Significance of c/sqrt(2) in Relativistic Physics

Abstract

In the description of \emph{relative} motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation can be simply illustrated in the case of motion in one dimension. For one-dimensional motion, such first-order accelerations are multiplied by $(1-V^2/V_c^2)$, where $V_c=c/\sqrt{2}$ is the critical speed. If the speed of relative motion exceeds $V_c$, there is a sign reversal with consequences that are contrary to Newtonian expectations.

arXiv comment7 pages, 1 figure, slightly expanded version accepted for publication in Class. Quantum Grav

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• Double-Kasner Spacetime: Peculiar Velocities and Cosmic Jets
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• A Gravitational Mechanism for the Acceleration of Ultrarelativistic Particles
• Comment on "Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field" [Astropart. Phys. 86 (2017) 18-20]
• Gravitational clock compass in General Relativity