The discussion revolves around the application of Einstein's Field Equations (EFE) in the context of weak gravitational fields, specifically exploring the implications of a gravitational force that varies inversely with the cube of the distance (##1/r^3##). Participants are examining the theoretical framework and dimensional considerations necessary to achieve such a potential.
Participants exhibit disagreement regarding the feasibility of achieving a ##1/r^3## gravitational potential within the framework of 3+1 dimensions, with some asserting the necessity of higher dimensions while others explore the implications of their proposals.
The discussion highlights the dependence on dimensionality for gravitational potentials and the unresolved nature of how to reconcile non-Newtonian laws with general relativity in lower dimensions.
Yes, that's exactly what I mean, I want to begin with a non-Newtonian law of universal gravitation let's say: ## F = GMm/r^3 ## then find a curved spacetime (5 + 1 dimensions) to approximate this law in weak gravitational fields.Orodruin said:What should go as ##1/r^3##? This is not really a question of GR, it is a question of the solutions to the Laplace equation, which depends on the number of dimensions. For example, to get a potential that goes as ##\sim 1/r^3## you would need to add two additional spatial dimensions.