TL;DR
This paper explores solutions to quadratic gravity field equations in five-dimensional Kasner brane spacetimes, revealing vacuum solutions, brane configurations with vanishing bulk Einstein tensor, and matter trapping phenomena.
Contribution
It introduces new exact solutions in quadratic gravity for Kasner branes and analyzes matter trapping using energy conditions.
Findings
Double Kasner space admits a vacuum solution.
Certain brane solutions resemble radiation-dominated cosmology.
Matter trapping is feasible under specific energy conditions.
Abstract
Solutions are found to field equations constructed from the Pauli, Bach and Gauss-Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four branes a solution similar to radiation Robertson-Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.
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