Weyl–Lewis–Papapetrou coordinates explained

In general relativity, the Weyl–Lewis–Papapetrou coordinates are used in 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]}

Details

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

where

are the cylindrical Weyl–Lewis–Papapetrou coordinates in -dimensional spacetime, 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
• Stress–energy tensor
• Metric tensor (general relativity)
• Relativistic angular momentum
• Weyl metrics

Further reading

Selected papers

• Marek . J. . Sloane . A. . May 1979 . A finite rotating body in general relativity . Il Nuovo Cimento B Series 11 . en . 51 . 1 . 45–52 . 1979NCimB..51...45M . 10.1007/BF02743695 . 1826-9877 . 125042609.
• Richterek . L. . Novotný . J. . Horský . J. . 2002 . Einstein-Maxwell fields generated from the gamma-metric and their limits . . 52 . 9 . 1021–1040 . gr-qc/0209094v1 . 2002CzJPh..52.1021R . 10.1023/A:1020581415399 . 18982611.
• Sharif . M. . December 2007 . Energy-momentum distribution of the Weyl-Lewis-Papapetrou and the Levi-Civita metrics . . en . 37 . 4 . 1292–1300 . 0711.2721 . 2007BrJPh..37.1292S . 10.1590/S0103-97332007000800017 . 0103-9733 . 15915449.
• Sloane . A . 1978 . The Axially Symmetric Stationary Vacuum Field Equations in Einstein's Theory of General Relativity . . en . 31 . 5 . 429 . 1978AuJPh..31..427S . 10.1071/PH780427 . 0004-9506 . free.

Selected books

• Book: Friedman . John L. . Rotating relativistic stars . Stergioulas . Nikolaos . 2013 . . 978-0-521-87254-6 . Cambridge monographs on mathematical physics . 151.
• Book: Macías . A. . Exact solutions and scalar fields in gravity: recent developments . Cervantes-Cota . J. L. . Lämmerzahl . C. . 2001 . . 978-0-306-46618-2 . Macías . A. . New York . 39 . Cervantes Cota . Jorge Luis . Lämmerzahl . C..
• Book: Das . Anadijiban . The general theory of relativity: a mathematical exposition . DeBenedictis . Andrew . 2012 . . 978-1-4614-3658-4 . New York London . 317.
• Book: Hall . G. S. . General relativity: proceedings of the forty sixth Scottish Universities summer school in physics, Aberdeen, July 1995 . Pulham . J. R. . 1996 . . 978-0-7503-0395-8 . Hall . G. S. . SUSSP publications . 46 . 65, 73, 78 . Pulham . J. R..

Notes and References

1. Weyl . Hermann . 1917 . Zur Gravitationstheorie . . de . 359 . 18 . 117–145 . 1917AnP...359..117W . 10.1002/andp.19173591804 . 0003-3804.
2. Lewis . T. . 1932 . Some special solutions of the equations of axially symmetric gravitational fields . Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character . en . 136 . 829 . 176–192 . 1932RSPSA.136..176L . 10.1098/rspa.1932.0073 . 0950-1207 . free.
3. A. . Papapetrou . A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution . Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences. 52 . 191–204 . 1948 . 20488481 .
4. Book: Bičák . Jiří . Gravitation, following the Prague inspiration: a volume in celebration of the 60th birthday of Jiří Bičák . Semerák . O. . Podolský . Jiří . Žofka . Martin . 2002 . . 978-981-238-093-7 . Bičák . Jiří . River Edge, N.J . 122 . ocm51260088 . Semerák . O. . Podolský . J. . Žofka . M..