Quantization of horizon entropy and the thermodynamics of spacetime

This is a review of my work published in the papers [1-4]. It offers a more detailed discussion of the results than what was given in the published papers and it links my results to some conclusions recently made by other people. It also offers some new arguments for the conclusions previously made. The fundamental idea of this work is that the semi-classical quantization of the black hole entropy, as suggested by Bekenstein [5], 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 much larger class of horizons than only the black hole horizon, 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 [6]). The main result of this paper supports the conclusions made by other people in [7,8], but uses different arguments.