EddingtonFinkelsteinkoordinater

Eddington-Finkelstein coordinates are a coordinate system used in general relativity to describe the curvature of spacetime around rotating objects, particularly black holes. Developed by Arthur Eddington and David Finkelstein in the 1950s, these coordinates are a relativistic extension of the polar coordinates used in Newtonian gravity.

In Eddington-Finkelstein coordinates, the radial distance from the center of a source is given by the variable w, while the angular coordinates θ and φ remain the same as in Cartesian coordinates. The time coordinate t is, however, related to w in a non-trivial way, taking into account the curvature of spacetime. This curvature is encoded in the metric tensor, which describes how distances and times are affected by the presence of mass and energy.

The main advantage of Eddington-Finkelstein coordinates is that they allow for a more accurate description of the behavior of light and matter near rotating objects. In particular, these coordinates help to define the apparent horizon of a rotating black hole, which marks the boundary beyond which nothing, not even light, can escape.

Eddington-Finkelstein coordinates are widely used in the study of accretion disks, jets, and other relativistic astrophysical phenomena around rotating objects. They have been instrumental in the development of modern theories of black hole physics and have helped to reveal the complex behavior of spacetime in the vicinity of rotating sources. Despite their complexity, Eddington-Finkelstein coordinates have become a standard tool in the arsenal of relativistic astrophysicists.