View source for Physics:Weyl−Lewis−Papapetrou coordinates


In [[Physics:General relativity|general relativity]], the '''Weyl−Lewis−Papapetrou coordinates''' are a set of coordinates, used in the solutions to the [[Physics:Vacuum|vacuum]] region surrounding an axisymmetric distribution of mass–energy. They are named for [[Biography:Hermann Weyl|Hermann Weyl]], Thomas Lewis, and [[Biography:Achilles Papapetrou|Achilles Papapetrou]].<ref>{{cite journal |last=Weyl |first=H. |title=Zur Gravitationstheorie |journal=Ann. der Physik |volume=54 |year=1917 |pages=117–145 |doi=10.1002/andp.19173591804 }}</ref><ref>{{cite journal |first=T. |last=Lewis |title=Some special solutions of the equations of axially symmetric gravitational fields |journal=Roy. Soc., Proc. |volume=136 |issue= |pages=176–92 |year=1932 |doi=10.1098/rspa.1932.0073 |doi-access=free }}</ref><ref>{{cite journal |first=A. |last=Papapetrou |title=A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution |journal=Proc. R. Irish Acad. |series=A |volume=52 |issue= |pages=11 |year=1948 |jstor=20488481 }}</ref>

==Details==
The square of the [[Line element|line element]] is of the form:<ref>{{cite book|title=Gravitation, Following the Prague Inspiration: A Volume in Celebration of the 60th Birthday of Jiří Bičák|author=Jiří Bičák|author2=O. Semerák|author3=Jiří Podolský|author4=Martin Žofka|publisher=[[Company:World Scientific|World Scientific]]|page=122|date=2002|isbn=981-238-093-0|url=https://books.google.com/?id=Hen4Bb-bjgUC&pg=PA122&lpg=PA122&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false}}</ref>

:<math>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)</math>

where (''t'',&nbsp;''ρ'',&nbsp;''ϕ'',&nbsp;''z'') are the cylindrical Weyl−Lewis−Papapetrou coordinates in 3&nbsp;+&nbsp;1 [[Physics:Spacetime|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]]
*[[Physics:Metric tensor (general relativity)|Metric tensor (general relativity)]]
*[[Relativistic angular momentum]]
*[[Astronomy:Weyl metrics|Weyl metrics]]

==References==
{{reflist}}

==Further reading==
===Selected papers===
*{{cite news|title= A finite rotating body in general relativity|author=J. Marek|author2=A. Sloane|date=1979|pages=45–52|volume=51|issue=1|journal=Il Nuovo Cimento B|bibcode=1979NCimB..51...45M|doi=10.1007/BF02743695}}
*{{cite news|title= Einstein−Maxwell fields generated from the gamma-metric and their limits|page=2|author=L. Richterek|author2=J. Novotny|author3=J. Horsky|date=2002|journal=Czechoslov. J. Phys. |volume=52 |doi=10.1023/A:1020581415399|arxiv=gr-qc/0209094v1|bibcode=2002CzJPh..52.1021R}}
*{{cite news|title=Energy-Momentum Distribution of the Weyl−Lewis−Papapetrou and the Levi-Civita Metrics|journal=Brazilian Journal of Physics|date=2007|volume=37|author=M. Sharif|url=http://www.sbfisica.org.br/bjp/files/v37_1292.pdf}}
*{{cite news|title=The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity|page=429|journal=Aust. J. Phys.|publisher=CSIRO|date=1978|volume=31|author=A. Sloane|bibcode=1978AuJPh..31..427S|doi=10.1071/PH780427}}

===Selected books===
*{{cite book|title=Rotating Relativistic Stars|page=151|author=J. L. Friedman|author2=N. Stergioulas|url=https://books.google.com/?id=pv8djXCCwToC&pg=PA151&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false|publisher={{wipe|Cambridge University Press}}|date=2013|series=Cambridge Monographs on Mathematical Physics|isbn=978-052-187-254-6}}
*{{cite book|title=Exact Solutions and Scalar Fields in Gravity: Recent Developments |page=39|publisher=Springer|date=2001|author=A. Macías|author2=J. L. Cervantes-Cota|author3=C. Lämmerzahl|url=https://books.google.com/?id=imA3YuKdFYoC&pg=PA39&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false|isbn=030-646-618-X}}
*{{cite book|title=The General Theory of Relativity: A Mathematical Exposition|page=317|publisher=Springer|date=2012|author=A. Das|author2=A. DeBenedictis|url=https://books.google.com/?id=wJR7SmPedWcC&pg=PA678&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false|isbn=978-146-143-658-4}}
*{{cite book|title=General relativity: proceedings of the forty sixth Scottish Universities summer school in physics, Aberdeen, July 1995|pages=65, 73, 78|publisher=Scottish Universities Summer School in Physics|date=1996|volume=46|series=SUSSP proceedings|author=G. S. Hall|author2=J. R. Pulham|url=https://books.google.com/?id=IfhAAQAAIAAJ&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates|isbn=075-030-395-6}}

{{Relativity}}

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[[Category:Coordinate charts in general relativity]]
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