Re: Black hole questions

On Sat, 25 Nov 2006 05:59:50 +0000, Tom Roberts wrote:

sal wrote:
On Fri, 24 Nov 2006 01:01:47 +0000, Tom Roberts wrote:
over a
non-local vertical path in Schwarzschild spacetime the measured speed
of light is NOT isotropic.

Back that up and run it over me again... It's _NOT_ isotropic over a
non-local vertical path, measured in Schwarzschild coordinates???
Then, which way's faster, down or up? Or did I misunderstand you?

Look at:
http://groups.google.com/group/sci.physics.relativity/msg/dd9168f6ec3220d2?dmode=source
and apply it to Schw. spacetime rather than an accelerated system in SR.

OK, I've been looking at it.

I'm still having trouble getting my head around the concept of locally
isotropic C which is globally anisotropic -- I've been fiddling with
taking the local limit on C in your second (coordinate-time) example
at various points located away from the origin to try to get a better
feel for what's going on, without a lot of luck; at time 0 it's
isotropic everywhere on the X axis (at least!) but at time C=/=0 the
limits get messier and I haven't got an answer yet.

But in the mean time, something in the section on standard-clock
measurements bothered me. Just over halfway through the next to the
last paragraph in that section, you say,

"(... events in the two regions cannot communicate in //either//
direction via light rays)" [emphasis added]

I don't see how that can be true. Of course, it's true that
positive-going signals emitted at points to the left of the horizon
will never reach any point to the right of the horizon in the
accelerated coordinate system, as the targets "run away" to the right
too fast to ever be caught by the photons.

However, space itself is flat here, and a photon emitted in the -x
direction, at any point on the plane, will eventually encounter every
point on the ray to the left of the emitter. Points in our
accelerated coordinate system are accelerating to the _right_ --
directly -toward- photons emitted in the -x direction. How
can any observer located to the left of the emitter be unable to
receive a light signal sent toward it? I do not see this.




For any sensible method of synchronizing standard clocks, you will
measure a speed faster than c going down and a speed slower than c going
up. But don't dally -- for both cases the value you measure depends on
the delay between the clock synchronization and the speed measurement.


Remember, please, that in GR the speed of light is isotropically c only
to the accuracy with which you can neglect the curvature of the manifold
over the region of the measurement.


Tom Roberts

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