Boyer-Lindquist coordinates
Encyclopedia
A generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.

The coordinate transformation from Boyer–Lindquist coordinates r, , to cartesian coordinates x, y, z is given by


The line element for a black hole with mass , angular momentum , and charge in Boyer–Lindquist coordinates and natural units
Natural units
In physics, natural units are physical units of measurement based only on universal physical constants. For example the elementary charge e is a natural unit of electric charge, or the speed of light c is a natural unit of speed...

 () is


where
, the angular momentum per unit mass of the black hole


Note that in natural units , , and all have units of length. This line element describes the Kerr-Newman metric
Kerr-Newman metric
The Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity, describing the spacetime geometry in the region surrounding a charged, rotating mass. It is assumed that the cosmological constant equals zero...

.

The Hamiltonian for test particle motion in Kerr spacetime was separable in Boyer–Lindquist coordinates. Using Hamilton-Jacobi theory one can derive a fourth constant of the motion known as Carter's constant
Carter constant
The Carter constant is a conserved quantity for motion around black holes in the general relativistic formulation of gravity. Carter's constant was derived for a spinning, charged black hole by Australian theoretical physicist Brandon Carter in 1968...

.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK