Eddington Finkelstein Coordinates + Black Holes

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Discussion Overview

The discussion centers around the Eddington-Finkelstein coordinates in the context of black holes, particularly focusing on their derivation from the Schwarzschild metric and the implications for light rays and coordinate systems above and below the event horizon.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the assumption that light rays travel on null-geodesics, specifically why ds²=0 is used in the context of Eddington-Finkelstein coordinates.
  • Another participant explains that light rays travel at the speed of light, leading to the conclusion that ds²=0, and this holds true in both flat and curved spacetime.
  • A participant raises a question about the use of ingoing null coordinates and the implications for evolving a system in the context of Eddington-Finkelstein coordinates, particularly regarding the distinction between time and space coordinates above and below the horizon.

Areas of Agreement / Disagreement

Participants express different levels of understanding and inquiry regarding the assumptions in the derivation of Eddington-Finkelstein coordinates, and there is no consensus on the implications of using these coordinates in evolving systems across the event horizon.

Contextual Notes

The discussion includes assumptions about the nature of light and the properties of coordinates in general relativity, which may not be fully explored or agreed upon by all participants.

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? :bugeye:
 
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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
 
Last edited:
Thanks a lot!
 
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?
 
Thanks
 

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