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In Newtonian Mechanics, the energy density of gravitational field is negative in comparison with the positive energy density assigned to mass density, meaning that that the total positive energy of matter occurring in a gravitational field is smaller than its positive energy without this gravity field.

For an extreme dense mass object, the negative energy of its self-gravity field may reach such value that the sum of total energies is equal to zero. This is the case for a sphere of constant mass density with a much smaller radius than the Schwarzschild radius.

Considering that General Relativity is approximated by Newtonian mechanics in the weak field, could this negative energy contribution solve the gravitational singularities inside black holes?

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    $\begingroup$ Black hole is relativistic and gravitational PE or self energy doesn't appear here $\endgroup$
    – paul230_x
    Commented Dec 5, 2023 at 20:47
  • $\begingroup$ @KP99 Yes, in General Relativity, the gravitational field energy density (or PE or self energy) is not included explicitly in the field equations (one could argue it is included in the nonlinearities of the field equations themselves), but we know gravity must gravitate similarly to PE or self energy in Newtonian gravity. $\endgroup$
    – Manuel
    Commented Dec 6, 2023 at 15:17
  • $\begingroup$ @safesphere All energy must gravitate. Einstein tried in 1913 to include the gravitational field energy density into his field equations, but failed to do so. A black hole singularity implies geodesic incompleteness, which could be solve by means of negative energy such as PE energy. $\endgroup$
    – Manuel
    Commented Dec 7, 2023 at 13:52

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