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curvature singularity

A type of spacetime singularity (i.e. a boundary where spacetime ends) that is associated with infinitely strong gravity and, hence, infinitely strong spacetime curvature.

Two different varieties of curvature singularity are Ricci- and Weyl singularities.

More information about the different types of singularities can be found in the spotlight text Spacetime singularities.

Definitioner

singularity

Irregular boundary of spacetime in general relativity - region where spacetime simply comes to an end. Often, such boundaries are associated with spacetime curvature growing beyond all bounds and becoming infinitely large - so-called curvature singularities (notably Ricci singularities or Weyl singularities - but there are exceptions (for instance a conic singularities). According to general relativity, a singularity exists inside every black hole, and the starting point of any universe described by a big bang model is a singularity as well. The occurrence of singularities is a failure of general relativity - and a strong indication that the theory is incomplete. Instead, one could describe the earliest universe and the interior of black holes using a theory of quantum gravity. More information about singularities can be found in the spotlight texts Spacetime singularities and Of singularities and breadmaking.

curvature

For a two-dimensional surface: criterion that allows us to decide whether that surface is a plane, or part of a plane (i.e. a surface on which the usual rules of high school geometry apply), or not. Two possibilities to define the curvature of a plane are the following: Sum of the angles of a triangle. In a plane, the sum of the three angles in a triangle formed by three straight lines is always 180 degrees. In a more general surface, the sum of the angles of a more general triangle formed by three straightest-possible lines (i.e. geodesics) can be larger or smaller than 180 degrees. The difference (the surplus or deficit), divided by the area of the triangle, is a measure for the curvature of that region of the surface. Second possibility: the circumference of a circle. In the plane, that circumference is equal to 2 times pi times the circle's radius. On a more general surface, it can be larger or smaller. The difference, divided by the third power of the radius, leads to the same measure for the curvature as the first definition. Simple examples for curved surfaces are the surface of a sphere (positive curvature, that is to say: sum of the angles in a triangle larger than 180 degrees, circumference of a circle smaller than 2 times pi times radius) and that of a saddle (negative curvature, that is to say: sum of the angles in a triangle smaller than 180 degrees, circumference of a circle larger than 2 times pi times radius). Curvature cannot only be defined for surfaces, but also for higher-dimensional, more general spaces or spacetimes. However, the generalized definition is substantially more complicated, and curvature is defined not by a single number, but by a set of numbers (that, together, form the "curvature tensor"). It's basic meaning, however, is the same: it measures the space's deviation from a flat space of the same dimension. For physics, an important aspect of curvature is its connection with gravity, as described in Einstein's general theory of relativity. Basic information about this can be found in the spotlight text Gravity: From weightlessness to curvature.

curvature singularity

A type of spacetime singularity (i.e. a boundary where spacetime ends) that is associated with infinitely strong gravity and, hence, infinitely strong spacetime curvature. Two different varieties of curvature singularity are Ricci- and Weyl singularities. More information about the different types of singularities can be found in the spotlight text Spacetime singularities.

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curvature singularity

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