The Cardy-Verlinde Formula and Asymptotically Flat Charged Black Holes

We show that the modified Cardy-Verlinde formula without the Casimir effect term is satisfied by asymptotically flat charged black holes in arbitrary dimensions. Thermodynamic quantities of the charged black holes are shown to satisfy the energy-temperature relation of a two-dimensional CFT, which supports the claim in our previous work (Phys. Rev. D61, 044013, hep-th/9910244) that thermodynamics of charged black holes in higher dimensions can be effectively described by two-dimensional theories. We also check the Cardy formula for the two-dimensional black hole compactified from a dilatonic charged black hole in higher dimensions.Comment: 6 pages, LaTeX, references adde

Quantum Description for the Decay of NSNS Brane-Antibrane Systems

The stringy description for the instabilities in the $RR$ charged $D_{p}-\bar{D}_{p}$ pairs is now well understood in terms of the open string tachyon condensation. The quantum interpretation presumably via the stringy description for the instabilities in the $NSNS$-charged $F1-\bar{F1}$ and $NS5-\bar{NS5}$ pairs in IIA/IIB theories, however, has not been established yet. This would be partly because of the absence (for the $F1-\bar{F1}$ case) or our relatively poor understanding (for the $NS5-\bar{NS5}$ case) of their worldvolume (gauge theory) dynamics. In the present work, using the well-known quantum description for instabilities in the $RR$-charged $D_{p}-\bar{D}_{p}$ systems and in the M-theory brane-antibrane systems and invoking appropriate string dualities, the stringy nature of the instabilities in the $NSNS$-charged $F1-\bar{F1}$ and $NS5-\bar{NS5}$ systems has been uncovered. For the annihilations to string vacua, the quantum, stringy interpretations are simple extensions of Sen's conjecture for those in $RR$-charged brane-antibrane systems.Comment: 22 pages, 4 eps figures, Latex, comments and references adde

w_{\infty} Algebras, Conformal Mechanics, and Black Holes

We discuss BPS solitons in gauged ${\cal N}=2$, D=4 supergravity. The solitons represent extremal black holes interpolating between different vacua of anti-de Sitter spaces. The isometry superalgebras are determined and the motion of a superparticle in the extremal black hole background is studied and confronted with superconformal mechanics. We show that the Virasoro symmetry of conformal mechanics, which describes the dynamics of the superparticle near the horizon of the extremal black hole under consideration, extends to a symmetry under the $w_{\infty}$ algebra of area-preserving diffeomorphisms. We find that a Virasoro subalgebra of $w_{\infty}$ can be associated to the Virasoro algebra of the asymptotic symmetries of $AdS_2$. In this way spacetime diffeomorphisms of $AdS_2$ translate into diffeomorphisms in phase space: our system offers an explicit realization of the $AdS_2/CFT_1$ correspondence. Using the dimensionally reduced action, the central charge is computed. Finally, we also present generalizations of superconformal mechanics which are invariant under ${\cal N} =1$ and ${\cal N} =2$ superextensions of $w_{\infty}$.Comment: Latex, 23 pages, minor errors corrected, references added; final version to appear in Class. Quant. Gra

Toda p-brane black holes and polynomials related to Lie algebras

Black hole generalized p-brane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold that contains a product of n - 1 Ricci-flat internal spaces. They are defined up to a set of functions H_s obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions H_s for intersections related to semisimple Lie algebras is suggested. This conjecture is proved for Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with the components of twice the dual Weyl vector in the basis of simple coroots. The coefficients of polynomials depend upon the extremality parameter \mu >0. In the extremal case \mu = 0 such polynomials were considered previously by H. L\"u, J. Maharana, S. Mukherji and C.N. Pope. Explicit formulas for A_2-solution are obtained. Two examples of A_2-dyon solutions, i.e. dyon in D = 11 supergravity with M2 and M5 branes intersecting at a point and Kaluza-Klein dyon, are considered.Comment: 24 pages, Latex, typos are eliminated, a correct relation on parameters of special block-orthogonal solution is added in third line after eq. (4.10

The Bekenstein Formula and String Theory (N-brane Theory)

A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the D- and M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation, and information loss; D-branes as probes of black holes; and the Matrix theory approach to charged and neutral black holes. Some introductory material is included.Comment: 53 pages, LaTeX. v3: Typos fixed, minor updates, references added, brief Note Added on AdS/CF

Gauge-Dependent Cosmological "Constant"

When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically-acceptable value at late epochs. We outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class. Quantum Gra

A Bestiary of Higher Dimensional Taub-NUT-AdS Spacetimes

We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have non-trivial topology. We discuss the global structure of these solutions, and their relevance within the context of M-theory.Comment: 11 pages, LaTex(v4: Comments and references added