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Accelerated reference systems in $\mathrm{AdS}$ space
S. N. Manida, M. E. Chaikovskii St. Petersburg State University, St. Petersburg, Russia
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 construction 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 coordinate 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 Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical.
Keywords:
Rindler coordinates, relativistic kinematics, anti-de Sitter space, Beltrami coordinates.
Received: 15.12.2015
Citation:
S. N. Manida, M. E. Chaikovskii, “Accelerated reference systems in $\mathrm{AdS}$ space”, TMF, 190:3 (2017), 494–501; Theoret. and Math. Phys., 190:3 (2017), 424–430
Linking options:
https://www.mathnet.ru/eng/tmf9127https://doi.org/10.4213/tmf9127 https://www.mathnet.ru/eng/tmf/v190/i3/p494
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Abstract page: | 365 | Full-text PDF : | 136 | References: | 57 | First page: | 21 |
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