The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity

A bstract We consider diffeomorphism invariant theories of gravity with arbitrary higher derivative terms in the Lagrangian as corrections to leading two theory Einstein’s general relativity. construct a proof zeroth law black hole thermo-dynamics such theories. assume that stationary solution an can be obtained by starting corresponding relativity and correcting it order perturbative expansion coupling constants Lagrangian. prove surface remains constant on its horizon when computed for holes, which is law. argue constancy related specific components equations motion further use boost symmetry near space-time constrain off-shell structure motion. Our valid up couplings.