Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic Property of Schwarzschild Black Hole in Non-Commutative
  Gauge Theory of Gravity   In this paper, we constructed the deformed Schwarzschild black hole in the
non-commutative (NC) gauge theory of gravity. Where the singularity at the
origin is shifted by the non-commutativity to the finite radius $r_h=2m$ and
changed the spherical symmetry of the black hole to the ellipse symmetry
(deformed the NC event horizon). The thermodynamics property of the NC black
hole is analyzed. As a first step, we describe the Hawking temperature and the
entropy of the NC Schwarzschild black hole, where the result shows a difference
in the pole-equator temperature of the black hole, and give us a new scenario
of the black hole evaporation. Our estimation for the NC parameter is close to
the Planck scale $\Theta\approx2.257\times 10^{-35}m$. Then, the description of
the ADM mass, the heat capacity, and the Gibbs free energy of the deformed
black hole show the effect of the NC gauge theory on the thermodynamic
stability and the phase transitions. Finally, we investigated the influence of
the pressure of the black hole in the first law of thermodynamics on the
stability and the phase transition of the Schwarzschild black hole in the NC
spacetime, where the result shows that the NC parameter plays a similar role as
the thermodynamical function and defined the critical point as the pressure in
the modified first law of thermodynamics which means a second-order phase
transition or a continuous one. The stability and the phase transition of the
Schwarzschild black hole are affected by the non-commutativity.

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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph