Authors: Steven Kenneth Kauffmann
It has recently been shown that self-gravitation reduces static spherically-symmetric cumulative energy distributions below the value of their radii times the "Planck force", which is the inverse of G times the fourth power of c. In this article quantitative treatment of self-gravitation is extended to any static energy density that is nonnegative, smooth and globally integrable. The resulting dimensionless local gravitational energy-reduction factor (namely the inverse of the local gravitational time-dilation factor) is shown to satisfy the zero-momentum nonrelativistic Lippmann-Schwinger quantum scattering equation for a repulsive potential which is proportional (with a known coefficient) to that static energy density. Standard perturbative Born-type iteration of Lippmann-Schwinger equations can diverge for sufficiently strong potentials, which in the gravitational case correspond to sufficiently large static energy densities. We have been able, however, to devise an alternate, completely nonperturbative iteration method for Lippmann-Schwinger equations in coordinate representation. Every one of this nonperturbative method's successive approximations to the local gravitational energy-reduction factor turns out to be positive and less than or equal to unity. In consequence, the self-gravitationally corrected static energy contained in any sphere is bounded by that sphere's diameter times the "Planck force".
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[v1] 2012-12-21 00:50:41
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