A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.
Günther,Skyrmion spacetime defect, degenerate metric, and negative gravitational mass, Master’s thesis, Karlsruhe Institute of Technology, September 2017
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Energy conditions in static, spherically symmetric spacetimes and effective geometries
A logarithmic correction to Schwarzschild in static spherical symmetry obeys all classical energy conditions and serves as an effective exterior for horizon-bearing and horizonless compact objects.