  We revisit the classical thermodynamic stability of the standard black hole
solutions by implementing the intrinsic necessary and sufficient conditions for
stable global and local thermodynamic equilibrium. The criteria for such
equilibria are quite generic and well-established in classical thermodynamics,
but they have not been fully utilized in black hole physics. We show how weaker
or incomplete conditions could lead to misleading or incorrect results for the
thermodynamic stability of the system. We also stress the importance of finding
all possible local heat capacities in order to fully describe the classical
equilibrium picture of black holes. Finally, we thoroughly investigate the
critical and phase transition curves and the limits of the classical analysis.
This paper is the first in the line of intended works on thermodynamic
stability of black holes in modified theories of gravity and holography.
