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Any path with a fixed longitude is at rest in comoving coordinates and******************************************************************************
only
travels into the future. All points with a fixed latitude have the
same
value of the cosmic time parameter.
movingfollow
through space as it/she/he moves from the BB-NP to the BC-SP will
always be
moving in a mostly southerly direction but at an angle which is
between 45
deg East of South and 45 deg West of South. Any photon will travel
either
due SE or due SW depending on which way around the circle it is
traveling
as the spatial circle expands and later contracts. Any change of
local
Lorentz frame at some point on the surface is locally like making an
ordinary
Lorentz transformation in the x-t plane for one dimensional motion in
special relativity where we make the origin of both of the coordinate
systems
at the local point where transformation is to be performed. The
original
t-axis goes from N to S and the x-axis goes from E to W. After making
the
transformation both the t'-axis and the x'-axis are tilted wrt the
original
x and t axes. If v is the boost velocity of the transformation then
the
x'-axis runs from the NE to the SW at an angle of arctan(v/c) wrt the
E-W
x-axis. The t'-axis also runs from the NE to the SW but at an angle
of
arctan(v/c) from the N-S t-axis. ****As we follow these axes they
paths******************************************************************************
which keep the same local directions wrt N-E-S-W.****