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A trapped null surface is a set of points defined in the context of general relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
 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

An apparent horizon is a surface defined in general relativity as the Boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards....
 which typically surrounds a black hole
Black hole

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation , can escape its pull after having fallen past its event horizon....
.

ake a (compact
Compact space

In mathematics, a topological space is called compact if each of its open covers has a finite set subcover.Note: Some authors such as Nicolas Bourbaki use the term "quasi-compact" for this instead, and reserve the term "compact" for topological spaces that are both Hausdorff spaces and "quasi-compact"....
, orientable
Orientability

A surface S in the Euclidean space R3 is orientable if a two-dimensional figure cannot be moved around the surface and back to where it started so that it looks like its own mirror image ....
, spacelike
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
) surface, and find its outward pointing normal
Surface normal

A surface normal, or simply normal, to a Flatness is a vector which 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 space to that surface at P....
 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.






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A trapped null surface is a set of points defined in the context of general relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
 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

An apparent horizon is a surface defined in general relativity as the Boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards....
 which typically surrounds a black hole
Black hole

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation , can escape its pull after having fallen past its event horizon....
.

Definition

We take a (compact
Compact space

In mathematics, a topological space is called compact if each of its open covers has a finite set subcover.Note: Some authors such as Nicolas Bourbaki use the term "quasi-compact" for this instead, and reserve the term "compact" for topological spaces that are both Hausdorff spaces and "quasi-compact"....
, orientable
Orientability

A surface S in the Euclidean space R3 is orientable if a two-dimensional figure cannot be moved around the surface and back to where it started so that it looks like its own mirror image ....
, spacelike
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
) surface, and find its outward pointing normal
Surface normal

A surface normal, or simply normal, to a Flatness is a vector which 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 space to that surface at P....
 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.

See also

  • Apparent horizon
    Apparent horizon

    An apparent horizon is a surface defined in general relativity as the Boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards....
  • Null surface
    Null surface

    In the theory of relativity, a null surface is a 3-surface whose normal vector is everywhere null , but the vector is not identically zero. For example, light cones are null surfaces....