Stationary trajectories in Minkowski spacetimes

Abstract

We determine the conjugacy classes of the Poincaré group ${\mathrm{ISO}}^{+}(n,1)$ and apply this to classify the stationary trajectories of Minkowski spacetimes in terms of timelike Killing vectors. Stationary trajectories are the orbits of timelike Killing vectors and, equivalently, the solutions to Frenet-Serret equations with constant curvature coefficients. We extend the $3+1$ Minkowski spacetime Frenet-Serret equations due to Letaw to Minkowski spacetimes of arbitrary dimension. We present the explicit families of stationary trajectories in $4+1$ Minkowski spacetime.

13 pages. v2: Added sentence to Section II B 2. after referee comments

References in corpus (2)

• Circular motion analogue Unruh effect in a $2+1$ thermal bath: Robbing from the rich and giving to the poor
• Skew-symmetric endomorphisms in ${\mathbb{M}}^{1,n}$: A unified canonical form with applications to conformal geometry

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