  Black holes pose great difficulties for theory since gravity and quantum
theory must be combined in some as yet unknown way. An additional difficulty is
that detailed black hole observational data to guide theorists is lacking. In
this paper, I sidestep the difficulties of combining gravity and quantum theory
by employing black hole thermodynamics augmented by ideas from the information
geometry of thermodynamics. I propose a purely thermodynamic agenda for
choosing correct candidate black hole thermodynamic scaled equations of state,
parameterized by two exponents. These two adjustable exponents may be set to
accommodate additional black hole information, either from astrophysical
observations or from some microscopic theory, such as string theory. My
approach assumes implicitly that the as yet unknown microscopic black hole
constituents have strong effective interactions between them, of a type found
in critical phenomena. In this picture, the details of the microscopic
interaction forces are not important, and the essential macroscopic picture
emerges from general assumptions about the number of independent thermodynamic
variables, types of critical points, boundary conditions, and analyticity. I
use the simple Kerr and Reissner-Nordstrom black holes for guidance, and find
candidate equations of state that embody a number of the features of these
purely gravitational models. My approach may offer a productive new way to
select black hole thermodynamic equations of state representing both
gravitational and quantum properties.
