Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy

Understand

There are certain black hole solutions in general relativity (GR) which are conformally related to the stationary solutions in GR.

• It is not obvious that the horizon entropy of these spacetimes is also one quarter of the area of horizon, like the stationary ones.
• Here I study this topic in the context of Virasoro algebra and Cardy formula.
• Using the fact that the conformal spacetime admits conformal Killing vector and the horizon is determined by the vanishing of the norm of it, the diffemorphisms are obtained which keep the near horizon structure invariant.