Three-dimensional BTZ Black Hole Research Articles

Quasi-normal modes of AdSblack holes: a superpotential approach

A novel method, based on superpotentials is proposed for obtaining thequasi-normal modes of anti-de Sitter black holes. This is inspired by thecase of the three-dimensional BTZ black hole, where the quasi-normalmodes can be obtained exactly and are proportional to the surface gravity.Using this approach, the quasi-normal modes of the five-dimensionalSchwarzschild anti-de Sitter black hole are computed numerically. Themodes again seem to be proportional to the surface gravity for very smalland very large black holes. They reflect the well known instability ofsmall black holes in anti-de Sitter space.

BTZ black holes from the five-dimensional general relativity with a negative cosmological constant

We show that the five-dimensional general relativity with a negative cosmological constant allows the solutions of the form M 3×M g where M 3 is the three-dimensional BTZ black hole and M g is a higher genus ( g>1) Riemann surface with a fixed size. It is shown that this type of spontaneous compactification on a Riemann surface is possible only for the genus larger than one. From type IIB string theory point of view, certain near horizon geometry of D three-branes wrapped on the compact Riemann surface ( g>1) is the BTZ (or AdS 3) space-time tensored with the Riemann surface and a constant size five-sphere. The relevance of our analysis to the positive energy conjecture of Horowitz and Myers is discussed.

String theory formulation of anti-de Sitter black holes

It is shown that the five-dimensional anti-de Sitter black hole is a supersymmetric solution of the low-energy field equations of type IIB string theory compactified on an Einstein space. A statistical interpretation of the mass dependence of the entropy can be obtained from considerations of the three-dimensional BTZ black hole.

Entropy of three-dimensional black holes in string theory

It is observed that the three-dimensional BTZ black hole is a supersymmetric solution of the low-energy field equations of heterotic string theory compactified on an Einstein space. The solution involves a non-zero dilaton and NS-NS H-field. The entropy of the extreme black hole can then be computed using string theory and the asymptotic properties of anti-de Sitter space, without recourse to a D-brane analysis. This provides an explicit example of a black hole whose entropy can be computed using fundamental string theory, as advocated by Susskind.

Three-dimensional BTZ black hole as a cylindrical system in four-dimensional general relativity.

It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.