal mass inflation does not require the introduction of global spacetime concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with nonextremal inner horizons, including the Kerr geometry in general relativity, and nonextremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived end point of gravitational collapse.

Weak energy condition, trapped surfaces and black hole third law

We consider the third law of thermodynamics for families of 4- and n-dimensional Vaidya black holes, including many of interest. Since there are several versions of the definition of surface gravity as well as the extremality condition for dynamical black holes, we first show that for the considered 4- and n-dimensional Vaidya families, these definitions are consistent with each other. We assume, first, that a non-extremal black hole evolves to an extremality state after a finite time and second, that the weak energy condition for the source holds at all times. We then compare the results of these assumptions and investigate whether there are ranges of black hole parameters where these two assumptions are in conflict.

The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

AbstractHawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full asymptotic expansion of any smooth vacuum metric at a non-degenerate Killing horizon is determined by the geometry of the horizon. This gives a new perspective on the black hole uniqueness conjecture. In spacetime dimension 4, we also prove an existence theorem: Given any non-degenerate horizon geometry, Einstein’s vacuum equations can be solved to infinite order at the horizon in a unique way (up to isometry). The latter is a gauge invariant version of Moncrief’s classical existence result, without any restriction on the topology of the horizon. In the real analytic setting, the asymptotic expansion is shown to converge and we get well-posedness of this characteristic Cauchy problem.

Entanglement islands and the Page curve of Hawking radiation for rotating Kerr black holes

We initiate the study of the information paradox of rotating Kerr black holes by employing the recently proposed island rule. It is known that the scalar field theory near the Kerr black hole horizon can be reduced to the two-dimensional effective theory. Working within the framework of the two-dimensional effective theory and assuming the small angular momentum limit, we demonstrate that the entanglement entropy of Hawking radiation from the nonextremal Kerr black hole follows the Page curve and saturates the Bekenstein-Hawking entropy at late times. In addition, we also discuss the effect of the black hole rotation on the Page time and scrambling time. For the extreme Kerr black hole, the entanglement entropy at late times also approximates the Bekenstein-Hawking entropy of the extreme Kerr black hole. These results imply that entanglement islands can provide a semiclassical resolution of the information paradox for rotating Kerr black holes. Published by the American Physical Society 2024

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Entanglement island and Page curve for one-sided charged black hole

In this paper, we extend the method of calculating the entanglement entropy of Hawking radiation of black holes using the “in” vacuum state, which describes one-sided asymptotically flat neutral black hole formed by gravitational collapse, to dynamic charged black holes. We explore the influence of charge on the position of the boundary of island ∂I and the Page time. Due to their distinct geometric structures, we discuss non-extremal and extremal charged black holes separately. In non-extremal cases, the emergence of island saves the bound of entropy at late times, and the entanglement entropy of Hawking radiation satisfies the Page curve. Moreover, we also find that the position of the boundary of island ∂I depends on the position of the cutoff surface (observers), differing from the behavior in eternal charged black holes. In extremal black holes, when the island exists, the entanglement entropy is approximately equal to the Bekenstein-Hawking entropy, while the entanglement entropy becomes ill-defined when island is absent. Our analysis underscores how different geometric configurations significantly influence the behavior of entropy.

On the role of closed timelike curves and confinement structure around Kerr–Newman singularity

In this study, the particle motion around the naked singularity and black hole of Kerr–Newman spacetime is investigated with a special attention on the closed timelike orbits. It is found that both in the naked singularity (NS) and in black hole (BH), the singularity is concealed by causality violating regions, and the Cauchy surface consistently resides inside the inner horizon in nonextremal black holes. For neutral particles and particles with an identical charge to the source, only particles with positive angular momentum are permitted to traverse the closed timelike curves. Conversely, for particles with the opposite charge to the source, the strong Coulomb attraction draws all particles inside the Cauchy surface, allowing them to be present in the closed timelike curves irrespective of their angular momentum. However, in both the NS and BH (both extremal and nonextremal), test particles are confined at a considerable distance from the singular point such that there always exists an empty region surrounding the singularity which prevents particles from interacting with it. The radius of the empty surface that depends on the source parameters and the particle characteristics is investigated with an accurate expression.

Quasinormal modes in noncommutative Schwarzschild black holes: a spectral analysis

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous claims in the literature regarding the instability of these black holes but also reveal remarkable stability for both non-extreme and extreme Schwarzschild black holes under various perturbations.

Particle acceleration near a rotating charged black hole in 4D Einstein-Gauss-Bonnet gravity

We investigate the horizon structure and ergosphere in a charged rotating black hole within 4D Einstein-Gauss-Bonnet gravity, which introduces additional parameters (Q) because of the charge and Gauss-Bonnet parameter (β), besides the mass (M) and rotation parameter (a). Interestingly, for each value of the parameter Q (β), there is a critical GB parameter β=βE (Q=QE) that corresponds to an extremal black hole with degenerate horizons. For β<βE (Q<QE), it describes a non-extremal black hole with two horizons, and for β>βE (Q>QE), no black hole exists. The extremal value βE (QE) is also affected by the GB parameter α and the ergosphere. We also study the collision of two equal-mass particles near the horizon of this black hole and explicitly show the effect of the parameter β (Q). The innermost stable circular orbits (ISCO) and the effective potential, which governs the motion of particles in spacetime, have been analyzed for different parameter values. The centre-of-mass energy (ECM) depends on the rotation parameter a and the parameters β and Q. We investigate the ECM of two colliding particles near the horizon for both extremal and non-extremal cases. It is shown that in extremal cases, when one of the colliding particles has a critical angular momentum, the ECM can be arbitrarily high, suggesting that the charged rotating in 4D Einstein-Gauss-Bonnet gravity can function as a particle accelerator. Despite the complexity of the BH solution, an exact expression for the thermodynamic quantities of black holes, such as the mass, Hawking temperature, and entropy, is derived in terms of the horizon radius. These quantities show significant deviations from the Kerr solution because of the influence of the Gauss-Bonnet parameter and electric charge.

Gravitational radiations of Kerr black hole from warped symmetries

The warped conformal symmetries have been found in the covariant phase space of a set of non-trivial diffeomorphism near the Kerr black hole horizon. In this paper, we consider the retarded Green’s function and the absorption probability for the scalar and higher spin perturbations on a generic non-extreme Kerr black hole background, and perform their holographic calculations in terms of the warped CFT. This provide further evidence on the conjecture that the warped CFT is relevant to the microstate description of the Kerr black hole.

Logarithmic correction to BPS black hole entropy from supersymmetric index at finite temperature

It has been argued by Iliesiu, Kologlu and Turiaci in arXiv:2107.09062 that one can compute the supersymmetric index of black holes using black hole geometry carrying finite temperature but a specific complex angular velocity. We follow their prescription to compute the logarithmic correction to the entropy of BPS states in four dimensions, defined as the log of the index of supersymmetric black holes, and find perfect agreement with the previous results for the same quantity computed using the near horizon AdS2 × S2 geometry of zero temperature black holes. Besides giving an independent computation of supersymmetric black hole entropy, this analysis also provides a test of the procedure used previously for computing logarithmic corrections to Schwarzschild and other non-extremal black hole entropy.

α′ corrections to 4-dimensional non-extremal stringy black holes

We compute the first-order α′ corrections to a family of 4-dimensional, 4-charge, non-extremal black hole solutions of Heterotic Supergravity in the case with 3 independent charges. The solutions are fully analytic, reproduce the extremal limit previously found in the literature and, applying T-duality, they transform as expected. If we reduce to the case with a single independent charge we obtain the corrections to four embeddings of the Reissner-Nordström black hole in string theory. We completely characterize the black hole thermodynamics computing the Hawking temperature, Wald entropy, mass, gauge charges and their dual thermodynamic potentials. We verify that all these quantities are related by the first law of extended black hole mechanics and the Smarr formula once we include a potential associated to the dimensionful parameter α′ and the scalar charges. We found that the latter are not identified with the poles at infinity of the scalar fields because they receive α′ corrections.

Monodromy approach to pair production of charged black holes and electric fields

To find the pair production, absorption cross section and quasi-normal modes in background fields, we advance the monodromy method that makes use of the regular singular points of wave equations. We find the mean number of pairs produced in background fields whose mode equations belong to the Riemann differential equation and apply the method to the three particular cases: (i) charges near the horizon of near-extremal black holes, (ii) charges with minimal energy under the static balance in nonextremal charged black holes, and (iii) charges in the Sauter-type electric fields. We then compare the results from the monodromy with those from the exact wave functions in terms of the hypergeometric functions with three regular singular points. The explicit elaboration of monodromy and the model calculations worked out here seem to reveal evidences that the monodromy may provide a practical technique to study the spontaneous pair production in general black holes and electromagnetic fields.

Like black holes, Buchdahl stars cannot be extremalized

It was shown long back in [1] that a non-extremal black hole cannot be converted into an extremal one by test particle adiabatic accretion. The Buchdahl star is the most compact object without horizon and is defined by Φ(R)=4/9, while black hole by Φ(R)=1/2. Here Φ(R) is the gravitational potential experienced by a particle, radially falling for static and axially for the rotating object. In this short note we examine the question of extremalization of the Buchdhal star and show that the same result holds good as for the black hole. That is, a non-extremal Buchdahl star cannot be extremalized by test particle accretion. Further since extremal limit for BS is >1, it could facilitate formation of extremal black holes by neutral and spinless accretion. That is perhaps the only way they could be formed.

Rotating Bardeen black hole surrounded by perfect fluid dark matter as a particle accelerator

We study the event horizon of a rotating Bardeen black hole surrounded by perfect fluid dark matter and the black hole as a particle accelerator. The black hole is represented by four parameters: mass M, rotation parameter a, dark matter parameter α and magnetic charge g. It is interesting that when we determine the values of magnetic charge g and dark matter parameters α we can get a critical rotation parameter a E and then we get a contour plane with Δ = 0 taking three parameters as coordinates. We also derive the effective potential of the particle and the center-of-mass (CM) energy of the two particles outside the black hole by using the motion equations of the particle in the equatorial plane of the black hole. We find that the CM energy depends not only on the rotation parameter a, but also on the parameters g and α. We discuss the CM energy for two particles colliding at the black hole horizon in the extreme and non-extreme cases, respectively. It is found that the CM energy can become arbitrarily high when the angular momentum of one of the two particles is the critical angular momentum under the background of extreme black holes and there is no such result for non-extreme black holes, because the particles do not reach the black hole horizon when the angular momentum of the particles is critical angular momentum. Therefore, we prove that the rotating Bardeen black hole surrounded by perfect fluid dark matter can be used as a particle accelerator.

Pole-skipping in rotating BTZ black holes

Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin s = 1/2, 1, 2/3, extending the previous research for s = 0, 2. We derive an analytic full tower of the pole-skipping points of fermionic (s = 1/2) and vector (s = 1) fields by the exact holographic Green’s functions. For the non-extremal black hole, the leading pole-skipping frequency is ωleading = 2πiTh(s − 1 + νΩ)/(1 − Ω2) where Th is the temperature, Ω the rotation, and ν := (∆+ − ∆−)/2, the difference of conformal dimensions (∆±). These are confirmed by another independent method: the near-horizon analysis. For the extremal black hole, we find that the leading pole-skipping frequency can occur at {omega}_{textrm{leading}}^{textrm{extremal}} = −2πiTR(s + 1) only when ν = s + 1, where TR is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit (Th → 0, Ω → 1) of the non-extremal black hole result.

Statistical ensembles and logarithmic corrections to black hole entropy

In this paper, we consider general statistical ensembles and compute logarithmic corrections to the microcanonical entropy resulting due to thermodynamic fluctuations which are controlled by the boundary conditions, i.e. due to choice of ensemble. The framework is applied to the case of non-extremal black holes to give certain logarithmic corrections to the Bekenstein–Hawking entropy. We argue that within the framework of black hole chemistry, where the cosmological constant is identified with bulk pressure, the isoenthalpic-isobaric entropy rather than microcanonical entropy carries a more natural and consistent thermodynamic interpretation as black hole entropy. Logarithmic corrections to both microcanonical and isoenthalpic-isobaric entropies of black holes are computed, and we show that the latter set of corrections in black hole chemistry are of the same form as corrections to the microcanonical entropy in theories where the cosmological constant is not interpreted as a thermodynamic pressure. Finally, we compute logarithmic corrections to entropy in the framework of holographic black hole chemistry. We emphasize upon the choice of statistical ensemble, both in the bulk and on the boundary, in order to have a consistent comparison between them. The corrections studied in this paper are distinct from those obtained from Euclidean quantum gravity.

Note on the action with the Schwarzian at the stretched horizon

In this paper, we discuss the quantization of an interesting model of Carlip which appeared recently. It shows a way to associate boundary degrees of freedom to the stretched horizon of a stationary non-extremal black hole, as has been done in JT gravity for near-extremal black holes. The path integral now contains an integral over the boundary degrees of freedom, which are time reparametrizations of the stretched horizon keeping its length fixed. These boundary degrees of freedom can be viewed as elements of $Diff(S^1)/S^1$, which is the coadjoint orbit of an ordinary coadjoint vector under the action of the Virasoro group. From the symplectic form on this manifold, we obtain the measure in the boundary path integral. Doing a one-loop computation about the classical solution, we find that the one-loop answer is not finite, signalling that either the classical solution is unstable or there is an indefiniteness problem with this action, similar to the conformal mode problem in quantum gravity. Upon analytically continuing the field, the boundary partition function we get is independent of the inverse temperature and does not contribute to the thermodynamics at least at one-loop. This is in contrast to the study of near-extremal black holes in JT gravity, where the entire contribution to thermodynamics is from boundary degrees of freedom.

Vacuum transitions in two-dimensions and their holographic interpretation

We calculate amplitudes for 2D vacuum transitions by means of the Euclidean methods of Coleman-De Luccia (CDL) and Brown-Teitelboim (BT), as well as the Hamiltonian formalism of Fischler, Morgan and Polchinski (FMP). The resulting similarities and differences in between the three approaches are compared with their respective 4D realisations. For CDL, the total bounce can be expressed as the product of relative entropies, whereas, for the case of BT and FMP, the transition rate can be written as the difference of two generalised entropies. By means of holographic arguments, we show that the Euclidean methods, as well as the Lorentzian cases without non-extremal black holes, provide examples of an AdS2/CFT1 ⊂ AdS3/CFT2 correspondence. Such embedding is not possible in the presence of islands for which the setup corresponds to AdS2/CFT1 ⊄ AdS3/CFT2. We find that whenever an island is present, up-tunnelling is possible.