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 = const 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 = e^gx t.
@ References: Born AdP(09) [precursor]; Rindler AJP(66); Felix da Silva & Dahia IJMPA(07) [non-Euclidean geometry of spatial sections].

And Classical Field Theory > see dirac fields.

And Quantum Field 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); Nikolic MPLA(01)gq [criticism of use]; Xiang & Zheng IJTP(01) [horizon entropy]; > s.a. radiation; quantum field theory effects in curved spacetime.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 16 jun 2008