Resolving the Schwarzschild singularity in both classic and quantum gravity

Abstract

The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like "orbital" quantisation assumption, we show that for each black hole of horizon radius $r_h$, there are about $e^{r_h^2/{\ell }_{\mathrm{pl}}^2}$ allowable eigen-energy-density profile. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.

19 pages, 5 figures, final published version

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• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• The Black Hole Information Problem
• Quantum gravitational collapse: non-singularity and non-locality
• Non-local (but also non-singular) physics at the last stages of gravitational collapse
• New Insights into Quantum Gravity from Gauge/gravity Duality

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• Exact Inner Metric and Microscopic State of AdS${}_3$-Schwarzschld BHs
• Microscopic State of BHs and an Exact One Body Method for Binary Dynamics in General Relativity
• Brane universe and holography in spacetime of charged AdS dilaton black hole
• Gravity Induced Spontaneous Radiation
• Chaotic D1-D5 Black Hole Dynamics through Networks