DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

One interesting particular case is the Goto–
Nambu string, for which we simply haveK µ =
0 as the sole equation. See covariant derivative,
equation of state (cosmic string), Goto–Nambu
string, metric, summation convention, Witten
conducting string.
future/past causal horizon The boundary
that separates two disconnected regionsI andO
of space-time such that: 1. no physical signal
originating fromI can ever reach (at least) a particular
class of observers in O (future horizon)
or 2. (at least) a particular class of observers in
O cannot send signals intoI (past horizon). By
causal horizon (with no further specifications)
case 1. is usually meant.
future/past event horizon A future event
horizon is the future causal horizon which separates
an eternal black hole B from the disconnected
external region O such that no physical
signal originating from inside B can ever reach
© 2001 by CRC Press LLC
future/past event horizon
any observer located inO. On the other hand, it
is possible to send signals fromO intoB (a mechanical
analog would be a one-way permeable
membrane).
Anyexternalobserver(inO)notfallinginthe
gravitational field of the black hole sees a signal
sent towards the black hole approach the horizon
but never cross it. An observer co-moving with
the signal, as any locally inertial observer, would
instead cross the horizon at a finite (proper) time
without noticing any local effect (without experiencing
any particular discomfort).
It can be proven that an event horizon is a
light-like surface which necessarily shares the
symmetry ofO. This leads to a classification of
all possible families of black holes in terms of
the ADM mass and a few other parameters see
No-hair theorems.
A past event horizon is the past causal horizon
circumventing a white hole. See ADM
mass, black hole, black hole horizon, future/past
causal horizon, Rindler observer, white hole.
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