Counting the microstates of a Kerr black hole in M theory

We show that an extremal Kerr black hole, appropriately lifted to M theory, can be transformed to a Kaluza-Klein black hole in M theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M theory.     

Evaporation of microscopic black holes in string theory and the bound on species

We address the question how string compactifications with D‐branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza‐Klein particles, both longitudinal and transversal to the D‐branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species‐counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentially growing number of Regge states does not preclude the existence of semi‐classical black holes of sub‐stringy size. Our analysis indicates that the effective number of string resonances to which such micro black holes evaporate is not exponentially large but is bounded by N = 1/g_s², which suggests the interpretation of the well‐known relation between the Planck and string scales as the saturation of the black hole bound on the species number. In addition, we also discuss some other issues in D‐brane compactifications with a low string scale of order TeV, such as the masses of light moduli fields.     

Black holes and beyond

The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome ‘remnants’. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta in the bound state. The interior of the black hole gets completely altered to a ‘fuzzball’ structure, and information is able to escape in radiation from the hole. The semiclassical approximation can break at macroscopic scales due to the large entropy of the hole: the measure in the path integral competes with the classical action, instead of giving a subleading correction. Putting this picture of black hole microstates together with ideas about entangled states leads to a natural set of conjectures on many long-standing questions in gravity: the significance of Rindler and de Sitter entropies, the notion of black hole complementarity, and the fate of an observer falling into a black hole.     

Exotic branes in string theory

Besides the familiar D-branes, string theory contains a vast number of other non-perturbative objects. While a complete classification is lacking, many of these objects are related to each other through various dualities. Codimension two objects play a special role, because their charges are no longer additive but are instead expressed in terms of holonomies of scalar fields, which is given by an element of the relevant duality group. In this paper we present a detailed exposition of these “exotic” objects, the charges they carry, and their connection to non-geometric compactifications. Despite the name “exotic branes”, these objects are in fact ubiquitous in string theory, as they can automatically appear when describing bound states of conventional branes, and as such may be of particular importance in describing the microscopic degrees of freedom of black holes.     

Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

We investigate two physical quantities that might observationally distinguish between Kerr black holes and rotating naked singularities. These are the Lense–Thirring precession frequency as measured by a Copernican observer, and tidal forces. We establish strong enhancement for both these quantities due to a Janis–Newman–Winicour naked singularity background, as compared to the Kerr case. We first show that the precession frequency of a test gyroscope at a given radius can be enhanced by almost an order of magnitude in the background of the naked singularity, as compared to the Kerr black hole. We then show that a critical mass for celestial objects below which these disintegrate due to tidal forces might increase by more than an order of magnitude in the naked singularity background, compared to the black hole. Our results complement the existing ones in the literature regarding differences in observable quantities in such backgrounds, and might be of significance in futuristic experiments.     

Order parameter in the critical phenomena of Kerr–Newman black holes

An order parameter is introduced in describing the singular thermodynamical behaviour of Kerr–Newman black holes in the vicinity of a certain critical temperature. The mean square fluctuation of the order parameter is calculated. The analogy between the critical temperature of a black hole and the Hagedorn temperature in hadronic physics and string theory is discussed.     

Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a p-dimensional torus, for D = (10 − p) = 4,…,9. We study in particular a one-parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.     

Primordial black hole formation by stabilized embedded strings in the early universe

Primordial black hole formation by cosmic string collapses is reconsidered in the case where the winding number of the string is larger than unity. The line energy density of a multiple winding string becomes greater than that of a single winding string so that the probability of black hole formation by string collapse during loop oscillation would be strongly enhanced. Moreover, this probability could be affected by changes in gravity theory due to large extra dimensions based on the brane universe model. In addition, a wider class of strings which are stable compared to conventional cosmic strings can contribute to such a scenario. Although the production of the multiple winding defect is suppressed and its number density should be small, the enhancement of black hole formation by the increased energy density may provide a large number of evaporating black holes in the present universe which gives more stringent constraints on the string model compared to the ordinary string scenario.     

Formation of a Kerr black hole from two stringy NUT objects

In this paper we show that an isolated Kerr black hole can be interpreted as arising from a pair of identical counter-rotating NUT objects placed on a symmetry axis at the appropriate critical distance from each other.     

Light-cone distribution amplitudes of the ground state bottom baryons in HQET

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel–Killing and Killing–Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of “prime” Kerr–Sen black holes into “target” off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Gravity beyond quantum theory: Electron as a closed heterotic string

The observable gravitational and electromagnetic parameters of an electron determine that its background should be the Kerr-Newman (KN) solution of the rotating black hole without horizons. This metric has a topological defect—the Kerr singular ring which, as we show, is a closed heterotic string of the Compton radius a = ?/(2m). We show that the Dirac equation emerges as a consequence of the underlying KN gravity and string theory. Regularization of the KN solution leads to a model of gravitating soliton of the oscillon type, in which the closed heterotic string is positioned on the edge rim of a disklike vacuum bubble. It is suggested that the string-like core of the electron should be experimentally observable by the novel methods of the “Deeply Virtual (nonforward) Compton scattering”.     

The string spectrum on the horizon of a non-extremal black hole

We investigate the conformal string σ-model corresponding to a general five-dimensional non-extremal black hole solution. In the horizon region the theory reduces to an exactly solvable conformal field theory. We determine the modular invariant spectrum of physical string states, which expresses the Rindler momentum operator in terms of three charges and string oscillators. For black holes with winding and Kaluza-Klein charges, we find that states made with only right-moving excitations have ADM mass equal to the black hole ADM mass, and thus they can be used as sources of the gravitational field. A discussion on statistical entropy is included.     

Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling g _s , the situation can tentatively be interpreted as classical indication on the black hole—string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of the theory with the S-duality symmetric dilaton function as required by the heterotic string theory. The article is published in the original.     

Kerr Black Hole Entropy and its Quantization

By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.     

Kerr度规中的Bose子束缚态

本文讨论在Kerr度规中带质量和无质量Bose子的束缚态,结果指出:1)无质量Bose子不能形成Kerr黑洞束缚态,在极端黑洞情形和角量子数l很大的条件下,这与deFelic的结论相符,但我们将他的结论推广到任意l及非极端Kerr黑洞的情形。2)对于有质量Bose子,若满足束缚态条件,则可能和极端Kerr黑洞组成束缚态。本文给出了束缚态的能量模式,波函数和束缚态条件。 关键词：     

Extreme gravity tests with gravitational waves from compact binary coalescences: (II) ringdown

The LIGO/Virgo detections of binary black hole mergers marked a watershed moment in astronomy, ushering in the era of precision tests of Kerr dynamics. We review theoretical and experimental challenges that must be overcome to carry out black hole spectroscopy with present and future gravitational wave detectors. Among other topics, we discuss quasinormal mode excitation in binary mergers, astrophysical event rates, tests of black hole dynamics in modified theories of gravity, parameterized “post-Kerr” ringdown tests, exotic compact objects, and proposed data analysis methods to improve spectroscopic tests of Kerr dynamics by stacking multiple events.     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.