Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lightlike simultaneity, comoving observers and distances in general
  relativity   We state a condition for an observer to be comoving with another observer in
general relativity, based on the concept of lightlike simultaneity. Taking into
account this condition, we study relative velocities, Doppler effect and light
aberration. We obtain that comoving observers observe the same light ray with
the same frequency and direction, and so gravitational redshift effect is a
particular case of Doppler effect. We also define a distance between an
observer and the events that it observes, that coincides with the known affine
distance. We show that affine distance is a particular case of radar distance
in the Minkowski space-time and generalizes the proper radial distance in the
Schwarzschild space-time. Finally, we show that affine distance gives us a new
concept of distance in Robertson-Walker space-times, according to Hubble law.

11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg