XL Workshop on Geometric Methods in Physics Białowieża, 2-8.07.2023 XII School on Geometry and Physics Białystok, 26-30.06.2023

Slimane Zaiem

Evaporation of black hole in the non-commutative gauge theory of gravity

In this work, we used the non-commutative (NC) gauge theory of gravity to analysis the thermodynamic
properties of a deformed Schwarzschild black hole (SBH). As a first step, the Hawking temperature with all
order in theta, and the entropy of NC SBH. The non-commutativity removes the divergence behavior of temperature
and these corrections reveal an estimation of the NC parameter theta which is founded at the Planck scale order. Then, the description of the heat capacity of the deformed black hole shows the effect of the NC
geometry on the thermodynamic stability and the phase transitions. Finally, we investigate the influence of the
non-commutativity on the Luminosity of SBH, where this geometry removes the divergence behavior of SBH
luminosity. In this study, we found that the NC geometry show the same role of the quantization of the black
body radiation in the classical theory.
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