  The central equations in classical general relativity are the Einstein Field
Equations, which accurately describe not only the generation of
pseudo-Riemannian curvature by matter and radiation manifesting as
gravitational effects, but more importantly mass-energy dynamics, evolution and
distribution on the space-time manifold. Herein, we introduce a geometric phase
in general relativity corresponding to Schwarzschild black hole information
content. This quantity appropriately satisfies a local conservation law subject
to minimal coupling, with other desirable properties such as the quantization
of the black hole horizon in units of Planck area. The local conservation law
is imposed by field equations, which not only contain the trace of Einstein
Field Equations, but also a complex-valued function with properties analogous
to the quantum-mechanical wave function. Such success attests to the utility of
the proposed field equations in capturing key aspects of quantum gravity
theories.
