^{1}

^{1}

We apply Debbasch proposal to obtain mean metric of coarse graining (statistical ensemble) of quantum perturbed Reissner-Nordstöm black hole

Every observation in any arbitrary system is necessarily finite which deals with a finite number of measured quantities with a finite precision. A given system is therefore generally susceptible of different, equally valid descriptions and building the bridges between those different descriptions is the task of statistical physics (see introduction in [

Similar to study of thermodynamic behavior of single RNBH [

In Section

Exterior metric tensor of a single charged, nonrotating, spherically symmetric body is given by

One can obtain event horizon location of the mean metric (

In the next section we will consider massless, chargeless quantum scalar field effects on luminosity of the quantum perturbed coarse graining RNBHs where its electric charge becomes invariant quantity. Hence it is useful to define dimensionless black hole mass

Diagram of mass loss

Diagram of

Diagram of

Diagram of

Diagram of interior and exterior horizons heat capacities

Exterior and interior horizon Gibbs free energies are defined by

Diagram of interior and exterior horizons Gibbs free energies

One of other suitable quantities which should be calculated is pressure of black hole microparticles which coincide with the interior horizon as follows. If a quantum particle is collapsed inside of the interior (exterior) horizon then its de Broglie wave length must be at least

We applied massless, chargeless quantum scalar field Hawking thermal radiation effects on single quantum unstable RNBH and calculated time dependence mass loss function in [

Diagram of exterior and interior horizons luminosity

Diagram of interior horizon pressure

According to the Debbasch approach we calculated mean metric of RNBHs statistical ensemble to obtain locations of interior and exterior horizons. We calculated corresponding entropy, temperature, heat capacity, Gibbs free energy, and pressure. At last section of the paper we considered interaction of massless, chargeless quantum scalar matter field on quantum perturbed mean metric of coarse graining RNBHs. Our mathematical calculations predict evaporation of the mean metric which reduces to a remnant stable mini black hole metric with nonvanishing mass. Before the evaporation reaches its final state, the mean metric exhibits a first-order phase transition and Bose-Einstein condensation state happens microscopically. Our results approve outputs of the published work [

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.