Quantization of Horizon Entropy and the Thermodynamics of Spacetime

This is a review of my work published in the papers of Skakala (JHEP 1201:144, 2012; JHEP 1206:094, 2012) and Chirenti et al. (Phys. Rev. D 86:124008, 2012; Phys. Rev. D 87:044034, 2013). It offers a more detailed discussion of the results than the accounts in those papers, and it links my results to some conclusions recently reached by other authors. It also offers some new arguments supporting the conclusions in the cited articles. The fundamental idea of this work is that the semiclassical quantization of the black hole entropy, as suggested by Bekenstein (Phys. Rev. D 7:2333-2346, 1973), holds (at least) generically for the spacetime horizons. We support this conclusion by two separate arguments: (1) we generalize Bekenstein's lower bound on the horizon area transition to a much wider class of horizons than only the black-hole horizon, and (2) we obtain the same entropy spectra via the asymptotic quasi-normal frequencies of some particular spherically symmetric multi-horizon spacetimes (in the way proposed by Maggiore (Phys. Rev. Lett. 100:141301, 2008)). The main result of this paper supports the conclusions derived by Kothawalla et al. (Phys. Rev. D 78:104018, 2008) and Kwon and Nam (Class. Quant. Grav. 28:035007, 2011), on the basis of different arguments.