Spacetime can be represented minimally as an arbitrary set equipped with a family of real functions that, the author argues, retains the essential causal, topological, and metric content.
Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes
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abstract
We extend the classical Avez-Seifert theorem to trajectories of charged test particles with fixed charge-to-mass ratio. In particular, given two events x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, we find an interval I=]-R,R[ such that for any q/m in I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x_0 and x_1, we prove that to any value of |q/m| there correspond at least two connecting timelike solutions which coincide only if they are geodesics.
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gr-qc 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Destructuring Physics: A functional derivation of spacetime
Spacetime can be represented minimally as an arbitrary set equipped with a family of real functions that, the author argues, retains the essential causal, topological, and metric content.