Abstract
We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct
coordinate transformations for the transition from an inertial reference system to a uniformly accelerated
reference system for all acceleration values, both greater and less than critical. The basis for the con-
struction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion
because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described
by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian,
a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordi-
nate system of an accelerated observer using this auxiliary comoving inertial reference system requires
additional transformations that not only equalize the velocities of the two systems but also equalize the
system origins. The presence of a critical acceleration in anti-de Si
Original language | Undefined |
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Pages (from-to) | 422–428 |
Journal | Theoretical and Mathematical Physics |
Volume | 190 |
Issue number | 3 |
State | Published - 2017 |
Externally published | Yes |
Keywords
- Rindler coordinates
- relativistic kinematics
- anti-de Sitter space
- Beltrami coordinates