Universality of Area Product: Solutions with Conical Singularity

It has been observed that the area product of horizons for many black hole solutions is mass independent and satisfy the universality relation $A_+A_-=(8\pi)^2 N$, where $N$ is related to the quantized charges of the solution as angular momentum and electric charge. In this work the same analysis is done for black hole and black ring solutions with conical singularity. We find that the area product is still mass independent and regardless of the horizon topology, the conical characteristic ($\kappa$) of the solutions, appears in the universality relation as $\kappa A_+A_-=(8\pi)^2 N$. We also check that the first law of black hole inner mechanics is satisfied for these solutions.