3.2.2 Horizons
Schwarzschild (1916) derived a special solution to the original Einstein equations. The Schwarzschild metric has the line element
with = 1  (2m / r).
Eddington (1924) showed that the introduction of the cosmological constant led to an extended factor
in the line element and thus to a second horizon, the `world horizon'.
Different usage of the term horizon made standardization desirable. It was provided by Rindler (1956).
``We shall define a horizon as a frontier between things observable and things unobservable. (The vague term thing is here used deliberately). There are then two quite different horizon concepts in cosmology which satisfy our definition and to which cosmologists have at different times devoted their attention. The first, which I shall call an eventhorizon, is exemplified by the de Sitter modeluniverse. It may be defined as follows: An eventhorizon, for a given fundamental observer A, is a (hyper) surface in spacetime which divides all events into two nonempty classes: those that have been, are or will be observable by A, and those that are forever outside A's Possible Powers of observation . . . .
The other type of horizon, which I shall call a particlehorizon ^{(8)}, is exemplified by the Einsteinde Sitter modeluniverse. It may be defined as follows: A particlehorizon, for any given fundamental observer A and cosmic instant t_{0} is a surface in the instantaneous 3space t = t_{0} to, which divides all fundamental particles into two nonempty classes: Those that have already been observable by A at time t_{0} and those that have not.''
Fig. 27 gives an illustration of horizons.
Figure 27. Lightpaths in a
modeluniverse (similar to a
FriedmannLemaitre model) possessing both a particle horizon and an
eventhorizon
(Rindler 1956):
