Killing horizon


A Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field.
In Minkowski space-time, in pseudo-Cartesian coordinates with signature an example of Killing horizon is provided by the Lorentz boost
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 horizons

Exact black hole metrics such as the Kerr–Newman metric contain Killing horizons which coincide with their ergospheres. For this spacetime, the Killing horizon is located at
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 horizons

has a Killing horizon at which emits thermal radiation at temperature.