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It is well-known that Birkhoff's theorem is no longer valid in theories withmore than four dimensions. Thus, in these theories the effective 4-dimensionalpicture allows the existence of different possible, non-Schwarzschild,scenarios for the description of the spacetime outside of a spherical star,contrary to general relativity in 4D. We investigate the exterior spacetime ofa spherically symmetric star in the context of Kaluza-Klein gravity. We take awell-known family of static spherically symmetric solutions of the Einsteinequations in an empty five-dimensional universe, and analyze possible stellarexteriors that are conformal to the metric induced on four-dimensionalhypersurfaces orthogonal to the extra dimension. All these exteriors arecontinuously matched with the interior of the star. Then, without making anyassumptions about the interior solution, we prove the following statement: thecondition that in the weak-field limit we recover the usual Newtonian physicssingles out an unique exterior. This exterior is "similar" to Scharzschildvacuum in the sense that it has no effect on gravitational interactions.However, it is more realistic because instead of being absolutely empty, it isconsistent with the existence of quantum zero-point fields. We also examine thequestion of how would the deviation from the Schwarzschild vacuum exterioraffect the parameters of a neutron star. In the context of a model star ofuniform density, we show that the general relativity upper limit M/R < 4/9 issignificantly increased as we go away from the Schwarzschild vacuum exterior.We find that, in principle, the compactness limit of a star can be larger than1/2, without being a black hole. The generality of our approach is alsodiscussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum  Gravit

Exterior spacetime for stellar models in five-dimensional Kaluza–Klein gravity