Cold black holes in scalar-tensor theories

TL;DR

This paper investigates the existence and properties of black holes in scalar-tensor theories of gravity, revealing unique features such as zero temperature and infinite horizon area in certain anomalous cases, with detailed analysis of Brans-Dicke theory.

Contribution

It demonstrates the existence of black holes with unusual characteristics in scalar-tensor theories, especially in anomalous cases with negative kinetic terms, and analyzes their thermodynamic and geometric properties.

Findings

Black holes with zero Hawking temperature in scalar-tensor theories.

Infinite horizon area occurs in certain anomalous theories.

In Brans-Dicke theory, two types of infinite-area black holes are identified.

Abstract

We study the possible existence of black holes in scalar-tensor theories of gravity in four dimensions. Their existence is verified for anomalous versions of these theories, with a negative kinetic term in the Lagrangian. The Hawking temperature T_H of these holes is zero, while the horizon area is (in most cases) infinite. It is shown that an infinite value of T_H can occur only at a curvature singularity rather than a horizon. 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.