Geometrization of Heat Conduction in Perturbative Spacetimes

We prove that the problem of symmetry determination linked to first-order perturbations of a metric, can be elegantly expressed using geometric conditions. In particular, an important feature of this study is that for any spacetime that contains small perturbations, any equation constructed on such a space will inherit the perturbations. Intrigued by this connection between geometry and perturbations, we take the heat conduction equation and explore how the inherited perturbations affect the geometric symmetry conditions.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author