Accelerated reference systems in AdS space

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Accelerated reference systems in AdS space. / Manida, S. N.; Chaikovskii, M. E.

In: Theoretical and Mathematical Physics(Russian Federation), Vol. 190, No. 3, 01.03.2017, p. 424-430.

Research output: Contribution to journal › Article › peer-review

Author

Manida, S. N. ; Chaikovskii, M. E. / Accelerated reference systems in AdS space. In: Theoretical and Mathematical Physics(Russian Federation). 2017 ; Vol. 190, No. 3. pp. 424-430.

BibTeX

@article{46b18eba509a4f7285f68d81c222328d,

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 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 = "anti-de Sitter space, Beltrami coordinates, relativistic kinematics, Rindler coordinates",

author = "Manida, {S. N.} and Chaikovskii, {M. E.}",

note = "Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd.",

year = "2017",

month = mar,

day = "1",

doi = "10.1134/S0040577917030114",

language = "English",

volume = "190",

pages = "424--430",

journal = "Theoretical and Mathematical Physics (Russian Federation)",

issn = "0040-5779",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Accelerated reference systems in AdS space

AU - Manida, S. N.

AU - Chaikovskii, M. E.

PY - 2017/3/1

Y1 - 2017/3/1

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 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.

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 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.

KW - anti-de Sitter space

KW - Beltrami coordinates

KW - relativistic kinematics

KW - Rindler coordinates

UR - http://www.scopus.com/inward/record.url?scp=85016819197&partnerID=8YFLogxK

U2 - 10.1134/S0040577917030114

DO - 10.1134/S0040577917030114

M3 - Article

AN - SCOPUS:85016819197

VL - 190

SP - 424

EP - 430

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -

ID: 97790352