Estimating Hawking radiation for exotic black holes

Abstract

We study about an approximation method of the Hawking radiation. We analyze an massless scalar field in exotic black hole backgrounds models which have peculiar properties in black hole thermodynamics (monopole black hole in SO(3) Einstein-Yang-Mills-Higgs system and dilatoic black hole in Einstein-Maxwell-dilaton system). A scalar field is assumed not to be couple to matter fields consisting of a black hole background. Except for extreme black holes, we can well approximate the Hawking radiaition by 'black body' one with Hawking temperature estimated at a radius of a critical impact parameter. [4][5][6][7][8][9][10], it has been less investigated because many of them are only obtained numerically that it takes much works compared with ones of analytically obtained. But we need to investigate for many reasons. Particularly, a monopole black hole which was found in SO(3) Einstein-Yang-Mill-Higgs (EYMH) system [11][12][13][14] is important because it is one of the counterexample of the black hole no hair conjecture [15]. Moreover, if we consider the evaporation process of the Reissner-Nortström (RN) black hole, it may become a monopole black hole and the final product (a regular gravitating monopole) could be a good candidate for the remnant of the Hawking radiation in such a system.From such view points, we study an approximation method of the Hawking radiation which may reduce our labor and discuss its validity in this paper. Throughout this paper we use units c =h = 1. Notations and definitions as such as Christoffel symbols and curvature follow Misner-Thorne-Wheeler [16].We consider two models in which black hole solutions have peculiar properties in black hole thermodynamics.(I) The SO(3) EYMH model as * electronic mail:tamaki@gravity.phys.waseda.ac.jp † electronic mail:maeda@gravity.phys.waseda.ac.jpwhere κ 2 ≡ 8πG with G being Newton's gravitational constant. L m is the Lagrangian density of the matter fields which are written asF a µν is the field strength of the SU(2) YM field and expressed by its potential A a µ aswith a gauge coupling constant e. Φ a is a real triplet Higgs field and D µ is the covariant derivative:The parameters v and λ are the vacuum expectation value and a self-coupling constant of the Higgs field, respectively.(II) The Einstein-Maxwell-dilaton (EMD) model aswhere φ and F are a dilaton field and U(1) gauge field, respectively. For black hole solutions, we assume that a space-time is static and spherically symmetric, in which case the metric is written aswhere f (r) = 1 − 2Gm(r)/r. We consider spacetime, which have a regular horizon and is asymptotically flat. In such a background spacetime, we consider a neutral and massless scalar field which does not couple to the matter fields such as the YM field or the Higgs field. The eq. of motion is described by the Klein-Gordon equation as Φ ;µ ,µ = 0.This equation is separable, and we should only solve the radial equation 1

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

“…Other studies connected with magnetic monopoles in the Einstein−Yang-Mills−Higgs theory can be mentioned: (i) The thermodynamical properties of these monopole black holes were further studied by Maeda et al [25,26,27] in the low Higgs mass case, and by Lue and Weinberg [22] for high Higgs mass; (ii) Ridgeway and Weinberg found the existence of non-spherically symmetric magnetic monopole configurations [28]; (iii) Dyonic solutions were found by Brihaye et al [29,30]; (iv) Monopole solutions in other theories were found, like in a Brans-Dicke theory [31], and in SU(3), SU (5), and SU(N) gauge theories [32,33,34]. Now, in a different context, the study of the Einstein-Maxwell system goes back to the origins of general relativity where Reissner in 1916 and Nordström in 1918 found the Reissner-Nordström solution (see [35] for the appropriate references), and Weyl studied axisymmetric gravito-electric vacuum systems in four dimensions [36].…”

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Feasibility analysis for attosecond X-ray pulses at FERMI@ELETTRA free electron laser

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Black Holes with Hair

“…At this point, nonzero vector meson fields begin to appear outside the horizon, producing a black hole with hair whose Hawking temperature, like that of a Schwarzschild black hole, never vanishes. Radiation continues unimpeded until the horizon has contracted to a point, leaving behind a nonsingular monopole [15].…”