- Art Gallery -

In general relativity, the Weyl−Lewis−Papapetrou coordinates are a set of coordinates, used in the solutions to the vacuum region surrounding an axisymmetric distribution of mass–energy. They are named for Hermann Weyl, Thomas Lewis, and Achilles Papapetrou.[1][2][3]


The square of the line element is of the form:[4]

\( ds^{2}=-e^{{2\nu }}dt^{2}+\rho ^{2}B^{2}e^{{-2\nu }}(d\phi -\omega dt)^{2}+e^{{2(\lambda -\nu )}}(d\rho ^{2}+dz^{2}) \)

where (t, ρ, ϕ, z) are the cylindrical Weyl−Lewis−Papapetrou coordinates in 3 + 1 spacetime, and λ, ν, ω, and B, are unknown functions of the spatial non-angular coordinates ρ and z only. Different authors define the functions of the coordinates differently.
See also

Introduction to the mathematics of general relativity
Stress–energy tensor
Metric tensor (general relativity)
Relativistic angular momentum
Weyl metrics


Weyl, H. (1917). "Zur Gravitationstheorie". Ann. Der Physik. 54 (18): 117–145. Bibcode:1917AnP...359..117W. doi:10.1002/andp.19173591804.
Lewis, T. (1932). "Some special solutions of the equations of axially symmetric gravitational fields". Roy. Soc., Proc. 136 (829): 176–92. Bibcode:1932RSPSA.136..176L. doi:10.1098/rspa.1932.0073.
Papapetrou, A. (1948). "A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution". Proc. R. Irish Acad. A. 52: 191–204. JSTOR 20488481.

Jiří Bičák; O. Semerák; Jiří Podolský; Martin Žofka (2002). Gravitation, Following the Prague Inspiration: A Volume in Celebration of the 60th Birthday of Jiří Bičák. World Scientific. p. 122. ISBN 981-238-093-0.

Further reading
Selected papers

J. Marek; A. Sloane (1979). "A finite rotating body in general relativity". Il Nuovo Cimento B. 51 (1). pp. 45–52. Bibcode:1979NCimB..51...45M. doi:10.1007/BF02743695.
L. Richterek; J. Novotny; J. Horsky (2002). "Einstein−Maxwell fields generated from the gamma-metric and their limits". Czechoslov. J. Phys. 52. p. 2. arXiv:gr-qc/0209094v1. Bibcode:2002CzJPh..52.1021R. doi:10.1023/A:1020581415399.
M. Sharif (2007). "Energy-Momentum Distribution of the Weyl−Lewis−Papapetrou and the Levi-Civita Metrics" (PDF). Brazilian Journal of Physics. 37.
A. Sloane (1978). "The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity". Aust. J. Phys. 31. CSIRO. p. 429. Bibcode:1978AuJPh..31..427S. doi:10.1071/PH780427.

Selected books

J. L. Friedman; N. Stergioulas (2013). Rotating Relativistic Stars. Cambridge Monographs on Mathematical Physics. Cambridge University Press. p. 151. ISBN 978-052-187-254-6.
A. Macías; J. L. Cervantes-Cota; C. Lämmerzahl (2001). Exact Solutions and Scalar Fields in Gravity: Recent Developments. Springer. p. 39. ISBN 030-646-618-X.
A. Das; A. DeBenedictis (2012). The General Theory of Relativity: A Mathematical Exposition. Springer. p. 317. ISBN 978-146-143-658-4.
G. S. Hall; J. R. Pulham (1996). General relativity: proceedings of the forty sixth Scottish Universities summer school in physics, Aberdeen, July 1995. SUSSP proceedings. 46. Scottish Universities Summer School in Physics. pp. 65, 73, 78. ISBN 075-030-395-6.



Principle of relativity (Galilean relativity Galilean transformation) Special relativity Doubly special relativity


Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Proper length Proper time Relativistic mass


Lorentz transformation


Time dilation Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox


Light cone World line Minkowski diagram Biquaternions Minkowski space

Spacetime curvature

Introduction Mathematical formulation


Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach's principle


ADM formalism BSSN formalism Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation


Black hole Event horizon Singularity Two-body problem

Gravitational waves: astronomy detectors (LIGO and collaboration Virgo LISA Pathfinder GEO) Hulse–Taylor binary

Other tests: precession of Mercury lensing redshift Shapiro delay frame-dragging / geodetic effect (Lense–Thirring precession) pulsar timing arrays


Brans–Dicke theory Kaluza–Klein Quantum gravity


Cosmological: Friedmann–Lemaître–Robertson–Walker (Friedmann equations) Kasner BKL singularity Gödel Milne

Spherical: Schwarzschild (interior Tolman–Oppenheimer–Volkoff equation) Reissner–Nordström Lemaître–Tolman

Axisymmetric: Kerr (Kerr–Newman) Weyl−Lewis−Papapetrou Taub–NUT van Stockum dust discs

Others: pp-wave Ozsváth–Schücking metric


Poincaré Lorentz Einstein Hilbert Schwarzschild de Sitter Weyl Eddington Friedmann Lemaître Milne Robertson Chandrasekhar Zwicky Wheeler Choquet-Bruhat Kerr Zel'dovich Novikov Ehlers Geroch Penrose Hawking Taylor Hulse Bondi Misner Yau Thorne Weiss others

► Theory of relativity

Physics Encyclopedia



Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License