Black Hole Entropy and Dilatations

TL;DR

This paper explores how dilatations affect black hole entropy calculations, examining different interpretations and normalization choices for Kerr black holes, including those with cosmic strings.

Contribution

It introduces a novel perspective on dilatations as conformal mappings and analyzes their impact on black hole entropy normalization methods.

Findings

Dilatations can be viewed as conformal transformations affecting entropy.

Different normalization choices lead to varying entropy values.

The study includes Kerr black holes with cosmic strings and their unique properties.

Abstract

Dilatations by means of a constant factor can be seen in a double way: as a simple change of units length or as a conformal mapping of the starting spacetime into a ``stretched'' one with the same units length. The numerical value of the black hole entropy depends on the interpretations made for the stretched manifold. Further, we study the possibility to choose an unusual ``mass dependent'' normalization for the timelike Killing vector for a Kerr black hole with and without a cosmic string.