 2317 Christian Corda
 Black hole spectra from Vaz's quantum gravitational collapse
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Apr 13, 23

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Abstract. In 2014, in a famous paper Hawking strongly criticized the firewall
paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead.
On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the WheelerDeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged.
The approach of Vaz as also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell.
In this work we derive the BH mass and energy spectra via a Schrodinger
like approach, by further supporting Vaz's conclusions that instead of a
spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated.
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