Recall that , respectively
, is the set covered by past-directed timelike, respectively
causal, curves originating from
, while
denotes the boundary of
, etc. The sets
, etc., are
defined as
, etc., after changing time-orientation. See [143
, 16, 256, 236, 266, 66] and references
therein for details of causality theory.
Consider an asymptotically-flat, or -asymptotically-flat, spacetime with a Killing vector
,
which is timelike on the asymptotic end
. The exterior region
and the domain of outer
communications
, for which we will also use the abbreviation d.o.c., are then defined as (see
Figure 1
)
The white-hole region and the white-hole event horizon
are defined as above after changing
time orientation:
By standard causality theory, an event horizon is the union of Lipschitz null hypersurfaces.
It turns out that event horizons in stationary spacetimes satisfying energy conditions are as
smooth as the metric allows [76, 69
]; thus, smooth if the metric is smooth, analytic if the metric
is.
http://www.livingreviews.org/lrr-2012-7 |
Living Rev. Relativity 15, (2012), 7
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