Re: opposite of relativistic time contraction

Tim Little wrote:

> On 2008-03-16, Erik Max Francis <max@[EMAIL PROTECTED]
> wrote:
>> This doesn't sound right to me.  Remember that geodesic
>> gravitational time dilations are actually very minor effects; the
>> maximal time dilation effect you can get from orbiting close to a
>> black hole is only about a factor of two.
> 
> It can be arbitrarily great, depending upon how close your orbit is to
> the photon sphere.

Not according to every source I could find.  Gravitational time dilation 
for an object in a circular orbit in a Schwarzschild geometry is

	tau'/tau = (1 - R/r)^(1/2),

where tau' is the proper time experienced by the orbiting clock, tau is 
the proper time experienced by a far away clock, r is the Schwarzschild 
coordinate, and R is the Schwarzschild radius.  Orbits by massive 
particles are unstable within the photon sphere (r = (3/2) R), so the 
maximum time dilation that's possible is a ratio of about 58%.

If you hover at constant radial r, rather than stay in orbit, and then 
get arbitrarily close the _event horizon_ -- not the photon sphere -- 
then you can achieve arbitrarily high time dilations.  But this requires 
  arbitrarily high thrusts.

-- 
Erik Max Francis && max@[EMAIL PROTECTED]
 && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
   If you are afraid of loneliness, do not marry.
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