Effective spatial dimension of extremal non-dilatonic black p-branes and the description of entropy on the world volume

TL;DR

This paper investigates the critical behavior of extremal non-dilatonic black p-branes, revealing their effective spatial dimensions and providing insights into the entropy's world volume interpretation.

Contribution

It determines the effective spatial dimension of non-dilatonic black p-branes using critical exponents and scaling laws, explaining the entropy's simple interpretation.

Findings

Effective dimension of non-dilatonic black p-branes is p.

Critical exponents obey scaling laws.

Entropy has a simple world volume interpretation for non-dilatonic cases.

Abstract

By investigating the critical behavior appearing at the extremal limit of the non-dilatonic, black p-branes in (d+p) dimensions, we find that some critical exponents related to the critical point obey the scaling laws. From the scaling laws we obtain that the effective spatial dimension of the non-dilatonic black holes and black strings is one, and is p for the non-dilatonic black p-branes. For the dilatonic black holes and black p-branes, the effective dimension will depend on the parameters in theories. Thus, we give an interpretation why the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the non-dilatonic black p-branes.