The field strength of gravitational fields around neutron stars is extremely high. This would lead to an extreme negative value for the energy density. But if an absolute negative energy density is not possible because gravitational waves contain a positive energy, this negative energy density must be compensated. The compensation would be something like dark energy and would be omnipresent. The gravitational field of earth would reduce the energy density of this dark energy field by a factor $f$ with $f=(1.0-4.0$E-22). (The gravitational field around neutron stars is about 2.0E+11 times stronger as the earth field.)
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$\begingroup$ Hi, welcome to Physics SE. If there's any way for your question to make sense (I'm not sure there is, but it depends on what you're asking), the answer will be some multiple of $GM^2/R^4$, depending on internal composition. $\endgroup$– J.G.Commented Jul 5 at 8:25
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