NOTES ON DERIVATION OF GENERALIZED GRAVITATIONAL ENTROPY
https://doi.org/10.18384/2224-0209-2014-1-935
Abstract
A novel derivation of generalized gravitational entropy associated to co-dimension 2 'entangling' hypersurfaces is given. The approach is similar to the Jacobson- Myers 'Hamiltonian' method in a sense that the entropy appears from a boundary term in the action when one isolates a small domain around the entangling surface. In our arguments we also use the idea by Lewkowycz and Maldacena and interpret the boundary term in the gravity action as a 'cosmic string' (brane) action. However, the important difference between our approach and the original formulation of the generalized gravitational entropy by Lewkowycz and Maldacena is that we never use manifolds with conical singularities as a tool to carry out the computations. Variations of gravity actions over the replica parameter imply changing position of the 'cosmic string'. By requiring that the entangling surface is an extremum of the entropy functional we come to the entropy formula which coincides with known results for black hole entropy formula when the entangling surface is a black hole horizon.When our approach is applied to Lovelock theories of gravity the generalized entropy formula coincides with results derived by other methods.
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