Abstract
The null surface formulation of general relativity (NSF) differs from the standard approach by featuring a function \(Z\), describing families of null surfaces, as the prominent variable, rather than the metric tensor. It is possible to reproduce the metric, to within a conformal factor, by using \(Z\) (entering through its third derivative, which is denoted by \(\varLambda \)) and an auxiliary function \(\varOmega \). The functions \(\varLambda \) and \(\varOmega \) depend upon the spacetime coordinates, which are usually introduced in a manner that is convenient for the null surfaces, and also upon an additional angular variable. A brief summary of the (\(2+1\))-dimensional null surface formulation is presented, together with the NSF field equations for \(\varLambda \) and \(\varOmega \). A few special solutions are found and the properties of one of them are explored in detail.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Frittelli, S., Kozameh, C., Newman, E.: Lorentzian metrics from characteristic surfaces. J. Math. Phys. 36, 4975 (1995). doi:10.1063/1.531209
Frittelli, S., Kozameh, C., Newman, E.: GR via characteristic surfaces. J. Math. Phys. 36, 4984 (1995). doi:10.1063/1.531210
Frittelli, S., Kozameh, C., Newman, E.: Linearized Einstein theory via null surfaces. J. Math. Phys. 36, 5005 (1995). doi:10.1063/1.531211
Forni, D., Iriondo, M., Kozameh, C.: Null surfaces formulation in three dimensions. J. Math. Phys. 41, 5517 (2000). doi:10.1063/1.533422
Forni, D., Iriondo, M., Kozameh, C., Parisi, M.: Understanding singularities in Cartan’s and null surface formulation geometric structures. J. Math. Phys. 43, 1584 (2002). doi:10.1063/1.1408282
Tanimoto, M. : On the null surface formalism—formulation in three dimensions and gauge freedom, ArXiv:e-prints arXiv:gr-qc/9703003 (1997)
Silva-Ortigoza, G.: Null surfaces and their singularities in three-dimensional Minkowski space-time. Gen. Relativ. Gravit. 32, 2243 (2000). doi:10.1023/A:1001943407824
Harriott, T., Williams, J.: Light cone cut solution in the \(2+1\) null surface formulation. In: Damour, T., Jantzen, R., Ruffini, R. (eds.) Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, vol. 12, pp. 1896–1898. World Scientific, Singapore; Hackensack, NJ (2012). doi:10.1142/9789814374552_0355
Acknowledgments
This work was supported by the Mount Saint Vincent University Dean of Arts and Science Travel Fund. Discussions with Dr. Ted Newman and Dr. Simonetta Frittelli during the authors’ visits to Pittsburgh are gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Harriott, T.A., Williams, J.G. (2014). Solutions in the \(2+1\) Null Surface Formulation. In: Bičák, J., Ledvinka, T. (eds) Relativity and Gravitation. Springer Proceedings in Physics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-06761-2_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-06761-2_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06760-5
Online ISBN: 978-3-319-06761-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)