The discussion centers on the properties of the Ricci and Riemann tensors in the context of accelerating frames and curved spacetime. It is established that both the Ricci tensor and the Riemann tensor are zero in an accelerating frame within a vacuum space, indicating that the spacetime remains flat despite the non-inertial coordinates. The equivalence principle is clarified, emphasizing that gravitational effects can be perceived without intrinsic curvature. The conversation also touches on the implications of these tensors for local inertial frames and the calculation of geodesics.
PREREQUISITESPhysicists, mathematicians, and students of general relativity seeking to deepen their understanding of spacetime curvature, tensor calculus, and the implications of non-inertial frames in gravitational contexts.
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.)