Quote:
Originally Posted by mjc
Steven
Thanks for your reply - I think you've given me the nudge or clue that I was seeking. By viewing the problem in space-time I can see that at the event horizon the past light-cone of an observer would be outside the event horizon while the future light cone will lie within and the light-like edge boundary of the light cones will lie on the event horizon.
Your post led me onto this page - and both have helped considerably.
http://www.phy.syr.edu/courses/modul...arzschild.html
I can't say that I immediately understand the tipping inwards of the light cone - but at least I have some handle to the answer.
Regards
Mark C. |
Mark,
In flat space the future light cone (and also the past light cone) forms a 45 degree angle with the time and spatial axes. This means the photon can move both in time and space from an observer's frame of reference.
The 45 degree angle tells us why photons travel in null geodesics and that the speed of light is the same for all inertial observers.
The situation becomes somewhat more complicated in gravitational fields. The closer a photon is to the event horizon the greater the gravitational redshift of the photon. The amount of tipping of the light cone is related to the gravitational redshift. A photon at the event horizon appears to be "stationary" to all observer's outside the event horizon. Each observer is still able to measure the passage of time but the photons do not appear to move spatially. An outgoing light cone edge that is vertical or parallel to the time axis means that the photon is spatially restricted to a particular value which in this case is the radius of the event horizon.
Inside the event horizon the light cone will never intercept the outside observer's world line hence it will never be seen.
Regards
Steven