Thermodynamics of rotating black branes in gravity with first order string corrections

In this paper, the rotating black brane solutions with zero curvature horizon of classical gravity with first order string corrections are introduced. Although these solutions are not asymptotically anti de Sitter, one can use the counterterm method in order to compute the conserved quantities of these solutions. Here, by reviewing the counterterm method for asymptotically anti de Sitter spacetimes, the conserved quantities of these rotating solutions are computed. Also a Smarr-type formula for the mass as a function of the entropy and the angular momenta is obtained, and it is shown that the conserved and thermodynamic quantities satisfy the first law of thermodynamics. Finally, a stability analysis in the canonical ensemble is performed, and it is shown that the system is thermally stable. This is in commensurable with the fact that there is no Hawking-Page phase transition for black object with zero curvature horizon.