Cold black holes and conformal continuations

TL;DR

This paper investigates cold black holes in Einstein-scalar gravity with phantom fields, revealing their properties, explicit solutions, and how conformal transformations affect their horizons and singularities in scalar-tensor theories.

Contribution

It provides explicit solutions for cold black holes with nonzero potentials and analyzes their behavior under conformal transformations, introducing a new type of conformal continuation.

Findings

Cold black holes have infinite horizon area and zero temperature.

Explicit solutions include a nonzero potential case.

Conformal transformations can turn horizons into singularities.

Abstract

We study Einstein gravity minimally coupled to a scalar field in a static, spherically symmetric space-time in four dimensions. Black hole solutions are shown to exist for a phantom scalar field whose kinetic energy is negative. These ``scalar black holes'' have an infinite horizon area and zero Hawking temperature and are termed ``cold black holes'' (CBHs). The relevant explicit solutions are well-known in the massless case (the so-called anti-Fisher solution), and we have found a particular example of a CBH with a nonzero potential $V(\phi)$. All CBHs with $V(\phi) \not \equiv 0$ are shown to behave near the horizon quite similarly to those with a massless field. The above solutions can be converted by a conformal transformation to Jordan frames of a general class of scalar-tensor theories of gravity, but CBH horizons in one frame are in many cases converted to singularities in the other, which gives rise to a new type of conformal continuation.