On (2 + 2)-dimensional space-times, strings and black holes

Abstract:

We study black hole-like solutions (space-times with singularities) of Einstein field equations in 3 + 1 and 2 + 2 dimensions. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid ℋ2 and which is quite different from the static spherically symmetric (3 + 1)-dimensional solution. Static circular symmetric solutions for metrics in 2 + 2 are found that are singular at ρ = 0 and whose asymptotic ρ → ∞ limit leads to a. flat (1 + 2)-dimensional boundary of topology S1 × R2. Finally we discuss the (1 + 1)-dimensional Bars-Witten stringy black hole solution and show how it can be embedded into our (3 + 1)-dimensional solutions. Black holes in a (2 + 2)-dimensional "space-time" from the perspective of complex gravity in 1 + 1 complex dimensions and their quaternionic and octonionic gravity extensions deserve furher investigation. An appendix is included with the most general Schwarzschild-like solutions in D ≥ 4. © World Scientific Publishing Company.

Año de publicación:

2007

Keywords:

• black holes
• 2+2 dimensions
• strings
• General relativity

Fuente:

scopus