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Quantum gravity seeks a consistent quantum description of gravitational dynamics, including regimes where treating spacetime geometry as a prescribed classical background is insufficient. The issue is not merely adding a gravitational potential to a nonrelativistic Schrödinger equation: the gravitational field itself can require quantum degrees of freedom and backreaction.

Weak-field perturbation theory describes a spin-two graviton, while string theory supplies a framework with a richer spectrum. A candidate theory must reproduce established classical gravity in its appropriate limit and make quantum predictions with a controlled domain of validity. Semiclassical gravity instead sources a classical field by a quantum expectation value; it is a distinct approximation whose success for some observables does not establish a full quantum theory of geometry.

For a large isolated Schwarzschild black hole with a fixed effective set of radiated species, Hawking radiation has $T\propto M^{-1}$ and luminosity $P=\alpha /M^2$ in natural units. Integrating $dM/dt=-\alpha /M^2$ gives the displayed law. A horizon-area blackbody radiation estimate gives $\alpha =1/(15360\pi )$; greybody factors and species change it. With mass-dependent $\alpha$, integrate $t={\int }_{M(t)}^{M_0}{m}^{2}dm/\alpha (m)$ instead. The semiclassical gravity approximation fails near Planck mass, so a formal zero of the cubic law does not settle the final state.

Semiclassical gravity couples a classical spacetime metric to quantum matter. In its simplest expectation-value form, the classical gravitational field is sourced by the quantum expectation of the matter stress-energy tensor.