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We propose an entropy current for dynamical black holes in a theory with arbitrary four derivative corrections to Einsteins gravity, linearized around a stationary black hole. The Einstein-Gauss-Bonnet theory is a special case of the class of theories that we consider. Within our approximation, our construction allows us to write down a completely local version of the second law of black hole thermodynamics, in the presence of the higher derivative corrections considered here. This ultra-local, stronger form of the second law is a generalization of a weaker form, applicable to the total entropy, integrated over a compact `time-slice of the horizon, a proof of which has been recently presented in arXiv:1504.08040. We also provide a general algorithm to construct the entropy current for the four derivative theories, which may be straightforwardly generalized to arbitrary higher derivative corrections to Einsteins gravity. This algorithm highlights the possible ambiguities in defining the entropy current.
We present a class of new black hole solutions in $D$-dimensional Lovelock gravity theory. The solutions have a form of direct product $mathcal{M}^m times mathcal{H}^{n}$, where $D=m+n$, $mathcal{H}^n$ is a negative constant curvature space, and are
We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter
We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonica
Using the Sens mechanism we calculate the entropy for an $AdS_{2}times S^{d-2}$ extremal and static black hole in four dimensions, with higher derivative terms that comes from a three parameter non-minimal Einstein-Maxwell theory. The explicit result
Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and d