Trapped null surface
Encyclopedia
A trapped null surface is a set of points defined in the context of general relativity
as a closed surface on which outward-pointing light rays are actually converging (moving inwards).
Trapped null surfaces are used in the definition of the apparent horizon
which typically surrounds a black hole
.
, orientable
, spacelike) surface, and find its outward pointing normal
vectors. The basic picture to think of here is a ball with pins sticking out of it; the pins are the normal vectors.
Now we look at light rays that are directed outward, along these normal vectors. The rays will either be diverging (the usual case one would expect) or converging. Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface.
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
as a closed surface on which outward-pointing light rays are actually converging (moving inwards).
Trapped null surfaces are used in the definition of the apparent horizon
Apparent horizon
In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outwards but moving inwards.Apparent horizons are not invariant properties of a spacetime...
which typically surrounds a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
.
Definition
We take a (compactCompact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
, orientable
Orientability
In mathematics, orientability is a property of surfaces in Euclidean space measuring whether or not it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the...
, spacelike) surface, and find its outward pointing normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
vectors. The basic picture to think of here is a ball with pins sticking out of it; the pins are the normal vectors.
Now we look at light rays that are directed outward, along these normal vectors. The rays will either be diverging (the usual case one would expect) or converging. Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface.