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Title: Wick rotation in the tangent space
Authors: Samuel, J.
Keywords: Euclidean methods
Issue Date: Jan-2016
Publisher: IOP Publishing Ltd.
Citation: Classical and Quantum Gravity, 2016, Vol.33, p015006
Abstract: Wick rotation is usually performed by rotating the time coordinate to imaginary values. In a general curved spacetime, the notion of a time coordinate is ambiguous. We note here, that within the tetrad formalism of general relativity, it is possible to perform a Wick rotation directly in the tangent space using considerably less structure: a timelike, future pointing vector field, which need not be killing or hypersurface orthogonal. This method has the advantage of yielding real Euclidean metrics, even in spacetimes which are not static. When applied to a black hole exterior, the null generators of the event horizon reduce to points in the Euclidean spacetime. Requiring that the Wick rotated holonomy of the null generators be trivial ensures the absence of a 'conical singularity' in the Euclidean space. To illustrate the basic idea, we use the tangent space Wick rotation to compute the Hawking temperature by Euclidean methods in a few spacetimes including the Kerr black hole.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 0264-9381
1361-6382 (Online)
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Copyright: 2016 IOP Publishing Ltd.
Appears in Collections:Research Papers (TP)

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