Quantum Gravity and String Theory

    

On the Geometrization of Quantum Mechanics, Frozen Stars, the Bohm-Poisson and Nonlinear Klein-Gordon Equations

Authors: Carlos Castro

We revisit the nonlinear Klein-Gordon-like equation that was proposed by us which capture how quantum mechanical probability densities curve spacetime, and find an exact solution that may appear to be ``trivial" but with important physical implications related to the physics of frozen stars and with Mach's principle. The nonlinear Klein-Gordon-like equation is essentially the static spherically symmetric relativistic analog of the Newton-Schr"{o}dinger equation. We finalize by studying the higher dimensional generalizations of the nonlinear Klein-Gordon-like equation and examine the relativistic Bohm-Poisson equation as yet another equation capturing the interplay between quantum mechanical probability densities and gravity.

Comments: 14 Pages.

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Submission history

[v1] 2024-05-07 08:07:21

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