Cold Scalar-Tensor Black Holes: Causal Structure, Geodesics, Stability

TL;DR

This paper investigates the structure, geodesics, and stability of specific scalar-tensor black hole solutions in Brans-Dicke theory, revealing conditions for regularity, causality issues, and demonstrating their linear stability.

Contribution

It provides a detailed analysis of spherically symmetric Brans-Dicke black holes with infinite horizon area, classifies solutions based on horizon crossing properties, and proves their linear stability for a broad class of scalar-tensor theories.

Findings

Solutions split into two classes with different horizon properties.

Certain solutions are globally regular for specific parameter values.

All static, spherically symmetric solutions with ^-3/2 are linearly stable.

Abstract

We study the structure and stability of 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, depending on finite (B1) or infinite (B2) proper time needed for an infalling particle to reach the horizon. Class B1 metrics can be extended through the horizon only for discrete values of mass and scalar charge, depending on two integers m and n. For even m-n, the space-time is globally regular; for odd m, the metric changes its signature on the horizon but remains Lorentzian. Geodesics are smoothly continued across the horizon, but for odd m timelike geodesics become spacelike and vice versa. Causality problems, arising in some cases, are discussed. Tidal forces are shown to grow infinitely near type B1 horizons. All vacuum static, spherically symmetric solutions of the Brans-Dicke theory with $\omega<-3/2$ are found to be linearly stable against spherical perturbations. This result extends to the generic case of the Bergmann-Wagoner class of scalar-tensor theories with the coupling function $\omega(\phi) < -3/2$.