1

If we defined spacetime as a purely geometrical (not physical) structure of the kind that is in general relativity (a 4-dimensional Lorentzian manifold), would it automatically have properties that would behave like energy and momentum in Einstein field equations?

I am wondering whether the purely geometrical properties of a 4D Lorentzian manifold impose existence of matter (that is, properties that behave like energy and momentum).

From what I have read, it seems that the answer is no, and so energy and momentum seem to be encoded in the points of the manifold rather than in its geometry.

Qmechanic
  • 220,844
glidingforward
  • 11
  • 1

1 Answers1

0

Given a Lorentzian manifold, one can calculate $$ R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu}$$ If you want, you can declare that this quantity represents energy and momentum, and then the Einstein field equations are satisfied. Is this what you are asking?

Daniel
  • 1,184