What is the gravitational redshift inside a thin hollow sphere?

Question

Suppose we have a thin hollow sphere of mass M and radius R. Suppose a photon is emitted towards the centre of the sphere. What would be the gravitational redshift an observer would see in the photon at any point between the edge and the centre?

Related: Is spacetime flat inside a spherical shell? – Qmechanic Jan 27 '23 at 15:55 — Qmechanic, Jan 27 '23 at 15:55

score 3 · Answer 1 · answered Jan 27 '23 at 15:13

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Any redshift effects are constrained to comparisons between the outside of the sphere and the inside. Within the sphere, Birchoff's theorem (the GR generalization of Gauss's law) tells us that the spacetime is locally Minkowski everywhere, and therefore, there are no gravitational effects.

answered Jan 27 '23 at 15:13

Zo the Relativist

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Thanks, Jerry. Does that mean a photon will just travel from one side of the sphere to the other and lose no energy at all? – MattEdwards Jan 27 '23 at 20:46

What is the gravitational redshift inside a thin hollow sphere?

1 Answers1