Quantum geometrodynamics: whence, whither?

TL;DR

Quantum geometrodynamics, centered on the Wheeler--DeWitt equation, remains a viable approach to quantum gravity, offering insights into the problem of time, covariant relations, and applications in black holes and cosmology.

Contribution

This paper provides an overview of the current status and challenges of quantum geometrodynamics, emphasizing its ongoing relevance and potential in quantum gravity research.

Findings

Quantum geometrodynamics addresses the problem of time.

It maintains a connection with covariant quantum gravity.

Applications include black hole physics and cosmology.

Abstract

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.