[share_ebook] On Black Hole Entropy - Ted Jacobson, Gungwon Kang, and Robert C. Myers - PDF - Free ebook download

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Posted on 2012-01-26, by nightbat.

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Ted Jacobson, Gungwon Kang, and Robert C. Myers, <<On Black Hole Entropy>>
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Abstract:

Two techniques for computing black hole entropy in generally covariant gravity theories
including arbitrary higher derivative interactions are studied. The techniques are Wald’s
Noether charge approach introduced recently, and a field redefinition method developed in
this paper. Wald’s results are extended by establishing that his local geometric expression
for the black hole entropy gives the same result when evaluated on an arbitrary cross-section
of a Killing horizon (rather than just the bifurcation surface). Further, we show that his
expression for the entropy is not affected by ambiguities which arise in the Noether construction.
Using the Noether charge expression, the entropy is evaluated explicitly for black
holes in a wide class of generally covariant theories. For a Lagrangian of the functional form
eL
= eL(ψm,∇aψm, gab,Rabcd,∇eRabcd), it is found that the entropy is given by
S = −2π
I 
Y abcd − ∇eZe:abcd

ˆǫabˆǫcd¯ǫ
where the integral is over an arbitrary cross-section of the Killing horizon, ˆǫab is the binormal
to the cross-section, Y abcd = ∂eL/∂Rabcd, and Ze:abcd = ∂eL/∂∇eRabcd.
Further, it is shown that the Killing horizon and surface gravity of a stationary black hole
metric are invariant under field redefinitions of the metric of the form ¯gab ≡ gab+ab, where
ab is a tensor field constructed out of stationary fields. Using this result, a technique is
developed for evaluating the black hole entropy in a given theory in terms of that of another
theory related by field redefinitions. Remarkably, it is established that certain perturbative,
first order, results obtained with this method are in fact exact. A particular result established
in this fashion is that a scalar matter term of the form ∇2pφ∇2qφ in the Lagrangian makes
no contribution to the black hole entropy.
The possible significance of these results for the problem of finding the statistical origin
of black hole entropy is discussed.






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