Generalized proofs of the first law of entanglement entropy

Abstract

In this paper, we develop generalized proofs of the holographic first law of entanglement entropy using holographic renormalization. These proofs establish the holographic first law for non-normalizable variations of the bulk metric; hence, relaxing the boundary conditions imposed on variations in earlier works. Boundary and counterterm contributions to conserved charges computed via covariant phase space analysis have been explored previously. Here, we discuss in detail how counterterm contributions are treated in the covariant phase approach to proving the first law. Our methodology would be applicable to generalizing other holographic information analyses to wider classes of gravitational backgrounds.