Dougherty: The geometry of black hole entropy

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Abstract

It is a commonplace that our best lead in the pursuit of a quantum theory of gravity comes from black hole thermodynamics (BHT). Entropy, in particular, has played a substantial role in linking gravitational physics with time and quantum theory, and Wald has given a notion of entropy for non-stationary spacetimes, as well. I consider the Wald entropy and the first law of BHT from a geometrical point of view. This allows for a simplification of Wald’s definition, as well as an extension to Lagrangian theories which may involve fixed background fields. I also argue that this understanding of gravitational entropy requires one to attribute independent physical significance to the connection and the metric.

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