No-hair Theorem - Changing The Reference Frame

Changing The Reference Frame

Every isolated unstable black hole decays rapidly to a stable black hole; and (modulo quantum fluctuations) stable black holes can be completely described (in a Cartesian coordinate system) at any moment in time by these eleven numbers:

• mass-energy M,
• linear momentum P (three components),
• angular momentum J (three components),
• position X (three components),
• electric charge Q.

These numbers represent the conserved attributes of an object which can be determined from a distance by examining its gravitational and electromagnetic fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole.

By changing the reference frame one can set the linear momentum and position to zero and orient the spin angular momentum along the positive z axis. This eliminates eight of the eleven numbers, leaving three which are independent of the reference frame. Thus any black hole which has been isolated for a significant period of time can be described by the Kerr–Newman metric in an appropriately chosen reference frame.