The discussion centers on the nature of curvature in accelerating frames, particularly in relation to the Ricci and Riemann tensors in vacuum space. Participants explore the implications of these tensors in the context of general relativity, the equivalence principle, and coordinate transformations between curved and flat spacetime.
Participants express differing views on the implications of the Ricci and Riemann tensors in accelerating frames, with no consensus reached on whether an accelerating frame can be considered flat or how the equivalence principle applies in this context. Multiple competing views remain regarding the interpretation of curvature and coordinate systems.
Limitations include unresolved mathematical steps regarding the implications of the Ricci tensor and the nature of spacetime in accelerating frames. The discussion also highlights the dependence on definitions of flatness and the properties of spacetime versus coordinate systems.
This is cool, yes it should violate it unless ##\nabla^2\Phi## is zero which it is according to the definition of Lapalacisn operator. Thank you.PeterDonis said:I'll respond to this with another question: how can ##\nabla^2 \Phi## be nonzero when ##\rho## is zero, which it is everywhere outside the source? Doesn't that violate Poisson's equation?
(Hint: you might want to check the actual definition of the Laplacian operator ##\nabla^2## in spherical coordinates.)