Comparative Study of Bulk and Surface Pressure of Charged AdS Black Hole

Abstract

One of the most interesting areas of research is the study of thermodynamic properties of black holes. In the extended phase, cosmological constant has been identified with the thermodynamic pressure of the black hole and phase transitions similar to Van der waals fluid is observed. On other side, fluid gravity correspondence which gives the connection between fluid on a d dimensional boundary and gravity theory in d + 1-dimensional bulk relates Einstein’s equations in the bulk with Navier-Stokes equations on the boundary. Projecting Einsteins equation onto a black hole horizon gives Damours Navier-Stokes equation and fluid pressure is found to be κ8π. In our present work, we are comparing the thermodynamic quantities in the bulk and boundary of charged AdS black holes. © 2021, Springer Nature Singapore Pte Ltd.