ACCELERATED REFERENCE SYSTEMS IN AdS SPACE

S. N. Manida, M. E. Chaikovskii

Research output ›

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 languageUndefined
Pages (from-to)422–428
JournalTheoretical and Mathematical Physics
Volume190
Issue number3
Publication statusPublished - 2017
Externally publishedYes

Cite this

Manida, S. N. ; Chaikovskii, M. E. / ACCELERATED REFERENCE SYSTEMS IN AdS SPACE. In: Theoretical and Mathematical Physics. 2017 ; Vol. 190, No. 3. pp. 422–428.
@article{2efcb87e6b2249f5ba1d4a7010b2731c,
title = "ACCELERATED REFERENCE SYSTEMS IN AdS SPACE",
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",
keywords = "Rindler coordinates, relativistic kinematics, anti-de Sitter space, Beltrami coordinates",
author = "Manida, {S. N.} and Chaikovskii, {M. E.}",
year = "2017",
language = "не определен",
volume = "190",
pages = "422–428",
journal = "Theoretical and Mathematical Physics",
issn = "0040-5779",
publisher = "Springer",
number = "3",

}

Manida, SN & Chaikovskii, ME 2017, 'ACCELERATED REFERENCE SYSTEMS IN AdS SPACE', Theoretical and Mathematical Physics, vol. 190, no. 3, pp. 422–428.

ACCELERATED REFERENCE SYSTEMS IN AdS SPACE. / Manida, S. N.; Chaikovskii, M. E.

In: Theoretical and Mathematical Physics, Vol. 190, No. 3, 2017, p. 422–428.

Research output ›

TY - JOUR

T1 - ACCELERATED REFERENCE SYSTEMS IN AdS SPACE

AU - Manida, S. N.

AU - Chaikovskii, M. E.

PY - 2017

Y1 - 2017

N2 - 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

AB - 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

KW - Rindler coordinates

KW - relativistic kinematics

KW - anti-de Sitter space

KW - Beltrami coordinates

M3 - статья

VL - 190

SP - 422

EP - 428

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 3

ER -

Manida SN, Chaikovskii ME. ACCELERATED REFERENCE SYSTEMS IN AdS SPACE. Theoretical and Mathematical Physics. 2017;190(3):422–428.