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arXiv · 2403.16229

Non-inertial frames that can mimic gravitational fields

Dawood Kothawala
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Abstract

One version of the principle of equivalence, as originally formulated by Einstein, states that ``gravity" can be mimicked locally by going to an ``accelerated frame of reference". As highlighted by Synge, the physical content of this principle remains obscure in so far as it does not refer to the Riemann tensor $R_{abcd}$, which encodes the true effects of gravity. We here give the acceleration profile of a $Born$ rigid, Rindler$esque$, frame that can mimic a gravitational field corresponding to a given $R_{abcd}$. The generalised deviation equation that yields this result also has Centrifugal and Coriolis terms appearing in a purely relational context, yielding a similar connection between angular velocity of rotating, rigid inertial frames and the Riemann tensor. We comment briefly on implications for Mach principle.

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Dawood Kothawala. 2024-03-24. Non-inertial frames that can mimic gravitational fields. https://doi.org/10.1103/physrevd.110.l121502

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