چکیده
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Focusing on the special case of generalized Rastall theory, as a
subclass of the non-minimal curvature-matter coupling theories in
which the field equations are mathematically similar to the
Einstein field equations in the presence of cosmological constant,
we find two classes of black hole (BH) solutions including $i$)
conformally flat solutions and $ii$) non-singular BHs. Accepting
the mass function definition and by using the entropy contents of
the solutions along with thermodynamic definitions of temperature
and pressure, we study the validity of Euler equation on the
corresponding horizons. Our results show that the thermodynamic
pressure, meeting the Euler equation, is not always equal to the
pressure components appeared in the gravitational field equations
and satisfies the first law of thermodynamics, a result which in
fact depends on the presumed energy definition. The requirements
of having solutions with equal thermodynamic and Hawking
temperatures are also studied. Additionally, we study the
conformally flat BHs in the Rastall framework. The consequences of
employing generalized Misner-Sharp mass in studying the
validity of the Euler equation are also addressed.
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