5D thermal field theory, Einstein field equations and spontaneous symmetry breaking

It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which remains in local thermal equilibrium. This is achieved by examining the thermal field theory in a five-dimensional (5D) space-time-temperature. The bulk thermodynamic quantity, namely the energy density, is calculated for a neutral scalar field with a time-dependent Hamiltonian. Furthermore, the concept of recasting thermal variations as a variation in the metric is extended to thermal systems in a gravitational field. The Einstein field equations, in the 5D space-time-temperature, is determined. It is shown that, if the scalar Lagrangian is non-minimally coupled with gravity, the resulting Ricci scalar can lead to spontaneous symmetry breaking, leading to the Higgs mechanism. In essence, the asymmetry in the distribution of temperature in space-time can translate to spontaneous symmetry breaking of particle fields, in a very strong gravitational field.