Eddington Finkelstein Coordinates + Black Holes

[discjockey]

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?

 

[Garth]

Hi, and welcome to these Forums discjockey!

Not knowing exactly what text you are using makes a response a little risky, however the most obvious answer is that light rays travel on null-geodesics with ds² = 0.

In flat space-time:
ds² = dx² + dy² + dx² - c²dt².

As a light ray travels at the speed of light c then
dx² + dy² + dx² = c²dt².

Hence ds² = 0.

The result also holds in curved space-time, it is a basic property of light to travel always at c as measured by local rulers and clocks.

Garth

 

[discjockey]

Thanks a lot!

 

[mersecske]

My question about Eddington-Finkelstein coordinates:
if we use ingoing null coordinate (v) and the radius (r) for basis
then we have a null-coordinate, and a space-coordinate above the horizon,
and a null-coordinate, and a time-coordinate below the horizon.
Usually we use time ad space coordinates together,
and we evolve a system in the direction increasing time.
In the case of EF-coordinates we can evolve the system
using the null-coordinate (v)?
But under the horizon r is a time coordinate,
we can evolve the system in r also?

 

[George Jones]

I've got to catch my bus, so I don't have time to look at this, but

https://www.physicsforums.com/showthread.php?p=2714132#post2714132

might be relevant.

 

[mersecske]

Thanks