A planar perturbation of the Bianchi type I metric

The standard procedure for finding analytic perturbations in General Relativity suffers from the drawback that it is cumbersome to use beyond linear order perturbations. Following up on our previous work, we continue to use an alternate method of finding perturbations. We find a plane symmetric perturbation of the cosmological Bianchi type I metric. The perturbation corresponds to a fluid with heat flow moving perpendicularly to a singular plane in a region which can be made to be either overdense or underdense relative to the background spacetime. The fluid satisfies both the Strong and Dominant energy conditions everywhere except the region close to the singularity.