Conserved charges and asymptotic symmetries of BTZ-like black holes in Einstein-bumblebee gravity

Using the solution phase space method, we investigate the conserved charges of BTZ-like black holes in Einstein-bumblebee gravity. Our study shows that the black hole mass, angular momentum and entropy are influenced by the Lorentz-violating parameter. Through the study of the AdS/CFT correspondence, we derive the asymptotic charge algebra, which consists of two copies of the Virasoro algebra with non-trivial central charges. By employing the Cardy formula, we calculate the microscopic entropy of dual conformal field theory, which precisely matches with the Bekenstein–Hawking entropy. Furthermore, by imposing the Detournay–Smoes–Wutte boundary conditions in the near horizon geometry of the extremal BTZ-like black hole, we obtain a Virasoro–Kac–Moody U(1) U ( 1 ) algebra, representing the symmetry algebra of a warped conformal field theory.