Study of anisotropic black branes in asymptotically anti-de Sitter

We investigate the four dimensional gravitational theories which admit homogeneous but anisotropic black brane solutions in asymptotically AdS space-time. The gravitational theories we consider are 1) Einstein-Maxwell-dilaton theory, and 2) Einstein-Maxwell-dilaton-axion theory with SL(2, R) symmetry. We obtain the solutions both analytically and numerically. Analytical solutions are obtained by perturbation from the isotropic solutions. Our solutions approach singular behavior at the horizon in the extremal limit but in non-extremal case, they are smooth everywhere. We also discuss how the third law of thermodynamics holds in our set-up.