The expressions for the corrected radius and the Hawking temperature of a Schwarzschild black hole are derived by calculating the total energy of a self-gravitating system of N fermions when the corrections to gravitational interaction due to post-Newtonian-like self-energy due to two graviton exchange- and one-loop contribution of quantum gravity effect are included. Since the particles are fermions, the exchange-correlation energy is also included consistently. It is found that though the three corrections are small, the correction due to the exchange-correlation is much more than the other two. The configuration of the many-particle system that we study is possible since it has no Buchdahl limit in the post-Newtonian approximation.

Using a single particle density distribution for the self-gravitating quantum particles that form an interacting N-particle system which ultimately forms a black hole, we from a condensed matter point of view derive the expressions of the Schwarzschild radius and the Hawking temperature. Including the quantum mechanical exchange correlation energy for the particles, we find small corrections to the above two physical quantities. The approximate expression of ground state energy and the numerical coefficient of the formula for Hawking temperature provide the hint to enable us to propose an exact expression for the ground state energy of the system.

Extending our model of Newtonian Quantum Gravity (NQG) in self-gravitating system [Mod. Phys. Lett.A 35, 2050081(2020)], we study here the energetics of a charged self-gravitating quantum many-particle system. The model is based on the use of uncertainty principle and the incorporation of necessary relativistic corrections. From the resulting ground state energy we have derived the effective radius of the system of charged particles, after it gets collapsed under its own gravity. Additional results like the Hawking temperature and the Buchdahl-Andréasson (BA) limit for this system are also explored. We further show a possible link of this collapsed system of self-gravitating charge particles, with the notion of a charged black hole.