Entropy of the Schwarzschild-de Sitter Black Hole due to arbitrary spin fields in different Coordinates

TL;DR

This paper calculates the entropy of Schwarzschild-de Sitter black holes caused by quantum massless fields of arbitrary spin in different coordinate systems, showing the entropy's invariance across these coordinates using the Newman-Penrose formalism and the brick wall method.

Contribution

It demonstrates the coordinate invariance of black hole entropy for arbitrary spin fields in Schwarzschild-de Sitter spacetime using advanced formalisms and approaches.

Findings

Entropies in Painlevé and Lemaitre coordinates match Schwarzschild-like coordinate results.

Coordinate transformations do not affect the entropy for arbitrary spin fields.

The method confirms the robustness of entropy calculations across different coordinate systems.

Abstract

By using the Newman-Penrose formalism and the improved thin-layer ``brick wall'' approach, the statistical-mechanical entropies of the Schwarzschild-de Sitter black hole arising from quantum massless arbitrary spin fields are studied in the Painlev\'e and Lemaitre coordinates. Although the metrics in both the Painlev\'e and the Lemaitre coordinates do not obviously possess the singularities as that in the Schwarzschild-like coordinate, we find that, for arbitrary spin fields, the entropies in the Painlev\'e and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.