Area spectra versus entropy spectra of black holes in topologically massive gravity

Abstract

The area and entropy spectra of black holes in topologically massive gravity with the gravitational Chern–Simons term are calculated. The examples we consider are the BTZ black hole and the warped AdS3 black hole. For the non-rotating BTZ black hole, we find that the gravitational Chern–Simons term does not affect the area and entropy spectra, so that they are equally spaced. For the rotating BTZ black hole, the spectra of the inner and outer horizon areas are not equally spaced and dependent on the coupling constant ν of the gravitational Chern–Simons term. However the entropy spectrum is equally spaced and independent of the coupling constant ν. For the warped AdS3 black hole, we again find that the entropy spectrum is equally spaced and independent of the coupling constant ν, while the spectra of the inner and outer horizon areas are not equally spaced and dependent on the coupling constant ν. Our result implies that the entropy spectrum has a universal behavior regardless of the presence of the gravitational Chern–Simons term, and therefore the entropy is more ‘fundamental’ than the horizon area. We propose to use this universal behavior of the entropy spectrum as criteria of a correct quasinormal mode.