Semiclassical Corrections to the Cardy-Verlinde Formula of Kerr Black Holes

In this letter, we compute the corrections to the Cardy-Verlinde formula of $4-$dimensional Kerr black hole. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitational effect. Then we show, one can taking into account the semiclassical corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator $L_0$ and the central charge $c$.Comment: 8 page

A Possible Resolution of the Black Hole Information Puzzle

The problem of information loss is considered under the assumption that the process of black hole evaporation terminates in the decay of the black hole interior into a baby universe. We show that such theories can be decomposed into superselection sectors labeled by eigenvalues of the third-quantized baby universe field operator, and that scattering is unitary within each superselection sector. This result relies crucially on the quantum-mechanical variability of the decay time. It is further argued that the decay rate in the black hole rest frame is necessarily proportional to $e^{-S_{tot}}$, where $S_{tot}$ is the total entropy produced during the evaporation process, entailing a very long-lived remnant.Comment: 15 pages, 3 uuencoded figures. Revised version contains some notational simplification

Space Noncommutativity Corrections to the Cardy-Verlinde Formula

In this letter we compute the corrections to the Cardy-Verlinde formula of Schwarzschild black holes. These corrections stem from the space noncommutativity. Because the Schwarzschild black holes are non rotating, to the first order of perturbative calculations, there is no any effect on the properties of black hole due to the noncommutativity of space.Comment: 7 pages, no figures, accepted for publication in Int. J. Mod. Phys.

Dimensional Mutation and Spacelike Singularities

I argue that string theory compactified on a Riemann surface crosses over at small volume to a higher dimensional background of supercritical string theory. Several concrete measures of the count of degrees of freedom of the theory yield the consistent result that at finite volume, the effective dimensionality is increased by an amount of order $2h/V$ for a surface of genus $h$ and volume $V$ in string units. This arises in part from an exponentially growing density of states of winding modes supported by the fundamental group, and passes an interesting test of modular invariance. Further evidence for a plethora of examples with the spacelike singularity replaced by a higher dimensional phase arises from the fact that the sigma model on a Riemann surface can be naturally completed by many gauged linear sigma models, whose RG flows approximate time evolution in the full string backgrounds arising from this in the limit of large dimensionality. In recent examples of spacelike singularity resolution by tachyon condensation, the singularity is ultimately replaced by a phase with all modes becoming heavy and decoupling. In the present case, the opposite behavior ensues: more light degrees of freedom arise in the small radius regime. I comment on the emerging zoology of cosmological singularities that results.Comment: 15 pages, harvmac big. v2: 18 pages, harvmac big; added computation of density of states and modular invariance check, enhanced discussion of multiplicity of solutions all sharing the feature of increased density of states, added reference

How many black holes fit on the head of a pin?

The Bekenstein-Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole ``molecules'' of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations.Comment: 4 pages, fourth prize in the Gravity Research Foundation Essay competition 200

On the timelike Liouville three-point function

In a recent paper, D. Harlow, J. Maltz, and E. Witten showed that a particular proposal for the timelike Liouville three-point function, originally due to Al. Zamolodchikov and to I. Kostov and V. Petkova, can actually be computed by the original Liouville path integral evaluated on a new integration cycle. Here, we discuss a Coulomb gas computation of the timelike three-point function and show that an analytic extension of the Selberg type integral formulas involved reproduces the same expression, including the adequate normalization. A notable difference with the spacelike calculation is pointed out.Comment: 11 pages. v2 comments and references added. Appropriate credit is given to Ref. arXiv:hep-th/0512346, where the Coulomb gas computation of the c<1 theory has already been discusse