Microscopic State of BHs and an Exact One Body Method for Binary Dynamics in General Relativity

In gravitational collapses, the horizon and singularity's realisation in the finite future of the proper time used co-moving observer happens in the future of infinitely far away future of the normal time used outside probe. To the latter the horizon and singularity of a black hole formed through gravitational collapse are physical realities only in the sense of uncertainty principle and ensemble interpretation. We provide two exact time dependent solution families to the Einstein equation and show that they form a pair of complementarity description for the microscopic state of black holes by showing that the Bekenstein-Hawking entropy formula follows properly from their canonical wave function's degeneracy. We also develop an eXact One Body method for general relativity two-body dynamics whose conservative part requires no perturbative input from post newtonian approximation and applies to the full three stages of black hole binary merger events. By this method, we analytically calculate the gravitational wave forms following from such merger processes. In the case black holes carry exact and apriori horizon and singularity our wave forms agree with those following from conventional effective one body method but exhibit more consistent late time behaviour. In the case the black holes carry only asymptotic horizon and extended inner structure thus experiencing banana shape deformation as the merger progresses, our wave forms exhibit all features especially the late time quasi-normal mode type oscillation seen in real observations.