In
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
, the Weyl–Lewis–Papapetrou coordinates are used in solutions to the
vacuum
A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
region surrounding an
axisymmetric
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in whic ...
distribution of
mass–energy. They are named for
Hermann Weyl
Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
, Thomas Lewis, and
Achilles Papapetrou.
Details
The square of the
line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc ...
is of the form:
:
where
are the cylindrical Weyl–Lewis–Papapetrou coordinates in
-dimensional
spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
, and
,
,
, and
, are unknown functions of the spatial non-angular coordinates
and
only. Different authors define the functions of the coordinates differently.
See also
*
Introduction to the mathematics of general relativity
The mathematics of general relativity is complicated. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be s ...
*
Stress–energy tensor
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress ...
*
Metric tensor (general relativity)
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as t ...
*
Relativistic angular momentum
In physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the thre ...
*
Weyl metrics
In general relativity, the Weyl metrics (named after the German-American mathematician Hermann Weyl) are a class of ''static'' and ''axisymmetric'' solutions to Einstein's field equation. Three members in the renowned Kerr–Newman family solution ...
References
Further reading
Selected papers
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Selected books
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{{DEFAULTSORT:Weyl-Lewis-Papapetrou coordinates
Metric tensors
Spacetime
Coordinate charts in general relativity
General relativity
Gravity