Problems in black-hole entropy interpretation

In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, I will firstly consider the so-called ''entanglement entropy'' interpretation, in the framework of the brick wall model ('T HOOFT G., Nucl. Phs. B, 256 (1985) 727), and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black-hole entropy based on peculiar topological structures of manifolds with ''intrinsic'' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy (tree level contribution in path integral approach) and topology of these Euclidean space-times. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation I shall propose a generalization of the Bekenstein-Hawking entropy in which the for mer and Euler characteristic are related in the equation S=chi A/8. The results, quoted above, are more largely exposed in previous works (BELGIORNO F. and LIBERATI S., Divergences problem in black hole brick-wall model, Preprint gr-qc/9503022.; LIBERATI S. and POLLIFRONE G., Entropy and topology for manifolds with boundaries, Preprint hep-th/9509093). Finally, I will try to expose some conclusions and hypotheses about possible further development of this research.