Structure and stability of cold scalar-tensor black holes

TL;DR

This paper analyzes the structure and stability of specific scalar-tensor black hole solutions in Brans-Dicke theory, revealing conditions for horizon regularity and demonstrating their linear stability for certain parameter ranges.

Contribution

It provides a detailed classification of spherically symmetric black hole solutions in Brans-Dicke theory and proves their linear stability for , extending to a broader class of scalar-tensor theories.

Findings

Solutions split into two classes with different horizon properties

Regularity depends on discrete parameters m and n

All solutions with  are linearly stable

Abstract

We study the structure and stability of the recently discussed spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant $\omega$. These solutions split into two classes: B1, whose horizon is reached by an infalling particle in a finite proper time, and B2, for which this proper time is infinite. Class B1 metrics are shown to be extendable beyond the horizon only for discrete values of mass and scalar charge, depending on two integers $m$ and $n$. In the case of even $m-n$ the space-time is globally regular; for odd $m$ the metric changes its signature at the horizon. All spherically symmetric solutions of the Brans-Dicke theory with $\omega<-3/2$ are shown to be linearly stable against spherically symmetric \pns. This result extends to the generic case of the Bergmann-Wagoner class of scalar-tensor theories of gravity with the coupling function $\omega(\phi) < -3/2$.