Résumé:
In this thesis, we study several applications of black hole (BH) physics in the presence of
two different deformed metrics. This deformation is implemented by the non-commutative
(NC) gauge theory of gravity. The first part of the thesis is devoted to obtain the deformed
metric in the presence of non-commutativity for two black holes (BHs), which are the
Schwarzschild and Reissener-Nordström (RN) metrics. The use of the NC gauge theory
affects the geometry of BH and their properties, such as singularity, static limit surface,
and event horizon. The second part is devoted for a detailed investigation of the particle
motions around a NC BH. Two cases are studied for each deformed metric. Firstly, we
study the motion of both massless and massive test particles in the NC Schwarzschild
spacetime for two kinds of motions: free fall and circular motion. For free-fall motion,
these two types of particles take an infinite time to reach the NC singularity. Moreover,
for the circular motion, the non-commutativity predicts a new stable circular orbit (SCO)
near the event horizon, which is not allowed in the commutative case. In the third part of
this thesis, we investigate in detail the effect of non-commutativity on the BH evaporation
process for different scenarios. In the first one, we study in detail the thermal proprieties
of the NC Schwarzschild BH in the context of the classical BH thermodynamics, where
we predict four important results, which are a new scenario of BH evaporation, a new
fundamental length, and a remnant BH in the final stage.We show then similarity between
the NC Schwarzschild BH and the Anti-de-Sitter (AdS) RN one in the grand canonical
ensemble. The second scenario is devoted to the investigation of the thermal stability and
the phase transition of this BH inside a thermal spherical cavity in the presence of this
geometry, in which this NC BH shows a two-coexistence phase transition. In the final
scenario, we present a detailed study of the NC effect on Hawking radiation, using the
quantum tunneling process for two cases. In the first one, we investigate pure thermal
radiation, where we show an equivalence between this approach and the thermodynamical
one, and then we show the effect of this geometry on the density number of particles that
are emitted from the NC Schwarzschild BH. Secondly, we investigate the non-thermal
radiation in the presence of this geometry, and then we check the correlation between two
successive particle emissions, in which the non-commutativity doesn’t preserve only the
correlation in this geometry but also reduces it compared to the commutative case, which
allows the information to come out with Hawking radiation. Finally, we show the effect of
this geometry on the BH evaporation process.
