Outside the surface of a non-rotating neutron star

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Differential geometry of curved spacetime · Einstein's field equations

The Geometry of Gravity, Ch The Einstein field equations and the Newtonian limit

Problem

Outside the surface of a non-rotating neutron star, in the vacuum region where no matter or radiation is present and Λ\Lambda can be taken as zero, someone argues: "The field equations say Rμν=0R_{\mu\nu}=0 here, so spacetime must be flat, and there can be no tidal stretching of an orbiting satellite." ((a)) Use the trace-reversed field equations to confirm that Rμν=0R_{\mu\nu}=0 in this vacuum region. ((b)) Explain why Rμν=0R_{\mu\nu}=0 does not imply that the Riemann tensor RρσμνR^\rho{}_{\sigma\mu\nu} vanishes, and hence why the claim above is wrong.

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