### metric

(mathematical generalization of the concept of distance)

A **metric** is a generalization of distance, capturing
some of its characteristics. It is a function
mapping pairs of points in a *space* to non-negative numbers,
such that the metric from a point to itself is zero,
that applying it to the reverse (i.e., B to A instead
of A to B) yields the same result, and that the metric
from A to C is always less than or equal to the metric
from A to B plus that of B to C, all statements that
would hold true of ordinary distance.

In physics, metrics of non-straight lines are of
interest, e.g., specifying "the metric of A to C through B",
and for curved
lines in continuous spaces, using a line integral.

A variation on the *metric* concept is relevant to
space-time in relativity, i.e., a metric,
but allowing a zero metric in some cases where points are distinct.
Examples of metrics used in astrophysics:

**Minkowski metric** - for special relativity (relativistically invariant, i.e., invariant under the Lorentz transformation).
**Schwarzschild metric** - for general relativity given the influence of a mass.
**Kerr metric** - a generalization of the Schwarzschild metric including the effects of rotation, used for the Kerr black hole model.
**Reissner-Nordström metric** - generalization including mass and electric charge.
**Kerr-Newman metric** - generalization including all three: mass, rotation, and charge.
**Robertson-Walker metric** incorporating GR and the expansion/contraction of a model universe.

Special cases or variations on GR (**modified GR**)
are often defined by a formula for its particular metric.

(*mathematics,physics,relativity*)
**Further reading:**

http://en.wikipedia.org/wiki/Metric

**Referenced by pages:**

Johannsen-Psaltis metric (JP metric)

Kerr black hole

theoretical modified GR metrics

Index