We compute exactly the semi-classical radiation spectrum for a class of non-asymptotically flat charged dilaton black holes, the so-called linear dilaton black holes. In the high frequency regime, the temperature for these black holes generically agrees with the surface gravity result. In the special case where the black hole is massless, we show that, although the surface gravity remains finite, there is no radiation, in agreement with the fact that massless objects cannot radiate.Comment: 9 page

We obtain a class of regular black hole solutions in four-dimensional f (R) gravity, R being the curvature scalar, coupled to a nonlinear electromagnetic source. The metric formalism is used and static spherically symmetric spacetimes are assumed. The resulting f (R) and nonlinear electrodynamics functions are characterized by a one-parameter family of solutions which are generalizations of known regular black holes in general relativity coupled to nonlinear electrodynamics. The related regular black holes of general relativity are recovered when the free parameter vanishes, in which case one has f (R) ∝ R. We analyze the regularity of the solutions and also show that there are particular solutions that violate only the strong energy condition

In this paper, we determine regular black hole solutions using a very general f (R) theory, coupled to a non-linear electromagnetic field given by a Lagrangian LNED. The functions f (R) and LNED are left in principle unspecified. Instead, the model is constructed through a choice of the mass function M (r) presented in the metric coefficients. Solutions which have a regular behaviour of the geometric invariants are found. These solutions have two horizons, the event horizon and the Cauchy horizon. All energy conditions are satisfied in the whole space-time, except the strong energy condition (SEC) which is violated near the Cauchy horizon.

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The surface gravity for the extreme Reissner-Nordstr\"om black hole is zero suggesting that it has a zero temperature. However, the direct evaluation of the Bogolubov's coefficients, using the standard semi-classical analysis, indicates that the temperature of the extreme black hole is ill definite: the Bogolubov's coefficients obtained by performing the usual analysis of a collapsing model of a thin shell, and employing the geometrical optical approximation, do not obey the normalization conditions. We argue that the failure of the employement of semi-classical analysis for the extreme black hole is due to the absence of orthonormal quantum modes in the vicinity of the event horizon in this particular case.Comment: Latex file, 10 pages. A new section was included. New title, new references and others minors modifications. To appear in Physics Letters

We consider the two classes cosh and sinh of normal and phantom black holes of Einstein-Maxwelldilaton theory. The thermodynamics of these holes is characterized by heat capacities that may have both signs depending on the parameters of the theory. Leaving aside the normal Reissner-Nordström black hole, it is shown that only some phantom black holes of both classes exhibit critical phenomena. The two classes share a nonextremality, but special, critical point where the transition is continuous and the heat capacity, at constant charge, changes sign with an infinite discontinuity. This point yields a classification scheme for critical points. It is concluded that the two unstable and stable phases coexist on one side of the criticality state and disappear on the other side, that is, there is no configuration where only one phase exists. The sinh class has an extremality critical point where the entropy diverges. The transition from extremality to nonextremality with the charge held constant is accompanied by a loss of mass and an increase in the temperature. A special case of this transition is when the hole is isolated (microcanonical ensemble), it will evolve by emission of energy, which results in a decrease of its mass, to the final state of minimum mass and vanishing heat capacity. The Ehrenfest scheme of classification is inaccurate in this case but the generalized one due to Hilfer leads to conclude that the transition is of order less than unity. Fluctuations near criticality are also investigated.

No abstract

The d-dimensional scalar field action may be reduced, in the background geometry of a black hole, to a 2-dimensional effective action. In the near horizon region, it appears a gravitational anomaly: the energymomentum tensor of the scalar field is not conserved anymore. This anomaly is removed by introducing a term related to the Hawking temperature of the black hole. Even if the temperature term introduced is not covariant, a gauge transformation may restore the covariance. We apply this method to compute the temperature of the dilatonic non asymptotically flat black holes. We compare the results with those obtained through other methods. *