On the Mathematical Analysis of Black-Hole Information Loss Paradox

A Black-hole is an astronomical entity which possesses infinite density at its gravitational singularity or singular point. The capacity of a black-hole to completely rip-off an entire solar system without leaving any evidence is to be noted. A debate has been going on over the past few decades regarding the information storage in black-holes. The discovery of Hawking radiation, which predicts complete evaporation of mass violates unitarity ie. Conservation of probability and energy fails. Recent discoveries suggest that regular remnant of black-hole survives evaporation , as a result information of the object devoured can be contained. These remnants are grouped into embedded sub-manifolds. These manifolds are the result of a five-dimensional constant curvature bulk in space-time. Five-dimensional gravity can be recovered from brane-world resulting from equations of bulk geometry. Gravity can be explained by space-time theory and also quantum theory in the form of Gravitons. On observing the manifold, the gravitons show deformations in dimensions, rather than being constant. The perturbations in geometry can be related to embedding functions which should remain differentiable and regular. Regularity is related to the inverse functions theorem. Manifold observations followed by a mathematical approach can possibly retain information about objects devoured by the black-hole.