Metric tensor at second perturbation order for spherically symmetric space-times
arXiv:2308.14271 · doi:10.1142/S0219887823501074
Abstract
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse radial one unless the underlying potential is inversely proportional to the radial coordinate. At the weak field limit of approximation, a general formula is calculated and applied to some useful cases.
5 pages, published in the International Journal of Geometric Methods in Modern Physics