Black Hole Thermodynamics in Higher Curvature Theories of Gravity

Details Black Hole Thermodynamics in Higher Curvature Theories of Gravity Black Hole Thermodynamics in Higher Curvature Theories of Gravity

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........23k&link_type=abstract

Thesis (PH.D.)--UNIVERSITY OF MARYLAND COLLEGE PARK, 1995.Source: Dissertation Abstracts International, Volume: 56-11, Section:

Physics

1

Entropy

Scientific paper

The laws of black hole thermodynamics are investigated within the context of effective gravitational actions including higher curvature interactions. Wald has shown that the First Law for Einstein gravity can be extended to generally covariant gravity theories. This generalized form of the First Law by using the so-called Noether charge method also demonstrates that black hole entropy can always be expressed as a local geometric density integrated over the bifurcation surface of the event horizon. This expression at the bifurcation surface is indeed same when evaluated on an arbitrary cross-section of a Killing horizon. Further, it is shown that Wald's expression for the entropy is not affected by ambiguities which arise in the Noether charge construction. Using both the Noether charge approach and a field redefinition method, the entropy is evaluated explicitly for black holes in a wide class of generally covariant theories of gravity including higher curvature interactions. For quasi-stationary processes, we show that entropy can never decrease if a black hole accretes positive energy matter. This result is a direct consequence of the First Law with positive energy condition, independent of the details of gravitational theories. In certain cases, it can also be shown that the Second Law holds in general for any dynamical process. One such simple example is considered from the class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar. By using the conformal invariance of black hole temperature, we also show that the Zeroth Law is satisfied for stationary black hole solutions with a Killing horizon in this class of theories. Finally, we introduce a new method for establishing the Second Law based on a generalization of the area theorem, which possesses general aspects applicable for a wider class of gravity theories. The possible significance of these results for the problem of finding the statistical origin of black hole entropy and candidate theories of quantum gravity is discussed.

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