Solar-System Bounds on Ricci-flat Spindle Deformations of Schwarzschild

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Original abstract

Recently, a new class of deformed black-hole exact solutions was constructed in four-dimensional general relativity. The deformation is controlled by a parameter $B$, which survives after demagnetizing a black hole immersed in an external Bertotti-Robinson magnetic field and changes the global structure of the spacetime into a non-asymptotically flat spindle geometry. Although no astrophysical mechanism for generating such a deformation is currently known, it is natural to ask phenomenologically how large such a geometric deformation could be if it extended over the weak-field solar exterior. Using two classical Solar-System tests, we derive the leading corrections to planetary perihelion precession and to the light travel time in a Shapiro-type configuration. Requiring the \(B\)-induced perihelion advance to be smaller than the observational uncertainties in the supplementary perihelion precessions of planets gives the strongest bounds, \( |B|\lesssim 10^{-24}\text{--}10^{-23}\ {\rm cm}^{-1}\), while a Cassini time delay estimate gives a complementary null-geodesic sensitivity at the level \( |B|\lesssim 10^{-21}\ {\rm cm}^{-1}\). These results show that any such spindle deformation, if extended to the solar exterior geometry, must be extremely suppressed on Solar-System scales.

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• Official / arXiv page
• PDF from original source

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