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In gravitational collapses, the horizon and singularity's realisation in thefinite future of the proper time used co-moving observer happens in the futureof infinitely far away future of the normal time used outside probe. To thelatter the horizon and singularity of a black hole formed through gravitationalcollapse are physical realities only in the sense of uncertainty principle andensemble interpretation. We provide two exact time dependent solution familiesto the Einstein equation and show that they form a pair of complementaritydescription for the microscopic state of black holes by showing that theBekenstein-Hawking entropy formula follows properly from their canonical wavefunction's degeneracy. We also develop an eXact One Body method for generalrelativity two-body dynamics whose conservative part requires no perturbativeinput from post newtonian approximation and applies to the full three stages ofblack hole binary merger events. By this method, we analytically calculate thegravitational wave forms following from such merger processes. In the caseblack holes carry exact and apriori horizon and singularity our wave formsagree with those following from conventional effective one body method butexhibit more consistent late time behaviour. In the case the black holes carryonly asymptotic horizon and extended inner structure thus experiencing bananashape deformation as the merger progresses, our wave forms exhibit all featuresespecially the late time quasi-normal mode type oscillation seen in realobservations.

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