Global Embeddings of Two-dimensional Dilatonic Black Holes

TL;DR

This paper constructs global flat embeddings of two-dimensional dilatonic black holes, calculates their Hawking temperatures, but finds minimal embeddings cannot reproduce their entropies, highlighting limitations in lower-dimensional models.

Contribution

It provides explicit global flat embeddings for (2+1) and (2+2) dimensional dilatonic black holes and analyzes their thermodynamic properties.

Findings

Successfully derived global embeddings for the black holes.

Calculated Hawking temperatures and black hole entropies.

Minimal embeddings do not reproduce proper entropies.

Abstract

We obtain minimal (2+1) and (2+2) dimensional global flat embeddings of uncharged and charged dilatonic black holes in (1+1) dimensions, respectively. Moreover, we obtain the Hawking temperatures and the black hole ones of these dilatonic black holes. However, even though the minimal flat embedding structures are mathematically meaningful, through this minimal embeddings the proper entropies are shown to be unattainable, contrast to the cases of other black holes in (2+1) or much higher dimensions.