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discjockey
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When deriving the Eddinton-Finkelstein Coordinates from the Schwarzschild metric, we start to examine light rays. However, in my relativity book, it states that ds^2=0: why do we assume that? 
Eddington Finkelstein Coordinates are a type of coordinate system used to describe the spacetime around a black hole. They were developed by British astrophysicist Arthur Eddington and American physicist David Finkelstein in the 1950s.
Eddington Finkelstein Coordinates are unique because they are specifically designed to eliminate the singularity at the center of a black hole in the coordinate system. This allows for a more accurate description of the spacetime around the black hole.
Eddington Finkelstein Coordinates are important in the study of black holes because they allow for a better understanding of the behavior of light and matter near the event horizon, the point of no return around a black hole. They also provide a way to describe the spacetime inside and outside of a black hole without encountering mathematical singularities.
Eddington Finkelstein Coordinates are particularly useful for describing the behavior of light and matter near the event horizon of a black hole. In these coordinates, the event horizon is represented as a null surface, meaning that the coordinates do not change as an object crosses the event horizon.
While Eddington Finkelstein Coordinates are primarily used in theoretical studies of black holes, they have also been used in practical applications such as simulations of black hole mergers and the calculation of gravitational wave signals. They have also been used to study other astrophysical phenomena, such as the behavior of particles near neutron stars.