Evaporation and fate of dilatonic black holes

Abstract

We study both spherically symmetric and rotating black holes with dilaton coupling and discuss the evaporation of these black holes via Hawking's quantum radiation and their fates. We find that the dilaton coupling constant a drastically affects the emission rates, and therefore the fates of the black holes. When the charge is conserved, the emission rate from the nonrotating hole is drastically changed beyond a = 1 (a superstring theory) and diverges in the extreme limit. In the rotating cases we analyze the slowly rotating black hole solution with arbitrary a as well as three exact solutions:the Kerr-Newman ( a = 0), Kaluza-Klein ( a = f i ) , and Sen black hole (a = 1 and with axion field).Beyond the same critical value of a N 1, the emission rate becomes very large near the maximally charged limit, while for a < 1 it remains finite. The black hole with a: > 1 may evolve into a naked singularity due to its large emission rate. We also consider the effects of a discharge process by investigating superradiance for the nonrotating dilatonic black hole.

Erratum: Hawking radiation from dilatonic black holes via anomalies [Phys. Rev. D75, 064029 (2007)]

“…The condition that the black hole has a regular horizon is µ 2 ≥ a 2 . It should be noticed that the solution, in the extreme limit (|Q| = 2M and J = 0), is no longer representing a black hole because a naked singularity appears [19]. This is quite different from the Kerr-Newman (α = 0) black hole.…”

“…When moving to the case α = 1, it has the nonzero finite value 1/(8πM ). Besides, the energy momentum tensor flux for each value of the dilaton coupling constant α coincides at Q = 0, since the black hole solution with any α is identically the Schwarzschild spacetime for Q = 0 [19]; the difference becomes large as the charge increases. When the charge of the black hole is fixed, the charge current flux is eliminated from the anomalous flux.…”

“…It is derived by a dimensional reduction of the boosted five-dimensional Kerr solution to four dimensions. The metric is given by [17,19] …”

“…In this paper, motivated by RobinsonWilczek's recent viewpoint, we study Hawking radiation from the static, spherically symmetric dilatonic black holes with arbitrary coupling constant, and that from the rotating Kaluza-Klein and Kerr-Sen dilatonic black holes [19] via gauge and gravitational anomalies. The result shows that, demanding gauge invariance or general coordinate covariance at the quantum level, one can find each partial wave of the scalar field to be in a state with a net charge current or energy momentum tensor flux, whose values are exactly equal to that of (1 + 1)-dimensional blackbody radiation at the Hawking temperature with an appropriate chemical potential.…”

Estimating Hawking radiation for exotic black holes

“…Since the systematic error caused by it is below 1%, this does not affect the discussion below. The evaporation process of the monopole black hole and the dilatonic black holes were discussed numerically in [17] and in [18], respectively. In this note, we study an approximation method of the Hawking radiation and check how accurate it is.…”