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General relativity
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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 [ edit ]

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

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

where ${\displaystyle (t,\rho ,\phi ,z)}$ are the cylindrical Weyl?Lewis?Papapetrou coordinates in ${\displaystyle 3+1}$-dimensional spacetime , and ${\displaystyle \lambda }$, ${\displaystyle \nu }$, ${\displaystyle \omega }$, and ${\displaystyle B}$, are unknown functions of the spatial non-angular coordinates ${\displaystyle \rho }$ and ${\displaystyle z}$ only. Different authors define the functions of the coordinates differently.

See also [ edit ]

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

References [ edit ]

Further reading [ edit ]

Selected papers [ edit ]

• J. Marek; A. Sloane (1979). "A finite rotating body in general relativity". Il Nuovo Cimento B . 51 (1): 45?52. Bibcode : 1979NCimB..51...45M . doi : 10.1007/BF02743695 . S2CID   125042609 .
• L. Richterek; J. Novotny; J. Horsky (2002). "Einstein?Maxwell fields generated from the gamma-metric and their limits". Czechoslovak Journal of Physics . 52 (9): 1021?1040. arXiv : gr-qc/0209094v1 . Bibcode : 2002CzJPh..52.1021R . doi : 10.1023/A:1020581415399 . S2CID   18982611 .
• M. Sharif (2007). "Energy-Momentum Distribution of the Weyl?Lewis?Papapetrou and the Levi-Civita Metrics" (PDF) . Brazilian Journal of Physics . 37 (4): 1292?1300. arXiv : 0711.2721 . Bibcode : 2007BrJPh..37.1292S . doi : 10.1590/S0103-97332007000800017 . S2CID   15915449 .
• A. Sloane (1978). "The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity" . Australian Journal of Physics . 31 (5): 429. Bibcode : 1978AuJPh..31..427S . doi : 10.1071/PH780427 .

Selected books [ edit ]

• 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. Macias; J. L. Cervantes-Cota; C. Lammerzahl (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. Vol. 46. Scottish Universities Summer School in Physics. pp. 65, 73, 78. ISBN   075-030-395-6 .

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