Skip to main content

Lanczos Potential and Tetrad Formalism

  • Chapter
  • First Online:
The Potential of Fields in Einstein's Theory of Gravitation
  • 760 Accesses

Abstract

The Lanczos tensor and its importance in general relativity have been discussed. The basic equations describing the gravitational field, in terms of Lanczos tensor, have been expressed in the language of NP and GHP formalisms along with other related equations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A tensor quantity is said to be reducible if it can be decomposed into parts which transform along themselves. If such a decomposition is not possible, then the quantity is called irreducible (cf., [2]).

References

  1. Acevedo, M., Lopez-Bonilla, J., Sosa-Pedroza, J.: Apeiron 9, 43–48 (2002)

    Google Scholar 

  2. Ahsan, Z.: Tensors: Mathematics of Differential Geometry and Relativity. Second Printing: PHI Learning Pvt. Ltd, Delhi (2017)

    Google Scholar 

  3. Ahsan, Z., Bilal, M.: Int. J. Theo. Phys. 49, 2713–2722 (2010)

    Article  Google Scholar 

  4. Ahsan, Z., Bilal, M.: Int. J. Theo. Phys. 50, 1752–1768 (2011)

    Article  Google Scholar 

  5. Ahsan, Z., Bilal, M.: J. Tensor Soc. 6(2), 127–134 (2012)

    MathSciNet  Google Scholar 

  6. Ahsan, Z., Bilal, M.: Int. J. Theo. Phys. 52, 4275–4282 (2013)

    Article  Google Scholar 

  7. Ahsan, Z., Ahsan, N., Ali, S.: Bull. Cal. Math. Soc. 93(5), 407–422 (2001)

    Google Scholar 

  8. Ahsan, Z., Ahsan, N., Ali, S.: Maths. Today 19(2), 25–34 (2001)

    Google Scholar 

  9. Ahsan, Z., Caltenco, J.H., Lopez-Bonilla, J.L.: Annalen der Physik 16(4), 311–313 (2007)

    Article  MathSciNet  Google Scholar 

  10. Ahsan, Z., Caltencho, J.H., Linares, Y.M.R., Lopez-Bonilla, J.: Commun. Phys. 20(1), 9–14 (2010)

    Google Scholar 

  11. Ahsan, Z., Bilal, M., Lopez-Bonilla, J.: J. Vectorial Relativ. 5(3), 1–8 (2010)

    Google Scholar 

  12. Andersson, F.A., Edgar, S.B.: J. Math. Phys. 41, 2990–3001 (2000)

    Article  MathSciNet  Google Scholar 

  13. Aquino, N., Lopez Bonilla, J., Nunez-Yepez, H.N., Salas-Brito, A.L.: Phys. A-Math. Gen. 28, L375–L379 (1995)

    Article  Google Scholar 

  14. Ares de Parga, G., Lopez Bonilla, J., Ovando, G., Matos, T.: Rev. Mex. Fis. 35(3), 393–409 (1989)

    Google Scholar 

  15. Ares de Parga, G., Oscar Chavoya, A., Lopez Bonilla, J.L.: J. Math. Phys. 30, 1294–1295 (1989)

    Google Scholar 

  16. Arreaga, G., Lopez-Bonilla, J., Ovando, G.: Indian J. Pure Appl. Maths. 31, 85–91 (2000)

    Google Scholar 

  17. Bampi, F., Cavigilia, G.: Gen. Rel. Grav. 15, 375–386 (1983)

    Article  Google Scholar 

  18. Bergqvist, G.: J. Math. Phys. 38, 3142–3154 (1997)

    Article  MathSciNet  Google Scholar 

  19. Caltenco, J.H., Lopez-Bonilla, J., Morales, J., Ovando, G.: Chinese. J. Phys. 39, 397–400 (2001)

    Google Scholar 

  20. Cartin, D.: The Lanczos potential as a spin-2 field. arXiv:hep-th/0311185v1 (20 Nov. 2003)

  21. Dolan, P., Kim, C.W.: Proc. Roy. Soc. Lond. A 447, 557–575 (1994)

    Article  Google Scholar 

  22. Dolan, P., Kim, C.W.: Proc. Roy. Soc. Lond. A 447, 577–585 (1994)

    Article  Google Scholar 

  23. Dolan, P., Muratori, B.D.: J. Math. Phys. 39, 5404–5420 (1998)

    Article  Google Scholar 

  24. Edgar, S.B.: Mod. Phys. Lett. A 9, 479–482 (1994)

    Article  Google Scholar 

  25. Edgar, S.B.: Gen. Rel. Grav. 26, 329–332 (1994)

    Article  Google Scholar 

  26. Edgar, S.B., Höglund, A.: Proc. Roy. Soc. Lond. A 453, 835–851 (1997)

    Article  Google Scholar 

  27. Gaftoi, V., Lopez-Bonilla, J. L., Morales, J., Ovando, G., Pen̂a, J.J.: J. Moscow Phys. Soc. 6, 267–278 (1996)

    Google Scholar 

  28. Gaftoi, V., Lopez-Bonilla, J., Ovando, G.: Int. J. Theo. Phys. 38, 939–943 (1999)

    Article  Google Scholar 

  29. Gaftoi, V., Lopez-Bonilla, J., Ovando, G.: Nuovo Cimento B 113, 1489–1492 (1998)

    Google Scholar 

  30. Gaftoi, V., Lopez Bonilla J.L., Ovando, G., Pen̂a, J.J.: Nuovo Cimento B 113, 1493–1496 (1998)

    Google Scholar 

  31. Illge, R.: Gen. Rel. Grav. 20, 551–564 (1988)

    Article  MathSciNet  Google Scholar 

  32. Lanczos, C.: Rev. Mod. Phys. 34, 379–389 (1962)

    Article  Google Scholar 

  33. Lopez-Bonilla, J.L., Morales, J., Naverrete, D., Rosales, M.: Class. Quantum Grav. 10, 2153–2156 (1993)

    Article  Google Scholar 

  34. Lopez-Bonilla, J., Ovando, G., Rivera, J.: Nuovo Cimento B 112, 1433–1436 (1997)

    Google Scholar 

  35. Lopez-Bonilla, J., Ovando, G., Rivera, J.: Indian J. Pure Appl. Maths. 28, 1355–1360 (1997)

    Google Scholar 

  36. Lopez-Bonilla, J., Nunez-Yepez, H.N., Salas-Brito, A.L.: J. Phys. A : Math. Gen 30, 3663–3669 (1997)

    Article  Google Scholar 

  37. Lopez-Bonilla, J., Ovando, G.: Gen. Rel. Grav. 31, 1931–1934 (1999)

    Article  Google Scholar 

  38. Lopez-Bonilla, J., Morales, J., Ovando, G.: Gen. Rel. Grav. 31, 413–415 (1999)

    Article  Google Scholar 

  39. Massa, E., Pagani, E.: Gen. Rel. Grav. 16, 805–816 (1984)

    Article  Google Scholar 

  40. Mena, F.C., Tod, P.: Lanczos potential and a definition of gravitational entropy for perturbed FLRW spacetimes. arXiv:gr-qc/0702057v1 (9 Feb. 2007)

  41. Mora, C., Sanchez, R.: Lat. Am. J. Phys. Educ. 1(1), 78–82 (2007)

    Google Scholar 

  42. Novello, M., Velloso, A.L.: Gen. Rel. Grav. 19, 1251–1265 (1987)

    Article  Google Scholar 

  43. Roberts, M.D.: Gen. Rel. Grav. 20, 775–792 (1989). Mod. Phys. Lett. A 4, 2739 (1988)

    Google Scholar 

  44. Roberts, M.D.: Il Nouvo Cimento B110, 1105–1176 (1996)

    Google Scholar 

  45. Taub, A.H.: Comp. Math. Appl. 1, 377 (1975)

    Article  Google Scholar 

  46. del Castillo, T.: G. J. Math. Phys. 36, 195–200 (1995)

    Google Scholar 

  47. Zund, J.D.: Ann. Mat. Pure Appl. 104, 239–268 (1975)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zafar Ahsan .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ahsan, Z. (2019). Lanczos Potential and Tetrad Formalism. In: The Potential of Fields in Einstein's Theory of Gravitation. Springer, Singapore. https://doi.org/10.1007/978-981-13-8976-4_4

Download citation

Publish with us

Policies and ethics