Area Invariance of Apparent Horizons under Arbitrary Boosts

Understand

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $ t=constant $ slice, which can be quite arbitrary in general relativity.

• Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames.
• Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes.
• In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form.