Abstract
Exact self-similar solutions to Einstein’s field equations for the Kantowski-Sachs space-time are determined. The self-similarity property is applied to determine the functional form of the unknown functions that define the gravitational model and to reduce the order of the field equations. The consequences of matter, described by the energy-momentum tensor, are investigated in the case of a perfect fluid. Some physical features and kinematical properties of the obtained model are studied.
Highlights
Space-time symmetries are important in identifying features of space-time that exhibit some kind of symmetry
The most important symmetries are those that simplify Einstein’s field equations and provide a space-time classification based on the corresponding Li-algebra configuration
In the context of the theory of General Relativity (GR), symmetries have been studied based on Riemannian geometry and on Lyra geometry and in the framework of the theory of teleparallel gravity based on Weitzenböck geometry
Summary
Space-time symmetries are important in identifying features of space-time that exhibit some kind of symmetry. The most important symmetries are those that simplify Einstein’s field equations and provide a space-time classification based on the corresponding Li-algebra configuration These symmetries preserve certain physical properties of space-time, such as metric, geodesic, curvature, Ricci scalar, and energy-momentum tensor. One chooses a specific energy-momentum tensor model and studies the exact solutions corresponding to Einstein’s field equations while assuming some physically acceptable properties on the scale factors. We will focus our attention on the study of the homothetic symmetry of a Kantowski-Sachs space-time and solve Einstein’s field equations without making assumptions, either on variables or on physical properties, as is common in the literature.
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