Hall 123

Local Entropy Current on a Black-Hole Horizon and its Reparametrizations

Shuvayu Roy

NISER, Bhubanewshwar

Recently, working within the linearized regime of small amplitude expansion, an entropy current has been constructed on the horizons of dynamical black hole solution in any higher derivative theory of gravity. However, the construction is strongly dependent upon the spatial slicing of the horizon along its null-generators. In this talk, we will explore the effect of two types of reparametrizations of the null generators (1. affine to affine; 2. affine to non-affine) on the horizon entropy current. For the first case, we'll see that although the entropy current structures change non-trivially, the divergence of the entropy current remains invariant up to linear order in amplitude expansion. For the second case, we'll dualize the horizon entropy current to a boundary entropy current in an asymptotically AdS black hole metric with a dual description in terms of dynamical fluids living on the AdS boundary. Applying the construction to the Einstein-Gauss-Bonnet theory, we'll see that the Gauss-Bonnet terms do not add any corrections to the fluid entropy up to the first order in boundary derivative expansion. However, at the second order in derivative expansion, the boundary current will non-trivially depend on how we choose our horizon to boundary map, which need not be expressible entirely in terms of fluid variables. So, generically, the boundary entropy current generated by dualizing the horizon current will not admit a fluid dynamical description.