S. Deser

Republication of: The dynamics of general relativity

This article—summarizing the authors’ then novel formulation of General Relativity—appeared as Chap. 7, pp. 227–264, in Gravitation: an introduction to current research, L. Witten, ed. (Wiley, New York, 1962), now long out of print. Intentionally unretouched, this republication as Golden Oldie is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed–but not section nor equation numbering, etc. Current institutional affiliations are encoded in: arnowitt@physics.tamu.edu, deser@brandeis.edu, misner@umd.edu.

Three-dimensional Einstein gravity: dynamics of flat space

In three spacetime dimensions, the Einstein equations imply that source-free regions are flat. Localized sources can therefore only affect geometry globally rather than locally. Some of these effects, especially those generated by mass and angular momentum are discussed.

Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress-tensors

We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.

Three-Dimensional Cosmological Gravity: Dynamics of Constant Curvature

In three space-time dimensions, Einsteins equations with cosmological constant Λ imply that the curvature is constant outside sources. When particles are present, they alter the global properties of the exterior geometry. In the De Sitter case, space is a two-sphere and static many-body solutions are quite different from their Λ = 0 counterparts; in particular particles lie at antipodal points, with the great-circle wedge between them excised. These configurations are analyzed in terms of the general static solution to the exterior field equations.

“Self-duality” of topologically massive gauge theories

Abstract A recently proposed “self-dual” massive model is shown to be equivalent to topologically massive electrodynamics, even in the presence of external sources. The non-abelian generalization is also discussed.

Consistency problems of hypergravity

Abstract The constraints arising upon coupling a massless spin 5 2 field to gravity are analyzed. In contrast to supergravity, they depend not only on the Einstein tensor, but also on the off-shell (Weyl) components of the curvature. The latter contributions do vanish, however, for “self-dual” systems, i.e., half-flat gravitational and pure (left/right) helicity spin 5 2 fields.

Gauge invariance versus masslessness in de Sitter spaces

Abstract The connection between gauge invariance, masslessness and null cone propagation is a flat space property which does not persist even in constant curvature geometries. In particular, we show that both the gauge invariant spin 3 2 and 2 fields in anti-de Sitter space have support inside the cone, whereas where are conformally invariant, but gauge variant, models which do propagate on the light cone. The Maxwell field in constant curvature spaces of dimension other than four also does not have null cone propagation; again there is a conformally invariant model which does.

Scale invariance and gravitational coupling

A variant of General Relativity provides a model in which scale invariance of matter is a consistency requirement on its coupling to gravitation. Invariance breaking is introduced by giving a finite (cosmological) range to one of the gravitational variables; the Einstein and cosmological constants are then approximately determined by the average mass-density of the universe.

Stability of massive cosmological gravitons

We analyze the physics of massive spin-2 fields in (A)dS backgrounds and exhibit that: The theory is stable only for masses m2⩾2Λ/3, where the conserved energy associated with the background timelike Killing vector is positive, while the instability for m^2<2Λ/3 is traceable to the helicity 0 energy. The stable, unitary, partially massless theory at m^2=2Λ/3 describes 4 propagating degrees of freedom, corresponding to helicities (±2,±1) but contains no 0 helicity excitation.

Topologically massive supergravity

Abstract The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial) Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The systems energy, as well as that of the original topological gravity, is therefore positive.