2002/06/06 by O. B. Zaslavskii, O B Zaslavskii · 2 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/19/14/317
published as Class.Quant.Grav. 19 (2002) 3783-3798 · 24 pages. Accepted for publication in Class. Quant. Grav
arxiv created 2002/06/06 · openalex publication_date 2002/07/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
In some kinds of classical dilaton theory there exist black holes with (i) infinite horizon area A or infinite F (the coefficient at curvature in the Lagrangian) and (ii) zero Hawking temperature T H . For a generic static black hole, without an assumption about spherical symmetry, we show that infinite A is compatible with a regularity of geometry in the case T H = 0 only. We also point out that infinite T H is incompatible with the regularity of a horizon of a generic static black hole, both for finite or infinite A . A direct application of the standard Euclidean approach in the case of an infinite 'effective' area of the horizon A eff = AF leads to inconsistencies in the variational principle and gives an indefinite expression for black-hole entropy S , formally proportional to T H A eff . We show that treating a horizon as an additional boundary (that is, adding to the action some terms calculated on the horizon) may restore self-consistency of the variational procedure, if F does not grow too rapidly near the horizon. We apply this approach to Brans–Dicke black holes and obtain the same answer S = 0 as for 'usual' (e.g., Reissner–Nordström) extreme classical black holes. We also consider the exact solution for a conformal coupling, when A is finite but F diverges and find that in the latter case both the standard and modified approaches give rise to an infinite action. Thus, this solution represents a rare exception of a black hole without non-trivial thermal properties.