Cosmology in three dimensions: steps towards the general solution

Abstract

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the 3-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3-d cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3-d spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with non-zero (and zero) cosmological constant and generalise known solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3-d cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2+1 spacetimes.

35 pages, 2 figures

References in corpus (11)

• The Black Hole in Three Dimensional Space Time
• Gravitationally Collapsing Dust in $(2+1)$ Dimensions
• No Black Hole Theorem in Three-Dimensional Gravity
• Godel metric as a squashed anti-de Sitter geometry
• Dynamics and stability of the Godel universe
• Quasi-Spherical Gravitational Collapse in Any Dimension
• All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity
• (2+1) dimensional stars
• Gravitational Collapse of Inhomogeneous Dust in (2+1) Dimensions
• A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field
• Relationship between (2+1) and 3+1)--Friedmann--Robertson--Walker cosmologies

Cited by in corpus (27)

• Theory of cosmological perturbations in an anisotropic universe
• Predictions from an anisotropic inflationary era
• On the evolution of universes in quadratic theories of gravity
• Observational Constraints on New Exact Inflationary Scalar-field Solutions
• Some static spherically symmetric interior solutions of $f(R)$ gravity
• Gödel Type Metrics in Three Dimensions
• Mimetic $F(R)$ inflation confronted with Planck and BICEP2/Keck Array data
• Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions
• Finite Action Principle Revisited
• Piecewise Silence in Discrete Cosmological Models
• Szekeres Universes with Homogeneous Scalar Fields
• Scalar quantum fields in cosmologies with 2+1 spacetime dimensions
• Exact radial solution in 2+1 gravity with a real scalar field
• Three dimensional Eddington--inspired Born--Infeld gravity: solutions
• The generalized second law of thermodynamics for interacting $f(R)$ gravity
• All solutions of Einstein's equations in 2+1 dimensions: $\Lambda$-vacuum, pure radiation, or gyratons
• Dirac field as a source of the inflation in 2+1 dimensional Teleparallel gravity
• Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations
• Particle creation in (2+1) circular dust collapse
• (2+1) dimensional cosmological models in f(R; T) gravity with $\Lambda$(R; T)
• Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term
• Existence of Life in 2 + 1 Dimensions
• New Spacetimes for Rotating Dust in (2+1)-Dimensional General Relativity
• On scalar curvature invariants in three dimensional spacetimes
• Quantum dust collapse in 2+1 dimensions
• Radiation in (2+1)-dimensions
• On the asymptotics of 3+1D cosmologies with bounded scalar potential and isometry group forming 2-dimensional orbits