A note on the quantization of a multi-horizon black hole

We consider the quasinormal spectrum of a charged scalar field in the (charged) Reissner-Nordstrom spacetime, which has two horizons. The spectrum is characterized by two distinct families of asymptotic resonances. We suggest and demonstrate the according to Bohr's correspondence principle and in agreement with the Bekenstein-Mukhanov quantization scheme, one of these resonances corresponds to a fundamental change of Delta A=4hbar ln2 in the surface area of the black-hole outer horizon. The second asymptotic resonance is associated with a fundamental change of Delta Atot=4hbar ln3 in the total area of the black hole (in the sum of the surface areas of the inner and outer horizons), in accordance with a suggestion of Makela and Repo.Comment: 6 page

Asymptotic tails of massive scalar fields in a stationary axisymmetric EMDA black hole geometry

The late-time tail behavior of massive scalar fields is studied analytically in a stationary axisymmetric EMDA black hole geometry. It is shown that the asymptotic behavior of massive perturbations is dominated by the oscillatory inverse power-law decaying tail $t^{-(l+3/2)}\sin(\mu t)$ at the intermediate late times, and by the asymptotic tail $t^{-5/6}\sin(\mu t)$ at asymptotically late times. Our result seems to suggest that the intermediate tails $t^{-(l+3/2)}\sin(\mu t)$ and the asymptotically tails $t^{-5/6} \sin(\mu t)$ may be quite general features for evolution of massive scalar fields in any four dimensional asymptotically flat rotating black hole backgrounds.Comment: 6 page

Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations

We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page

Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole

We investigate the late-time tails of self-interacting (massive) scalar fields in the spacetime of dilaton black hole. Following the no hair theorem we examine the mechanism by which self-interacting scalar hair decay. We revealed that the intermediate asymptotic behavior of the considered field perturbations is dominated by an oscillatory inverse power-law decaying tail. The numerical simulations showed that at the very late-time massive self-interacting scalar hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.

Evidence for a null entropy of extremal black holes

We present some arguments in support of a {\it zero} entropy for {\it extremal} black holes. These rely on a combination of both quantum, thermodynamic, and statistical physics arguments. This result may shed some light on the nature of these extreme objects. In addition, we show that within a {\it quantum} framework the capture of a particle by an initially extremal black hole always results with a final nonextremal black hole.Comment: 11 page

Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes

The assimilation of a quantum (finite size) particle by a Reissner-Nordstr\"om black hole inevitably involves an increase in the black-hole surface area. It is shown that this increase can be minimized if one considers the capture of the lightest charged particle in nature. The unavoidable area increase is attributed to two physical reasons: the Heisenberg quantum uncertainty principle and a Schwinger-type charge emission (vacuum polarization). The fundamental lower bound on the area increase is $4 \hbar$, which is smaller than the value given by Bekenstein for neutral particles. Thus, this process is a better approximation to a reversible process in black-hole physics. The universality of the minimal area increase is a further evidence in favor of a uniformly spaced area spectrum for spherical quantum black holes. Moreover, this universal value is in excellent agreement with the area spacing predicted by Mukhanov and Bekenstein and independently by Hod.Comment: 10 page

Quasinormal Spectrum and Quantization of Charged Black Holes

Black-hole quasinormal modes have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We study {\it analytically} the asymptotic quasinormal spectrum of a {\it charged} scalar field in the (charged) Reissner-Nordstr\"om spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature $T_{BH}$, and its electric potential $\Phi$. We discuss the applicability of the results in the context of black-hole quantization. In particular, we show that according to Bohr's correspondence principle, the asymptotic resonance corresponds to a fundamental area unit $\Delta A=4\hbar\ln2$.Comment: 4 page

High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.Comment: 12 pages, 2 figure

Black-hole radiation, the fundamental area unit, and the spectrum of particle species

Bekenstein and Mukhanov have put forward the idea that, in a quantum theory of gravity a black hole should have a discrete mass spectrum with a concomitant {\it discrete} line emission. We note that a direct consequence of this intriguing prediction is that, compared with blackbody radiation, black-hole radiance is {\it less} entropic. We calculate the ratio of entropy emission rate from a quantum black hole to the rate of black-hole entropy decrease, a quantity which, according to the generalized second law (GSL) of thermodynamics, should be larger than unity. Implications of our results for the GSL, for the value of the fundamental area unit in quantum gravity, and for the spectrum of massless particles in nature are discussed.Comment: 4 page

Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem

We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an oscillatory term caused by the dragging of reference frames). The damping exponents characterizing the asymptotic solutions at timelike infinity and along the black-hole outer horizon are independent of the spin parameter of the fields. However, the damping exponents at future null infinity are spin dependent. The late-time tails at all the three asymptotic regions are spatially dependent on the spin parameter of the field. The rotational dragging of reference frames, caused by the rotation of the black-hole (or star) leads to an active coupling of different multipoles.Comment: 16 page