Abstract
The current use of computers in general relativity was reviewed at GR10. Today several groups have working codes which can calculate the coupled general relativity/hydrodynamics equations in two spatial dimensions plus time. These codes are compared and a critical review is made of the areas needing improvement. The potential uses of numerical relativity are discussed. In some situations the gravitational field can be chosen to be an analytically known solution, and hydrodynamics can be done in that background field. Regge calculus is still in its infancy numerically, but interesting new work has been done. Algebraic computing is becoming a mature technology, with the emphasis moving toward making these powerful software tools available to those relativists without previous computer training.
Alfred P. Sloan Fellow.
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
Bertotti, B., de Felice, F., and Pascolini, A. (eds): 1983, 10th International Conference on General Relativity and Gravitation. Contributed Papers, Vols 1–2, CNR, Roma.
Brewin, L.: 1983, “Computer generated solutions using Regge calculus”, p. 427.
Bicknell, G.V., and Gingold, R.A.: 1983, “Tidal detonation of stars by black holes”, p. 690.
Hawley, J., Smarr, L., and Wilson, J.R.: 1983, “Numerical simulation of flat disks around black holes”, p. 709.
Lanza, A., Miller, J.C., and Motta, S.: 1983, “Formation and damping of relativistic strong shocks”, p. 436.
Luminet, J.P., and Marck, J.A.: 1983, “Tidal effects in Kerr geometry”, p. 438.
Maallum, M.A.H.: 1983a, “Proposed format for recording the invariant characterisation of exact solutions”, p. 301.
Miller, J.C.: 1983, “Non-axisymmetric instabilities in gravitational collapse”, p. 443.
Williams, R.M., and Ellis, G.F.R.: 1983, “Observational results from Regge calculus”, p. 451.
Other References
Brill, D.R.: 1959, “On the Positive Definite Mass of the Bondi-Weber-Wheeler Time-Symmetric Gravitational Waves”, Ann. Phys., 7, 466.
Centrella, J. and Wilson, J. R.,: 1983a, “Planar numerical cosmology. I. The differential equations”, Astrophys. J., 273, 428.
Centrella, J., and Wilson, J.R.: 1983b, “Planar Cosmology. II. The difference equations and numerical tests”, University of Illinois, Astronomy preprint 83–11.
Collins, P.A., and Williams, R.M.: 1973, “Dynamics of the Friedmann Universe Using Regge Calculus”, Phys. Rev., D7, 965.
Eardley, D.M.: 1979, “Global problems in numerical relativity”, in L. Smarr (ed.), Sources of Gravitational Radiation, Cambridge University Press, Cambridge, pp. 127–138.
Eardley, D.M., and Smarr, L.: 1979, “Time functions in numerical relativity: marginally bound dust collapse”, Phys. Rev., D19, 2239.
Eppley, K.: 1979, “Pure gravitational waves”, in L. Smarr (ed.), Sources of Gravitational Radiation, Cambridge University Press, Cambridge, pp.275–292.
Estabrook, F., Wahlquist, H., Christensen, S., Ditt, B., Smarr, L., and Tsiang, E.: 1973, “Maximally Slicing a Black Hole”, Phys. Rev., D7, 2814.
Evans, C.: 1984, “A method for numerical simulation of gravitational collapse and gravitational radiation generation”, in J. Centrella, R. Bowers, J. LeBlanc, and M. LeBlanc (eds), Numerical Astrophysics: A Festschrift in Honor of James R. Wilson.
Evans, C., Smarr, L., and Wilson, J.R.: 1984, “Numerical relativistic collapse and collisions with spatial time slices”, in K.-H.A. Winkler, and M.L. Norman (eds), Radiation Hydrodynamics, Reiael, Dordrecht.
Geroch, R.: 1971, “A Method of Generating Solutions of Einstein’s Equations”, J. Math. Phys., 12, 918.
Haugan, M.P., Shapiro, S.L., and Wasserman, I.: 1982, “The soppression of gravitational radiation from finite-size stars falling into black holes”, Astrophys. J., 257, 283.
Hawley, J.F., Smarr, L., and Wilson, J.R.: 1983b, “A numerical study of nonspherical black hole accretion. I. Equations and test particles”, University of Illinois Astronomy preprint 83–9, to appear in Astrophys. J.
Hawley, J.F., Smarr, L., and Wilson, J.R.: 1983c, “A numerical study of nonspherical black hole accretion. II. Finite differencing and code calibration”, University of Illinois, Astronomy preprint, to appear in Astrophys. J. Suppl.
Isaacson, R.A., Wellings, J.S., and Winicour, J.: 1983, “Null cone computation of gravitational radiation”, J. Math. Phys., 24, 1824.
Maallum, M.A.H.: 1983b, “Classifying metrics in theory and practice”, in V. De Sabbata, and E. Schmutzer (eds), Unified Field Theory of more than 4 Dimension Including Exact Solutions, World Scientific Publishing, Singapore, p. 352.
May, M.M., and White, R.H.: 1967, “Stellar Dynamics and Gravitational Collapse”, Methods Comput. Phys., 7, 219.
Nakamura, T.: 1981, “General Relativistic Collapse of Axially Symmetric Stars Leading to the Formation of Rotating Black Holes”, Prog. Theor. Phys., 65, 1876.
Nakamura, T.: 1983, “General relativistic collapse of rotating stars”, to appear in the proceedings of the 11th Texas Symposium on Relativistic Astrophysics.
Piran, T.: 1980, “Numerical codes for cylindrical general relativistic systems”, J. Comput. Phys., 35, 254.
Press, W.H.: 1971, “Long wave trains of gravitational waves from a vibrating black hole”; Astrophys. J. Lett., 170, L105.
Shapiro, S. L., and Teukolsky, S. A.: 1980, “Gravitational collapse to neutron stars and black holes: computers generation of spherical spacetimes”, Astrophys. J., 235, 199.
Smarr, L.s 1979, “Gauge condition, radiation formulae and the two black hole collision”, in L. Smarr (ed.), Sources of Gravitational Radiation, Cambridge University Press, Cambridge, pp.245–274.
Smarr, L., and Hawley, J.F.: 1983, “General Relativistic Hydrodynamics and accretion physics: a numerical approach”, to appear in the Proceedings of the Toulouse Workshop on Gravitational Collapse.
Stewart, J.M., and Friedrich, H.: 1982, “Numerical Relativity. I. The characteristic initial value problem”, Proc. Roy. Soc., A384, 427.
Wilson, J.R.: 1979, “A numerical method for relativistic hydrodynamics”, in L. Smarr (ed.), Sources of Gravitational Radiation, Cambridge University Press, Cambridge, pp. 423–446.
Winkler, K.-H.A., and Norman, M.L.: 1984, “WH80’s: Numerical Radiation Hydrodynamics”, to appear in M.L. Norman, and K.-H.A. Winkler (eds), Radiation Hydrodynamics, Reidel, Dordrecht.
York, J.W., Jr.: 1979: “Kinematics and dynamics of general relativity”, in L. Smarr (ed.), Sources of Gravitational Radiation, Cambridge University Press, Cambridge, pp. 83–126.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company
About this chapter
Cite this chapter
Smarr, L. (1984). Computational Relativity: Numerical and Algebraic Approaches Report of Workshop A4. In: Bertotti, B., de Felice, F., Pascolini, A. (eds) General Relativity and Gravitation. Fundamental Theories of Physics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6469-3_11
Download citation
DOI: https://doi.org/10.1007/978-94-009-6469-3_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6471-6
Online ISBN: 978-94-009-6469-3
eBook Packages: Springer Book Archive