Godel type metrics in three dimensions

作者：Guerses Metin

来源：General Relativity and Gravitation, 2010, 42(6): 1413-1426.

DOI：10.1007/s10714-009-0914-7

• Godel type metrics
• Topologically massive gravity
• Einstein's equations in three dimensions
• Ricci and Cotton flows
• Einstein-perfect fluid solutions

We show that the Godel type metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. We also show that 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 Godel type metrics to solve the Ricci and Cotton flow equations. When the vector field u (mu) is a Killing vector field, we came to the conclusion that the stationary Godel 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.

• 出版日期2010-6