Non-inertial frames that can mimic gravitational fields

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.

v1: 7 pages, 2 figures; v2: version accepted in PRD Letters

References in corpus (1)

• Effect of tidal curvature on dynamics of accelerated probes

Cited by in corpus (2)

• Entanglement between accelerated probes in a de Sitter spacetime
• Velocity effects slightly mitigating the quantumness degradation of an Unruh-DeWitt detector