Abstract
A new approach to the numerical solution of Einstein’s Equations based on the characteristic initial value problem is outlined. Because this approach requires integration through caustics and up to singularities, this topic is described and some novel finite-differencing techniques are introduced for integrating up to singularities of non-linear differential equations. Finally some preliminary results from this new approach are presented.
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
Preview
Unable to display preview. Download preview PDF.
References
Walker, M.: 1982, “On the positivity of total gravitational energy at retarded times”1, preprint MPA 19, Max-Planck-Institute for Astrophysics.
Penrose, R.: 1968, “Battelle Rencontres”, (ed. DeWitt, CM., and Wheeler, J.A., Benjamin), pp. 121–235.
Schmidt, B.G.: 1979, “Isolated Gravitating Systems in General Relativity”, (ed. Ehlers, J., Soc. Italiana di Fisica), pp. 11–49.
Newman, E.T. and Tod, K.P.: 1980, “General Relativity and Gravitation”, (ed. Held, A., Plenum), pp. 1–36.
Friedrich, H.: 1981, Proc.Roy.Soc.Lond. A375, pp.169–184.
Stewart, J.M. and Friedrich, H.: 1982, Proc.Roy.Soc.Lond. (in press).
Friedrich, H. and Stewart, J. M.: 1982, Proc.Roy.Soc.Lond. (in press).
Corkill, R. and Stewart, J.M.: 1982, “Numerical Relativity II” preprint MPA 32, Max-Planck-Institute for Astrophysics.
Newman, E.T. and Penrose, R.: 1962, J.Math.Phys. 3, pp.566–578.
Tipler, F.J., Clarke, C.J.S. and Ellis, G.F.R.: 1980, “General Relativity and Gravitation”, (ed. Held,A., Plenum), pp. 97–206.
Lambert, J.D. and Shaw, B.: 1966, Mathematics of Computation 20, pp.11–20.
Hartree, D.R.: 1958, “Numerical Analysis”, (2nd ed., Oxford).
Szekeres, P.: 1972, J.Math.Phys. 13, pp.286–294.
Khan, X. and Penrose, R.: 1971, Nature 229, pp.185–186.
Curtis, G.E.: 1978, General Relativity & Gravitation 9, pp.999–1008.
D’Eath, P.D.: 1978, Phys.Rev. D18, pp. 990–1019.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 D. Reidel Publishing Company
About this chapter
Cite this chapter
Stewart, J.M. (1986). The Characteristic Initial Value Problem in General Relativity. In: Winkler, KH.A., Norman, M.L. (eds) Astrophysical Radiation Hydrodynamics. NATO ASI Series, vol 188. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4754-2_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-4754-2_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8612-7
Online ISBN: 978-94-009-4754-2
eBook Packages: Springer Book Archive