Eddington Finkelstein coordinates in the Schwarzschild spacetime

[vitaniarain]

Do the Eddington-Finkelstein coordinates allow to cover the maximal analytic extension of the Schwarzschild spacetime? ans if not what region do they cover?

 

[Dale]

They cover the entire manifold except for the "true" singularity at r=0.

 

[George Jones]

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 cover only half of the maximal analytic extension of Schwarzschild spacetime. Take a look at section 5.1.3 in Eric Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

Better yet, see if your library has a copy of the excellent book, A Relativist's Toolkit: The Mathematics of Black Hole Mechanics, into which the notes evolved.

Ingoing Eddington-Finkelstein coordinates cover half of the maximal analytic extension of the Schwarzschild spacetime, and outgoing Eddington-Finkelstein coordinates cover half of the maximal analytic extension of the Schwarzschild spacetime. Note that:

1) these are two different coordinate systems;

2) they cover different, but overlapping, halves of spacetime;

3) If "Eddington-Finkelstein coordinates" appears without either "ingoing" or "outgoing", than "ingoing" is usually meant;

4) Poisson labels the regions of spacetime differently than does Wald.

 

[Dale]

Sorry about my above answer, I think I am in error.

 

[vitaniarain]

Thank you for your answers and help!