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Cold black holes and conformal continuations

K. A. Bronnikov·M. S. Chernakova·J. C. Fabris·N. Pinto-Neto·M. E. Rodrigues
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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 $V(ϕ)$. All CBHs with $V(ϕ) \not \equiv 0$ 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.

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K. A. Bronnikov, M. S. Chernakova, J. C. Fabris, N. Pinto-Neto, M. E. Rodrigues. 2006-09-20. Cold black holes and conformal continuations. https://doi.org/10.1142/s0218271808011845

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