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.
Highlights
The various methods of quantization have settled on a spectrum of equidistant discreteness, In particular, one obtained c = 8π for various kinds of black holes in different spacetime dimensions. This universal result is closely related to the assumption that the black hole is in the thermal equilibrium state where the Hawking temperature is well defined
Realistic black holes are more likely to be in the nonequilibrium state due to their negative specific heat
For the spherical near-horizon topology, k = 1, we find that the correction to the area spectrum explicitly depends on l
Summary
A finite size system often displays a discrete energy spectrum as regards quantum fluctuations. 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, In particular, one obtained c = 8π for various kinds of black holes in different spacetime dimensions. This universal result is closely related to the assumption that the black hole is in the thermal equilibrium state where the Hawking temperature is well defined. 3 2 in the context of an adiabatic invariance approach for constant surface gravity
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