DiBeos

We propose another version of Black Hole information Paradox owing absence of Diffeomorphism symmetry for Black Hole Spacetime. The central idea is assumptions of semiclassical Gravity like locality, causality and diffeomorphism symmetry lead to another paradox. The paradox unlike many other recent versions of Information paradox is valid even at very early times. The possible suggestive way for the resolution of paradox has various approaches like validity of Black Hole Complementarity from the very beginning or the principle of Holography of Information proposed by Suvrat et.al. We discuss some subtleties with these approaches in the local nature of splitting of Hilbert Space (in some pseudoprecise way) of the dual CFT. Being as conservative as we can, to avoid such subtleties (which have been addressed in the paper) we suggest that absence of Diffeomorphism symmetry for Black Hole Spacetime implies it being a smooth Finsler manifold. We will discuss what we mean by this and the implications of it. We also give a recipe for recosntructing Null Hypersurface for Black Hole Spacetime in a different way in section 3.6, 3.7 of the paper. We are also lead to notion of Finsler Geometry for Black Hole Spacetime owing to asymmetry of line element.We also find that the Null Diffeomorphism Symmetry group of 2 dimensional Minokowski spacetime admits a superspace structure. However owing to analytical difficulty of solving coupled ordinary Raychaudhari differential equations and a consistency condition we could not verify the claim of superspace structure for Null Diffeomorphism group for Schwarschild spacetime.