Electrically Charged Cold Black Holes in Scalar-Tensor Theories

TL;DR

This paper explores the existence and properties of charged and neutral black holes in scalar-tensor theories of gravity, revealing infinite-area solutions with unique causal structures and analyzing their stability and thermodynamics.

Contribution

It demonstrates the existence of anomalous scalar-tensor black holes with infinite horizon area and zero temperature, and characterizes their causal and stability properties.

Findings

Existence of black holes with infinite horizon area in scalar-tensor theories.

Identification of solutions with finite and infinite proper time to reach the horizon.

Analysis of stability and causal structure of these black holes.

Abstract

We study the possible existence of charged and neutral black holes in the Bergmann-Wagoner class of scalar-tensor theories (STT) of gravity in four dimensions. The existence of black holes is shown for anomalous versions of these theories, with a negative kinetic term in the Lagrangian. The Hawking temperature of these holes is zero, while the horizon area is (in most cases) infinite. As a special case, the Brans-Dicke theory is studied in more detail, and two kinds of infinite-area black holes are revealed, with finite and infinite proper time needed for an infalling particle to reach the horizon; among them, analyticity properties select a discrete subfamily of solutions, parametrized by two integers, which admit an extension beyond the horizon. The causal structure and stability of these solutions with respect to small radial perturbations is discussed. As a by-product, the stability properties of all spherically symmetric electrovacuum STT solutions are outlined.