A new look at black holes via thermal dimensions and the complex coordinates/ temperature vectors correspondence

Abstract:

The action of active diffeomorphisms (diffs) r → ρ(r) on the Schwarzschild metric leads to metrics which are also static spherically symmetric solutions of the Einstein vacuum field equations. It is shown how in a limiting case it allows to introduce a deformation of the manifold such that ρ(r = 0) = 0, and ρ(r = 0+) = 2GM corresponding, respectively, to the spacelike singularity and horizon of the Schwarzschild metric. In doing so, one ends up with a spherical void surrounding the singularity at r = 0. In order to explore the "interior"region of this void, we introduce complex radial coordinates whose imaginary components have a direct link to the inverse Hawking temperature, and which furnish a path that provides access to interior region. In addition, we show that the black hole entropy A 4 (in Planck units) is equal to the area of a rectangular strip in the complex radial-coordinate plane associated to this path. The gist of the physical interpretation behind this construction is that there is an emergence of thermal dimensions which unfolds as one plunges into the interior void region via the use of complex coordinates, and whose imaginary components capture the span of the thermal dimensions. Namely, the filling of the void leads to an emergent internal/ thermal dimension via the imaginary part βr of the complex radial variable r = r + iβr.

Año de publicación:

2022

Keywords:

• General relativity
• black holes
• strings

Fuente:

scopus