The symmetries of Kerr black holes

The Kerr solution describes, in Einstein's theory, the gravitational field of a rotating black hole. The axial symmetry and stationarity of the solution are shown here to arise in a simple way from properties of the curvature tensor.A portion of this work was completed, in part, during the summer of 1972 at the University of Texas at Dallas, Division of Mathematics and Mathematical Physics, and at the Black Hole session of the Ecole d'été de Physique Théorique in Les Houches; supported, in part, by the National Science Foundation, Grants GP-8868, GP-3463 9X, GP-20023, and GU-1598; the Air Force Office of Scientific Research, Grant 903-67; the National Aeronautics and Space Administration, Grant 44-004-001; the Westinghouse Corparation; the Clark Foundation; and the Rhodes Trust at Oxford.     

Gravitational entropy of Kerr black holes

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol’s proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.’s estimator does not reproduce the Bekenstein–Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord–Gr \(\varnothing \) n–Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.     

Kerr black holes are not fragile

Certain AdS black holes are “fragile”, in the sense that, if they are deformed excessively, they become unstable to a fundamental non-perturbative stringy effect analogous to Schwinger pair-production [of branes]. Near-extremal topologically spherical AdS-Kerr black holes, which are natural candidates for string-theoretic models of the very rapidly rotating black holes that have actually been observed to exist, do represent a very drastic deformation of the AdS-Schwarzschild geometry. One therefore has strong reason to fear that these objects might be “fragile”, which in turn could mean that asymptotically flat rapidly rotating black holes might be fragile in string theory. Here we show that this does not happen: despite the severe deformation implied by near-extremal angular momenta, brane pair-production around topologically spherical AdS-Kerr-Newman black holes is always suppressed.     

Kerr black holes in horizon-generating form

New coordinates are given which describe nondegenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.     

A comment on the symmetries of Kerr black holes

Conditions are given for the linear dependence of the two Killing vectors, found by Hughston and Sommers to exist in a class of Einstein-Maxwell fields of Petrov typeD. The Killing tensors associated with these fields are shown to be contracted products of Killing Yano tensors.     

Quantum bound states around black holes

Quantum mechanics in the vicinity of black holes is a fascinating field of theoretical physics. It involves both general relativity and particle physics, opening new eras to establish the principles of unified theories. In this article, we show that quantum bound states with no classical equivalent – as can easily be seen at the dominant monopolar order – should be formed around black holes for massive scalar particles. We qualitatively investigate some important physical consequences, in particular for the Hawking evaporation mechanism and the associated greybody factors. PACS 04.62.+v; 04.70.Dy; 04.70-s     

Orbital resonances in discs around braneworld Kerr black holes

Rotating black holes in the brany universe of the Randall–Sundrum type with infinite additional dimension are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. We investigate the role of the tidal charge in the orbital resonance model of quasiperiodic oscillations (QPOs) in black hole systems. The orbital Keplerian frequency v _K and the radial and vertical epicyclic frequencies v _r, v _θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies involving the Keplerian and radial epicyclic frequencies. It is shown, how the tidal charge could influence matching of the observational data indicating the 3 : 2 frequency ratio observed in GRS 1915 + 105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v _K: v _θ : v _r = 3 : 2 : 1, is determined in dependence on the tidal charge. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of the spin and tidal charge are given also for existence of specific radius where v _K : v _θ : v _r = s : t : u with 5≥s >t >u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.     

Microscopic formulation of black holes in string theory

In this report we review the microscopic formulation of the five-dimensional black hole of type IIB string theory in terms of the D1–D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1–D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.     

Hawking radiation by Kerr black holes and conformal symmetry

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.     

U(N) monopoles on Kerr black holes

We describe U(N) monopoles (N>1) on Kerr black holes by the parameters of the moduli space of holomorphic vector U(N) bundles over S ² with the help of the Grothendieck splitting theorem. For N=2, 3 we estimate the corresponding monopole masses. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 1021–1026 (25 June 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Kerr black holes are not unique to general relativity

Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this Letter, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.     

On heterotic black holes and EVH/CFT correspondence

The European Physical Journal C - If produced in high energy particle collisions at the LHC, magnetic monopoles could stop in material surrounding the interaction points. Obsolete parts of the beam...     

Charged particle tunnels from the stationary and non-stationary Kerr–Newman black holes

Considering the unfixed background space-time and self-gravitational interaction, we view the Hawking radiation of a stationary Kerr–Newman black hole by Hamilton–Jacobi method. Meanwhile, extending this work to non-stationary black holes, we attempt to investigate the Hawking radiation of the non-stationary Kerr–Newman black hole. Both of the results show the tunneling probabilities are related to the change of Bekenstein- Hawking entropy and the radiation spectrums deviate from the purely thermal one, which is in accordance with the known result.