Gödel Type Metrics in Three Dimensions

Abstract

We show that the G{\" o}del type Metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. There exists only one first order partial differential equation satisfied by the components of fluid's velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the G{\" o}del Type Metrics to solve the Ricci and Cotton flow equations. When the vector field $u^{\mu }$ is a Killing vector field we finally show that the stationary G{\" o}del Type Metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors.

17 pages

References in corpus (7)

• Massive Gravity in Three Dimensions
• Solutions to Horava Gravity
• Three-dimensional Chern-Simons black holes
• Cosmology in three dimensions: steps towards the general solution
• Closed timelike curves and geodesics of Godel-type metrics
• Cotton flow
• Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field

Cited by in corpus (7)

• Warped black holes in 3D general massive gravity
• Gravitational Anomalies in nAdS${}_2$/nCFT${}_1$
• The Dirac Equation in (1+2)-dimensional Gürses space-time backgrounds
• Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations
• Godel Type Metrics in Einstein-Aether Theory II: Nonflat Background in Arbitrary Dimensions
• More on Cotton Flow
• Homogeneous anisotropic solutions of topologically massive gravity with cosmological constant and their homogeneous deformations