Gravitational string-membrane hedgehog and internal structure of black holes

TL;DR

This paper constructs and analyzes novel black hole solutions in Einstein-Maxwell theory involving charged string and membrane systems, revealing configurations with no internal singularities and potential explanations for black hole entropy.

Contribution

It introduces new charged string-membrane configurations that form regular black holes with flat interiors, expanding understanding of black hole internal structures in Einstein-Maxwell theory.

Findings

Black hole solutions with no internal singularities.

Membrane can form extremal Reissner-Nordstrom black holes.

Strings may account for black hole entropy due to their degrees of freedom.

Abstract

We investigate charged Nambu-Goto strings/membrane systems in the Einstein-Maxwell theory in 3+1 dimensions. We first construct a charged string hedgehog solution that has a single horizon and conical singularity. Then we examine a charged membrane system, and give a simple derivation of its self energy. We find that the membrane may form an extremal Reissner-Nordstrom black hole, but its interior is a flat spacetime. Finally by combining the charged strings and the membrane we construct black hole solutions that have no singularities inside the horizons. We study them in detail by varying the magnitude of the two parameters, namely, the charge times the membrane tension and the string tension. We also argue that the strings have, due to the large redshift inside the system, a fair amount of degrees of freedom that may explain the entropy of the corresponding black holes.