General relativity in two- and three-dimensional space–times

1977/09/01 by Peter Collas · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #Curvature #De Sitter space #De Sitter universe #General relativity #Geometry #Mathematical physics #Mathematics #One-dimensional space #Physics #Quantum mechanics #Relativity and Gravitational Theory #Space (punctuation) #Spacetime #Special relativity #Surface (topology) #Theoretical physics #Theory of relativity #Universe

paper · doi:10.1119/1.11057

openalex publication_date 1977/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

We consider the general relativity field equations in two- and three-dimensional space–times. We find that in a two-dimensional space–time we can have curvature but not matter. In a three-dimensional space–time we find that empty space must be flat, that a de Sitter solution exists, and that finite mass distributions with constant surface density must have zero ’’surface tension.’’ Finally, an expanding dust-filled universe turns out to be like Milne’s model.

Cited by

• General relativity in (1 + 1) dimensions
• Notes on a conformal characterization of 2-dimensional Lorentzian\n manifolds with constant Ricci scalar curvature
• Two Dimensional Conformal Symmetry and the Microscopic Interpretation of Black Hole Entropy
• A positive mass theorem for two spatial dimensions
• The causal structure of two-dimensional spacetimes

Related

• General Relativity as a SO(3) Gauge-Theory
• Dynamics of empty homogeneous isotropic three-dimensional spaces
• Matter from Space
• General Relativity Contains the Standard Model
• General Relativity Requires Absolute Space and Time