Psi function

2013-08-14T17:11:49Z

85.26.186.122:

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A '''Killing horizon''' is a [[null hypersurface]] defined by the vanishing of the norm of a [[Killing vector]] field (both are named after [[Wilhelm Killing]]). (Notice that in the case of flat space time Killing vectors are null all over the space time, so they do not define a hypersurface and we have no Killing horizon.)

Associated to a Killing horizon is a geometrical quantity known as [[surface gravity]], <math>\kappa</math>. If the surface gravity vanishes, then the Killing horizon is said to be degenerate.

== Black hole Killing horizons ==

Exact black hole metrics such as the [[Kerr-Newman metric]] contain Killing horizons which coincide with their [[event horizon]]s. It should be emphasized, however, that these two notions of horizon are independent. For this spacetime, the Killing horizon is located at

<math>r = r_+ := M + \sqrt{M^2 - Q^2 - J^2/M^2}</math>.

In the usual coordinates, outside the Killing horizon, the [[Killing vector]] field <math>\partial / \partial t</math> is timelike, whilst inside it is spacelike. The temperature of [[Hawking radiation]] is related to the [[surface gravity]] by <math>T_H = \kappa / 2 \pi</math>.

== Cosmological Killing horizons ==

[[De Sitter space]] has a Killing horizon at <math>r = \sqrt{3 / \Lambda}</math> which emits thermal radiation at temperature <math>T = (1 / 2 \pi) \sqrt{\Lambda / 3}</math>.

[[Category:Mathematical physics]]

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Psi function