Weyl–Lewis–Papapetrou-koordinater

Weyl–Lewis–Papapetrou-koordinater är i den allmänna relativitetsteorin en mängd koordinater som används i lösningar av vakuum-regionen kring en axialsymmetrisk fördelning av massa–energi, och namngavs efter Hermann Weyl, T. Lewis och Achilles Papapetrou.

Kvadraten av linjeelementet är på formen:[1]

d s 2 = − e 2 ν d t 2 + ρ 2 B 2 e − 2 ν ( d ϕ − ω d t ) 2 + e 2 ( λ − ν ) ( d ρ 2 + d z 2 ) {\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})}

där (t, ρ, ϕ, z) är de cylindriska Weyl–Lewis–Papapetrou-koordinaterna i 3 + 1-rumtid, och där λ, ν, ω och B är okända funktioner hos de rumsliga icke-vinkelformade koordinaterna ρ och z endast. Olika författare definierar funktionerna för koordinaterna på olika sätt.

Se även

  • Metrisk tensor
  • Stressenergitensor

Referenser

Noter

  1. ^ 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. sid. 122. ISBN 981-238-093-0. http://books.google.co.uk/books?id=Hen4Bb-bjgUC&pg=PA122&lpg=PA122&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&source=bl&ots=XZ0DxKeYf5&sig=as5plL8kYXPotV9kpnhlG1rpEb0&hl=en&sa=X&ei=WQhuUoX8FZPwhQeknYCoCQ&ved=0CF0Q6AEwCA#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false 

Källor

  • J. Marek, A. Sloane (1979). ”A finite rotating body in general relativity”. Il Nuovo Cimento B Series 11 51 (1): sid. 45–52. https://link.springer.com/article/10.1007%2FBF02743695. 
  • L. Richterek, J. Novotny, J. Horsky (2002). ”Einstein–Maxwell fields generated from the gamma-metric and their limits”. Czech.J.Phys. 52: sid. 2. doi:10.1023/A:1020581415399. https://arxiv.org/abs/gr-qc/0209094v1. 
  • M. Sharif (2007). ”Energy-Momentum Distribution of the Weyl–Lewis–Papapetrou and the Levi–Civita Metrics”. Brazilian Journal of Physics 37. http://www.sbfisica.org.br/bjp/files/v37_1292.pdf. 
  • A. Sloane (1978). ”The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity”. Aust. J. Phys (CSIRO) 31: sid. 429. http://adsabs.harvard.edu/full/1978AuJPh..31..427S. 
  • J. L. Friedman, N. Stergioulas (2013). Rotating Relativistic Stars. Cambridge Monographs on Mathematical Physics. Cambridge University Press. sid. 151. ISBN 052-187-254-5. http://books.google.co.uk/books?id=pv8djXCCwToC&pg=PA151&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&hl=en&sa=X&ei=5_1tUqz3JYa2hQf-u4D4Aw&redir_esc=y#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false 
  • A. Macías, J. L. Cervantes-Cota, C. Lämmerzahl (2001). Exact Solutions and Scalar Fields in Gravity: Recent Developments. Springer. sid. 39. ISBN 030-646-618-X. http://books.google.co.uk/books?id=imA3YuKdFYoC&pg=PA39&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&hl=en&sa=X&ei=5_1tUqz3JYa2hQf-u4D4Aw&redir_esc=y#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false 
  • A. Das, A. DeBenedictis (2012). The General Theory of Relativity: A Mathematical Exposition. Springer. sid. 317. ISBN 146-143-658-3. http://books.google.co.uk/books?id=wJR7SmPedWcC&pg=PA678&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&hl=en&sa=X&ei=jABuUqzEIs-ChQfBsYHABg&ved=0CEgQ6AEwBA#v=onepage&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou%20coordinates&f=false 
  • 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. sid. 65, 73, 78. ISBN 075-030-395-6. http://books.google.co.uk/books?id=IfhAAQAAIAAJ&q=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&dq=Weyl%E2%88%92Lewis%E2%88%92Papapetrou+coordinates&hl=en&sa=X&ei=cQFuUuv8Gs6rhQeD5YHgCQ&ved=0CDAQ6AEwADgK