nLab ADM mass

Contents

Context

Gravity

gravity, supergravity

Formalism

Definition

Einstein-Hilbert action, Einstein's equations, general relativity
- first-order formulation of gravity, D'Auria-Fre formulation of supergravity
- gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity

Spacetime configurations

Properties

Spacetimes

black hole spacetimes	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild spacetime	Kerr spacetime
positive charge	Reissner-Nordstrom spacetime	Kerr-Newman spacetime

black hole spacetimes with dark energy	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild-de Sitter spacetime	Kerr-de Sitter spacetime
positive charge	Reissner-Nordström-de Sitter spacetime	Kerr-Newman-de Sitter spacetime

wormhole spacetimes	vanishing angular momentum
vanishing charge	Schwarzschild wormhole
positive charge	Reissner-Nordström wormhole

Quantum theory

quantum gravity
- graviton, gravitino
- string theory

Contents

Idea
Related concepts
References

Idea

In general relativity the ADM mass is a notion of total mass contained in asymptotically flat spacetimes.

Related concepts

positive energy theorem

References

Dan N. Vollick, On the Meaning of Various Mass Definitions for Asymptotically Flat Spacetimes [arXiv:2101.12570]

Textbook account:

Tomás Ortín; Conserved charges in general relativity, §4.3 in: Gravity and Strings, Cambridge University Press (2010, 2015) [doi:10.1017/CBO9780511616563, doi:10.1017/CBO9781139019750]

See also:

Wikipedia, ADM formalism

Towards relating to AdS/CFT duality for D=3 gravity:

Nele Callebaut, Blanca Hergueta: Radial canonical $\Lambda \lt 0$ gravity [arXiv:2503.18522]

Last revised on May 16, 2026 at 09:34:52. See the history of this page for a list of all contributions to it.