Holographic information theoretic quantities for Lifshitz black hole

Abstract

Abstract In this paper, we have investigated the holographic entanglement entropy for a linear subsystem in a $$3+1$$ 3+1 -dimensional Lifshitz black hole. The entanglement entropy has been analysed in both the infra-red and ultra-violet limits, and has also been computed in the near horizon approximation. The notion of a generalized temperature in terms of the renormalized entanglement entropy has been introduced. This also leads to a generalized thermodynamics like law $$E=\frac{1}{2}T_g S_{REE}$$ E=12TgSREE . The generalized temperature has been defined in such a way that it reduces to the Hawking temperature in the infra-red limit. We find that the inverse of the generalized temperature ($$\beta _g=1/T_g$$ βg=1/Tg ) attains a non-zero value when the subsystem length becomes zero although it is zero in case of the Schwarzschild-AdS black hole. We have then computed the holographic subregion complexity. We find that the subregion complexity has logarithmic divergence which was absent in case of the $$3+1$$ 3+1 -dimensional Schwarzschild-AdS black hole. Then the Fisher information metric and the fidelity susceptibility for the same linear subsystem have also been computed using the bulk dual prescriptions. It has been observed that the two metrics are not related to each other.