
CosmoCoffee

Authors:  Hunter Monroe 
Abstract:  Because the equivalence principle holds as a theorem (of Iliev grqc/9709053)
in the general theory of relativity along any nonselfintersecting curve,
gravitational time dilation of 1/(1v^2)^(1/2) is indistinguishable (along a
curve) from time dilation caused by a relative velocity of v; time dilation and
relative velocity are two sides of the same coin even in the general theory.
Therefore, Einstein's velocity composition law u=(v+w)/(1+vw) can be rewritten
to accumulate time dilation in the general theory according to
1/(1u^2)^(1/2)=(1+vw)/[(1v^2)(1w^2)]^(1/2), not by direct multiplication of
time dilation factors 1/(1u^2)^(1/2)=1/[(1v^2)(1w^2)]^(1/2). The unbounded
intensification of time dilation observed as an event horizon emerges at the
center of a collapsing star is therefore indistinguishable (along a curve) from
a relative velocity of the center approaching the speed of light, implying a
bubblelike local inflation of the star's interior as the center recedes toward
infinity even as the star continues to collapse as seen from the outside (as
conjectured by Shatskiy astroph/0407222). This potentially provides a generic
mechanism through which trapped surfaces and therefore singularities do not
occur after gravitational collapse and before the big bang. 

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Do you accept the corrected Doppler formula? 
Yes 

33% 
[ 1 ] 
No 

66% 
[ 2 ] 

Total Votes : 3 

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Hunter Monroe
Joined: 17 Nov 2005 Posts: 4 Affiliation: IMF

Posted: March 23 2006 


This paper argues that time dilation and relative velocity v are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinateindependent language, in the tangent Minkowski space along the curve). I would be interested in reactions on the two points below.
For example, on a clock stationary at radius r, a distant observer sees time dilation of under the Schwarzschild metric and sees the clock receding with a relative velocity of under the PainlevéGullstrand free fall metric.
Two applications of this duality are presented. First, Einstein's velocity composition law can be rewritten as a Doppler shift law . Under Schwarzschild coordinates, the Doppler shift formula is not but . The second order term vw in the numerator provides a potential explanation of the Pioneer anomaly if it has been ignored.
Second, duality implies that during gravitational collapse, the intensifying time dilation observed at the star's center from a fixed radius r > 0 is indistinguishable (along a curve) from an increasing relative velocity at which the center recedes as seen from any direction, implying a local inflation. 

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