On the Completeness of the Black Hole Singularity in 2d Dilaton Theories

TL;DR

This paper investigates the completeness of black hole singularities in 2d dilaton theories, revealing that null geodesics can be complete in certain models, challenging previous assumptions about singularity structure.

Contribution

It demonstrates that a broad class of 2d dilaton theories can have globally complete null geodesics, extending understanding of black hole singularity properties beyond the standard models.

Findings

Null extremals can be complete in some 2d dilaton theories.

Certain generalized dilaton models exhibit Schwarzschild-like global structure.

Most models analyzed show no null geodesic incompleteness.

Abstract

The black hole of the widely used ordinary 2d--dilaton model (DBH) deviates from the Schwarzschild black hole (SBH) of General Relativity in one important feature: Whereas non-null extremals or geodesics show the expected incompleteness this turns out {\it not to be the case for the null extremals}. After a simple analysis in Kruskal coordinates for singularities with power behavior of this -- apparently till now overlooked -- property we discuss the global structure of a large family of generalized dilaton theories which does not only contain the DBH and SBH but also other proposed dilaton theories as special cases. For large ranges of the parameters such theories are found to be free from this defect and exhibit global SBH behavior.