A note on black-hole entropy, area spectrum, and evaporation

¹ Departamento de Física, Universidade Federal do Ceará - Caixa Postal 6030, CEP 60455-760, Fortaleza, Ceará, Brazil
² Instituto Federal de Educação Ciência e Tecnologia da Paraíba (IFPB), Campus Campina Grande Rua Tranquilino Coelho Lemos, 671, Jardim Dinamérica I, Brazil

^a calex@fisica.ufc.br
^b renan@fisica.ufc.br

Received: 10 July 2011
Accepted: 19 August 2011

Abstract

A model based on the topology change of a quantum manifold is used to explain the origin of the black-hole thermodynamics. We show that this model can explain the origin of the black-hole entropy, and why black-hole obey a generalized second law of thermodynamics. The method we use to do this is to analyze the selection rules for black-hole area transitions in the evaporation process driven by topology change. A discrete spectrum, which become increasingly spaced as the black hole approaches the Planck scale, is obtained for the black-hole area. As a striking consequence, as the lines of the area spectrum become more and more spaced, the black-hole radiation becomes less and less entropic. This result points to the possibility that some information about the black-hole initial quantum state can be recovered as it evaporates.