navyguy
03-07-2008, 12:36 AM
Kerr metric (or Kerr vacuum) describes the geometry of spacetime around a rotating massive body. According to this metric, such rotating bodies should exhibit frame dragging, an unusual prediction of general relativity; measurement of this frame dragging effect is a major goal of the Gravity Probe B experiment. Roughly speaking, this effect predicts that objects coming close to a rotating mass will be entrained to participate in its rotation, not because of any applied force or torque that can be felt, but rather because the curvature of spacetime associated with rotating bodies. At close enough distances, all objects — even light itself — must rotate with the body; the region where this holds is called the ergosphere.
The Kerr metric is often used to describe rotating black holes, which exhibit even more exotic phenomena. Such black holes have two event horizons where the metric appears to have a singularity. The outer horizon encloses the ergosphere and has an oblate spheroid shape, a flattened sphere similar to a discus. The inner horizon is spherical and marks the "radius of no return"; objects passing through this radius can never again communicate with the world outside that radius. Objects between these two horizons must co-rotate with the rotating body, as noted above; this feature can be used to extract energy from a rotating black hole, up to its invariant mass energy, Mc2. Even stranger phenomena can be observed within the innermost region of this spacetime, such as some forms of time travel. For example, the Kerr metric permits closed, time-like loops in which a band of travellers returns to the same place after moving for a finite time by their own clock; however, they return to the same place and time, as seen by an outside observer.
The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find. The Kerr metric is a generalization of the Schwarzschild metric, which was discovered by Karl Schwarzschild in 1916 and which describes the geometry of spacetime around an uncharged, perfectly spherical, and non-rotating body. The corresponding solution for a charged, spherical, non-rotating body, the Reissner-Nordström metric, was discovered shortly after (1916-1918). However, the exact solution for an uncharged, rotating body, the Kerr metric, remained unsolved until 1963, when it was discovered by Roy Kerr. The natural extension to a charged, rotating body, the Kerr-Newman metric, was discovered shortly afterwards in 1965
The Kerr metric is often used to describe rotating black holes, which exhibit even more exotic phenomena. Such black holes have two event horizons where the metric appears to have a singularity. The outer horizon encloses the ergosphere and has an oblate spheroid shape, a flattened sphere similar to a discus. The inner horizon is spherical and marks the "radius of no return"; objects passing through this radius can never again communicate with the world outside that radius. Objects between these two horizons must co-rotate with the rotating body, as noted above; this feature can be used to extract energy from a rotating black hole, up to its invariant mass energy, Mc2. Even stranger phenomena can be observed within the innermost region of this spacetime, such as some forms of time travel. For example, the Kerr metric permits closed, time-like loops in which a band of travellers returns to the same place after moving for a finite time by their own clock; however, they return to the same place and time, as seen by an outside observer.
The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find. The Kerr metric is a generalization of the Schwarzschild metric, which was discovered by Karl Schwarzschild in 1916 and which describes the geometry of spacetime around an uncharged, perfectly spherical, and non-rotating body. The corresponding solution for a charged, spherical, non-rotating body, the Reissner-Nordström metric, was discovered shortly after (1916-1918). However, the exact solution for an uncharged, rotating body, the Kerr metric, remained unsolved until 1963, when it was discovered by Roy Kerr. The natural extension to a charged, rotating body, the Kerr-Newman metric, was discovered shortly afterwards in 1965