Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Causality violation without time-travel: closed lightlike paths in
  G\"{o}del's universe   We revisit the issue of causality violations in G\"{o}del's universe,
restricting to geodesic motions. It is well-known that while there are closed
timelike curves in this spacetime, there are no closed causal geodesics. We
show further that no observer can communicate directly (i.e.\ using a single
causal geodesic) with their own past. However, we show that this type of
causality violation can be achieved by a system of relays: we prove that from
any event $P$ in G\"{o}del's universe, there is a future-directed lightlike
path - a sequence of future-directed null geodesic segments, laid end to end -
which has $P$ as its past and future endpoints. By analysing the envelope of
the family of future directed null geodesics emanating from a point of the
spacetime, we show that this lightlike path must contain a minimum of eight
geodesic segments, and show further that this bound is attained. We prove a
related general result, that events of a time orientable spacetime are
connected by a (closed) timelike curve if and only if they are connected by a
(closed) lightlike path. This suggests a means of violating causality in
G\"{o}del's universe without the need for unfeasibly large accelerations, using
instead a sequence of light signals reflected by a suitably located system of
mirrors.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin