The square of the norm of is
Therefore, is null only on the hyperplanes of equations
that, taken together, are the Killing horizons generated by .
Associated to a Killing horizon is a geometrical quantity known as surface gravity, . If the surface gravity vanishes, then the Killing horizon is said to be degenerate.
Black hole Killing horizonsEdit
In the usual coordinates, outside the Killing horizon, the Killing vector field is timelike, whilst inside it is spacelike. The temperature of Hawking radiation is related to the surface gravity by with the Boltzmann constant.
Cosmological Killing horizonsEdit
De Sitter space has a Killing horizon at which emits thermal radiation at temperature .
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