Question
Transcribed Text
Problem I
Consider a particle moving at fixed Rindler coordinate x = 1/g.
a) What is the infinitesimal proper time dr in terms of dT?
b) Compute the Minkowski components of the 4-velocity u° = dx°/dr by
differentiating
/ = x sinh T.
. = x coesh T.
with respect to T and then multiplying by dT/dr.
c)Repeat this procedure to compute the acceleration a° = du'/dr. Note
that this expression for the acceleration is valid only in Minkowski space! (Oth-
erwise a° = Vuv°.)
d) Finally, verify the result
a of
for this worldline.
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1. a)From the definition of the 2D Rindler metric, we see that
1
𝑑𝜏 = ------- 𝑑𝑇
𝑔...
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