vitaniarain said:Do the Eddington-Finkelstein coordinates allow to cover the maximal analytic extension of the Schwarzschild spacetime? ans if not what region do they cover?
Eddington Finkelstein coordinates are a set of coordinates used to describe the curvature of space-time in the vicinity of a non-rotating, uncharged black hole, known as the Schwarzschild spacetime. These coordinates were first introduced by Arthur Eddington and David Finkelstein in the early 20th century.
Eddington Finkelstein coordinates differ from other coordinate systems, such as Schwarzschild coordinates, in that they are regular at the event horizon of a black hole. This means they do not exhibit the coordinate singularity that other coordinate systems do at the event horizon.
Eddington Finkelstein coordinates have significant physical and mathematical significance in the study of black holes. They allow for a better understanding of the curvature of space-time near a black hole and have been used in the development of various theories, such as the theory of general relativity.
Eddington Finkelstein coordinates are calculated using the Schwarzschild metric, which describes the curvature of space-time in the Schwarzschild spacetime. This metric takes into account the mass and distance of the black hole, and the coordinates are then solved for using mathematical equations.
Eddington Finkelstein coordinates have practical applications in the study of black holes and their properties. They have also been used in the development of various theories, such as Hawking radiation, which describes the emission of particles from a black hole's event horizon. These coordinates have also been used in the study of gravitational lensing and the formation of galaxies and other celestial bodies.