Spectrum of Charged Black Holes - The Big Fix Mechanism Revisited

Following an earlier suggestion of the authors(gr-qc/9607030), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete two-parameter area spectrum of generic charged spherically symmetric black holes in any dimension. For the Reissner-Nordstrom black hole we get $A/4G\hbar=\pi(2n+p+1)$, where the integer p=0,1,2,.. gives the charge spectrum, with $Q=\pm\sqrt{\hbar p}$. The quantity $\pi(2n+1)$, n=0,1,... gives a measure of the excess of the mass/energy over the critical minimum (i.e. extremal) value allowed for a given fixed charge Q. The classical critical bound cannot be saturated due to vacuum fluctuations of the horizon, so that generically extremal black holes do not appear in the physical spectrum. Consistency also requires the black hole charge to be an integer multiple of any fundamental elementary particle charge: $Q= \pm me$, m=0,1,2,.... As a by-product this yields a relation between the fine structure constant and integer parameters of the black hole -- a kind of the Coleman big fix mechanism induced by black holes. In four dimensions, this relationship is $e^2/\hbar=p/m^2$ and requires the fine structure constant to be a rational number. Finally, we prove that the horizon area is an adiabatic invariant, as has been conjectured previously.Comment: 21 pages, Latex. 1 Section, 1 Figure added. To appear in Class. and Quant. Gravit

Bouncing Braneworlds Go Crunch!

Recently, interesting braneworld cosmologies in the Randall-Sundrum scenario have been constructed using a bulk spacetime which corresponds to a charged AdS black hole. In particular, these solutions appear to `bounce', making a smooth transition from a contracting to an expanding phase. By considering the spacetime geometry more carefully, we demonstrate that generically in these solutions the brane will encounter a singularity in the transition region.Comment: 17 pages, 4 figures, ref adde

Hamilton-Jacobi Tunneling Method for Dynamical Horizons in Different Coordinate Gauges

Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions on the sign of the energy.Comment: Standard Latex document, typos corrected, refined discussion of tunneling picture, subsection 5.1 remove