Green's functions for a static charge in a weakly-curved spacetime
We present our calculation of the Green's function for a static scalar and electric charge in a weakly-curved spacetime. We find that to leading order the scalar Green's function reduces to the Green's function for the Poisson equation in Euclidean space. We also calculate the next order correction in the scalar Green's function. We also present the recurrence relation for the Green's function of static electric charge. The calculations that we present here are needed to modernize the self-force expressions in a weakly-curved spacetime.
By submitting their manuscript to the Samahang Pisika ng Pilipinas (SPP) for consideration, the Authors warrant that their work is original, does not infringe on existing copyrights, and is not under active consideration for publication elsewhere.
Upon acceptance of their manuscript, the Authors further agree to grant SPP the non-exclusive, worldwide, and royalty-free rights to record, edit, copy, reproduce, publish, distribute, and use all or part of the manuscript for any purpose, in any media now existing or developed in the future, either individually or as part of a collection.
All other associated economic and moral rights as granted by the Intellectual Property Code of the Philippines are maintained by the Authors.