Nonthermal correction to black hole spectroscopy

Abstract

Area spectrum of black holes has been obtained via various methods such as quasinormal modes, adiabatic invariance and angular momentum. Among those methods, calculations were done by assuming black holes in thermal equilibrium. Nevertheless, black holes in the asymptotically flat space usually have a negative specific heat and therefore tend to stay away from thermal equilibrium. Even for black holes with a positive specific heat, the temperature may still not be well defined in the process of radiation, due to the back reaction of a decreasing mass. With respect to these facts, it is very likely that Hawking radiation is nonthermal and the area spectrum is no longer equidistant. In this note, we would like to illustrate how the area spectrum of black holes is corrected by this nonthermal effect. Area law and logarithmic correctionA finite size system often displays a discrete energy spectrum as regards quantum fluctuations. It was suggested that since the dynamics of a black hole is uniquely determined by its charge(s), which is closely related to the finite region enclosed by the horizon, one expects the mass or area spectrum to display a similar discreteness [1,2]. There were many proposals to obtain the area spectrum for various black holes since then. Earlier methods of quantizing the horizon area are mostly based on real or imaginary parts of the quasinormal modes [3][4][5][6][7][8][9][10][11][12]. Recently the application of an adiabatic invariant action variable did not use the quasinormal modes [13,14] and the idea of quantizing the angular momentum to obtain the area spectrum first appeared in the study of non-extremal RN black holes [15]. The various methods of quantization have settled on a spectrum of equidistant discreteness,a

Hawking radiation as stimulated emission

“…We may estimate its order by considering fluctuation in Newton's gravitational potential δU ∼ ωδg 00 ∼ Mωδr/r 2 | r=2M . Given the quantized radiation ω ∼ /4M [22] and δr ∼ ω, one obtains the energy gap ∆E ∼ δU ∼ /M 3 in agreement with [17]. However, its contribution to Ω is minor due to its small magnitude.…”