  Bearing the thermodynamic arguments together with the two definitions of mass
in mind, we try to find metrics with spherical symmetry. We consider the
adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$
element which points to a null hypersurface. In addition, we generalize the
thermodynamics laws to this hypersurface to find its temperature and thus the
corresponding surface gravity which enables us to get a relation for the
$g_{tt}$ element. Moreover, we investigate the mathematical and physical
properties of the discovered metric in the Einstein relativity framework which
shows that the primary mentioned null hypersurface is an event horizon. The
obtained energy-momentum tensor equals the energy-momentum tensor of a
polytropic black hole embedded into an anti-de Sitter background. We also show
that if one considers the Misner-Sharp mass in the calculations, the
Schwarzschild metric will be got. The relationship between the two mass
definitions in each metric is studied. The results of considering the
geometrical surface gravity are also addressed. Our investigation shows that
the geometrical surface gravity's definition is not always compatible with the
validity of the first law of thermodynamics on the horizons of spherically
symmetric static metrics.
