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Solutions to the equations of [[general relativity]] or another theory of [[gravity]] (such as [[supergravity]]), often result in encountering points where the metric blows up to [[infinity]]. However, many of these points are in fact completely regular. Moreover, the infinities are merely a result of using an inappropriate coordinate system at this point. Thus, in order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. [[scalar]]s) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.

Solutions to the equations of [[general relativity]] or another theory of [[gravity]] (such as [[supergravity]]), often result in encountering points where the metric blows up to [[infinity]]. However, many of these points are in fact completely regular. Moreover, the infinities are merely a result of using an inappropriate coordinate system at this point. Thus, in order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. [[scalar]]s) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.

An example is the Schwarzschild solution which describes a non-rotating, uncharged black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the [[event horizon]]. However, [[spacetime]] at the event horizon is regular.  The regularity becomes evident when changing to another coordinate system where the metric is perfectly smooth. On the other hand, in the center of the [[black hole]], where the metric becomes infinite as well, the solutions suggest singularity exists. The existence of the singularity can be verified by noting that the ''Kretschmann scalar'' or square of the [[Riemann tensor]], which is diffeomorphism invariant - is infinite.

An example is the Schwarzschild solution which describes a non-rotating, uncharged black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the [[event horizon]]. However, [[spacetime]] at the event horizon is regular.  The regularity becomes evident when changing to another coordinate system where the metric is perfectly smooth. On the other hand, in the center of the [[black hole]], where the metric becomes infinite as well, the solutions suggest singularity exists. The existence of the singularity can be verified by noting that the ''Kretschmann scalar'' or square of the ''Riemann tensor'', which is diffeomorphism invariant - is infinite.

While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, the singularity occurs on a ring (a circular line), defined as a "[[ring singularity]]". Such a singularity may also theoretically become a [[wormhole]]. If a rotating singularity is given a uniform electrical charge, a repellent force results, causing a ring singularity to form. The effect may be a stable [[wormhole]], a non-point-like puncture in spacetime which may be connected to a second ring singularity on the other end. Although such wormholes are often suggested as routes for faster-than-light travel, such suggestions ignore the problem of escaping the black hole at the other end, or even of surviving the immense tidal forces in the tightly curved interior of the wormhole.

While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, the singularity occurs on a ring (a circular line), defined as a "[[ring singularity]]". Such a singularity may also theoretically become a [[wormhole]]. If a rotating singularity is given a uniform electrical charge, a repellent force results, causing a ring singularity to form. The effect may be a stable [[wormhole]], a non-point-like puncture in spacetime which may be connected to a second ring singularity on the other end. Although such wormholes are often suggested as routes for faster-than-light travel, such suggestions ignore the problem of escaping the black hole at the other end, or even of surviving the immense tidal forces in the tightly curved interior of the wormhole.