Quantum Gravity and String Theory


On Finsler Geometry, MOND and Diffeomorphic Metrics to the Schwarzschild Solution

Authors: Carlos Castro

We revisit the construction of diffeomorphic but $not$ isometric solutions to the Schwarzschild metric. The solutions relevant to Black Holes are those which require the introduction of non-trivial areal-radial functions that are characterized by the key property that the radial horizon's location is $displaced$ continuously towards the singularity ($ r = 0 $). In the limiting case scenario the location of the singularity and horizon $merges$ and any infalling observer hits a null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the firewall problem and the complementarity controversy in black holes. Next we show how modified Newtonian dynamics (MOND) can be obtained from solutions to Finsler gravity, and which in turn, can also be modeled by metrics which are diffeomorphic but not isometric to the Schwarzschild metric. The key point now is that one will have to dispense with the asymptotic flatness condition, by choosing an areal radial function which is $finite$ at $ r = \infty$. Consequently, changing the boundary condition at $ r = \infty$ leads to MONDian dynamics. We conclude with some discussions on the role of scale invariance and Born's Reciprocal Relativity Theory based on the existence of a maximal proper force.

Comments: 18 Pages. Submitted to IJGMMP

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Submission history

[v1] 2018-06-01 05:58:33

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