Charge Loss (or the Lack Thereof) for AdS Black Holes

The evolution of evaporating charged black holes is complicated to model in general, but is nevertheless important since the hints to the Information Loss Paradox and its recent firewall incarnation may lie in understanding more generic geometries than that of Schwarzschild spacetime. Fortunately, for sufficiently large asymptotically flat Reissner-Nordstrom black holes, the evaporation process can be modeled via a system of coupled linear ordinary differential equations, with charge loss rate governed by Schwinger pair-production process. The same model can be generalized to study the evaporation of AdS Reissner-Nordstrom black holes with flat horizon. It was recently found that such black holes always evolve towards extremality since charge loss is inefficient. This property is completely opposite to the asymptotically flat case in which the black hole eventually loses its charges and tends towards Schwarzschild limit. We clarify the underlying reason for this different behavior.Comment: References updated. Published in JHE

The Fate of Monsters in Anti-de Sitter Spacetime

Black hole entropy remains a deep puzzle: where does such enormous amount of entropy come from? Curiously, there exist gravitational configurations that possess even larger entropy than a black hole of the same mass, in fact, arbitrarily high entropy. These are the so-called monsters, which are problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence paradigm since there is far insufficient degrees of freedom on the field theory side to account for the enormous entropy of monsters in AdS bulk. The physics of the bulk however may be considerably modified at semi-classical level due to the presence of branes. We show that this is especially so since monster spacetimes are unstable due to brane nucleation. As a consequence, it is not clear what the final fate of monsters is. We argue that in some cases there is no real threat from monsters since although they are solutions to Einstein's Field Equations, they are very likely to be completely unstable when embedded in string theory, and thus probably are not solutions to the full quantum theory of gravity. Our analysis, while suggestive and supportive of the claim that such pathological objects are not allowed in the final theory, by itself does not rule out all monsters. We comment on various kin of monsters such as the bag-of-gold spacetime, and also discuss briefly the implications of our work to some puzzles related to black hole entropy.Comment: Version accepted by JHE

Fourth Order Gradient Symplectic Integrator Methods for Solving the Time-Dependent Schr\"odinger Equation

We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require knowing the potential and the gradient of the potential. One 4th order algorithm only requires four Fast Fourier Transformations per iteration. In a one dimensional scattering problem, the 4th order error coefficients of these new algorithms are roughly 500 times smaller than fourth order algorithms with negative coefficient, such as those based on the traditional Ruth-Forest symplectic integrator. These algorithms can produce converged results of conventional second or fourth order algorithms using time steps 5 to 10 times as large. Iterating these positive coefficient algorithms to 6th order also produced better converged algorithms than iterating the Ruth-Forest algorithm to 6th order or using Yoshida's 6th order algorithm A directly.Comment: 11 pages, 2 figures, submitted to J. Chem. Phy

Cold Black Holes in the Harlow-Hayden Approach to Firewalls

Firewalls are controversial principally because they seem to imply departures from general relativistic expectations in regions of spacetime where the curvature need not be particularly large. One of the virtues of the Harlow-Hayden approach to the firewall paradox, concerning the time available for decoding of Hawking radiation emanating from charged AdS black holes, is precisely that it operates in the context of cold black holes, which are not strongly curved outside the event horizon. Here we clarify this point. The approach is based on ideas borrowed from applications of the AdS/CFT correspondence to the quark-gluon plasma. Firewalls aside, our work presents a detailed analysis of the thermodynamics and evolution of evaporating charged AdS black holes with flat event horizons. We show that, in one way or another, these black holes are always eventually destroyed in a time which, while long by normal standards, is short relative to the decoding time of Hawking radiation.Comment: 32 pages, 10 figures, fixed some typos and slow loading of Fig.3; version accepted by Nucl. Phys.