Non-Newtonian Limit Einstein Field Equations

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What do I have to do if I want the EFE's to approximate a weak gravitational field, where for example, an inversely proportional to the cube ( ##1 / r^3## ) of the distance law between the masses applies?
 

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Orodruin
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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.
 
  • #3
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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.
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.

Can I do the same for 3+1 dimensions?
 
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Orodruin
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In 5+1 dimensions the potential goes as ##1/r^3##. In 3+1 dimensions the potential goes as ##1/r##.
 

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