Rindler Space

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 e^gx cosh gt ,      T = g⁻¹ e^gx sinh gt ,

and coordinates (x', t') on the left wedge (X < 0, |T| < |X|) are defined by

X = −g⁻¹ e^gx' cosh gt' ,      T = −g⁻¹ e^gx' 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 = e^2gx (−dt² + dx²) ,

so proper time is related to coordinate time by τ = e^gx 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].

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