Dilaton gravity, charged dust, and (quasi-) black holes

TL;DR

This paper explores Einstein-Maxwell-dilaton gravity with charged dust, demonstrating that static black-hole and quasi-black-hole solutions can exist with positive energy densities, without assuming spatial symmetry, and generalizing classical systems.

Contribution

It introduces a broad class of static solutions in Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling, including black-hole and quasi-black-hole configurations, extending previous models.

Findings

Existence of static BH and QBH solutions with positive energy densities.

Solutions are possible without spatial symmetry assumptions.

Classical Majumdar-Papapetrou system is recovered when dilaton is constant.

Abstract

We consider Einstein-Maxwell-dilaton gravity with charged dust and interaction of the form $P(\chi) F_{\mu\nu} F^{\mu\nu}$, where $P(\chi)$ is an arbitrary function of the dilaton field $\chi$ that can be normal or phantom. For any regular $P(\chi)$, static configurations are possible with arbitrary functions $g_{00} = \exp(2\gamma(x^i))$ ($i=1,2,3$) and $\chi = \chi(\gamma)$, without any assumption of spatial symmetry. The classical Majumdar-Papapetrou system is restored by putting $\chi =$ const. Among possible solutions are black-hole (BH) and quasi-black-hole (QBH) ones. Some general results on BH and QBH properties are deduced and confirmed by examples. It is found, in particular, that asymptotically flat BHs and QBHs can exist with positive energy densities of matter and both scalar and electromagnetic fields.