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In General > minkowski space.
* Idea: Minkowski spacetime
with coordinates adapted to a boost Killing vector field, i.e., to a uniformly
accelerated observer.
* Coordinates: If (X,
T) are the Minkowski coordinates, Rindler coordinates (x, t)
are defined on the right wedge (X > 0, |T| < |X|) by
X = g−1 egx cosh gt , T = g−1 egx sinh gt ,
and coordinates (x', t') on the left wedge (X < 0, |T| < |X|) are defined by
X = −g−1 egx' cosh gt' , T = −g−1 egx' sinh gt' ;
In either case, the inverse transformation is given by
t, t' = g−1 tanh−1(T/X) , x, x' = (2g)−1 ln[g2(X 2 − T 2)] ;
The lines t = constant are straight half-lines, while x = constant are
hyperbolae of acceleration g e−gx.
* Line element: Given by
ds2 = e2gx (−dt2 + dx2) ,
so proper time is related to coordinate time by τ
= egx t.
@ General references:
Born AdP(09) [precursor];
Rindler AJP(66)dec;
Felix da Silva & Dahia IJMPA(07) [non-Euclidean geometry of spatial sections].
@ Related topics: Kowalski-Glikman PRD(09)-a0907 [deformed, κ-Rindler space];
Daszkiewicz MPLA(10)-a1004 [twisted];
Chung PRD(10) [asymptotic symmetries];
Bianchi & Satz PRD(13)-a1305 [mechanical laws of the Rindler horizon];
Araya & Bars PRD(18)-a1712
[infinite stack of identical Minkowski geometries as a multiverse model];
> s.a. black-hole geometry [interior];
modified theories of gravity [Rindler force];
tests of general relativity [Rindler-type acceleration].
> Online resources:
see Wikipedia page;
't Hooft page
with animated gif on Rindler coordinates.
And Classical Field Theory > see dirac fields.
And Quantum Theory > s.a. gravitational thermodynamics.
* Idea: The Minkowski
vacuum looks like a thermal state in Rindler space, for an observer moving
along x = constant, with temperature depending on its acceleration;
This makes it useful for mimicking black-hole radiation.
@ Thermal properties: Fulling PRD(73);
Unruh PRD(76);
Lapedes JMP(78);
Dray & Manogue pr(87);
Laflamme PLB(87);
Nikolić MPLA(01)gq [criticism of use];
Xiang & Zheng IJTP(01) [horizon entropy];
Socolovsky a1304 [application to the Unruh effect];
Kolekar & Padmanabhan PRD(14)-a1309 [Rindler-Rindler spacetime];
Chowdhury et al PRD-a1902 [and thermal bath];
Padmanabhan a1905 [simple derivation];
> s.a. radiation; quantum field theory in curved backgrounds.
@ Quantum mechanics: Dai PLA(16)-a1609 [hydrogen atom energy eigenvalues and wave functions].
@ Quantum field theory: Michel a1612 [quantization of scalar and gauge fields];
> s.a. mirrors.
@ Related topics:
Balasubramanian et al JHEP(13) [entropy of a "spherical Rindler space" hole in spacetime].
> Related topics:
see quantum technology [communication].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 22 may 2019