Summary
A new form of multipole expansions is presented. The method is economical and has many definite advantages over the older versions. It is applied to the linear wave equations and to the spherically symmetric strong-gravity solutions. By using the Hamiltonian formalism it is shown that the strong-gravity solutions are unstable under small perturbations.
Riassunto
Si presenta una nuova forma di espansioni di multipolo. Il metodo è economico e ha molti vantaggi definite rispetto alle versioni più vecchie. Lo si applica all'equazioni d'onda lineari ed a soluzioni a gravità forte per simmetriesferiche. Usando il formalismo hamiltoniano si mostra che le soluzioni per gravità forte sono instabili sotto forti perturbazioni.
Резюме
Предлагается новая форма мультипольных разложений. Этот метод является экономным и имеет ряд определенных преимуществ по сравнению с предыдущими подходами. Предложенный метод применяется к линейным волновым уравнеиям и к сферически симметричным решениям теории сильной гравитации. Используя Гамильтонов формализм, показывается, что решения сильной гравитации являются неустойчивыми относительно малых возмущений.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. M. Landau andE. M. Lifshitz:The Classical Theory of Fields, 3rd revised English edition, translated byM. Hamermesh (Oxford, and Reading, Mass., 1971);Abdus Salam andJ. Strathdee:Phys. Rev. D,16, 2668 (1977);Phys. Lett.,67 B, 429 (177).
T. Regge andJ. A. Wheeler:Phys. Rev.,108, 1063 (1957);F. Zerilli:Phys. Rev. Lett.,24, 737 (1970);C. V. Vishveshwara:Phys. Rev. D,1, 2870 (1970);V. Moncrief:Ann. of Phys.,88, 323, 343 (1974).
E. Newman andR. Penrose:Journ. Math. Phys.,7, 863 (1966);J. N. Goldberg, A. J. Macfarlane, E. T. Newman, F. Rohrlich andE. C. G. Sudarshan:Journ. Math. Phys.,8, 2155 (1967).
C. J. Isham, Abdus Salam andJ. Strathdee:Phys. Rev. D.,3, 867 (1971).
Abdus Salam andJ. Strathdee: IC/77/153 andPhys. Rev. D,16, 2668 (1977).
We use the conventions and notations ofC. W. Misner, K. S. Thorne andJ. A. Wheeler:Gravitation (San Francisco, Cal., 1973).
R. Arnowitt, S. Deser andC. Misner:The Dynamics of general relativity, inGravitation: An Introduction to Current Research edited byL. Witten (New York, N. Y., 1962), p. 227.
S. A. Baran:Unstability of strong gravity solution, to be published.
D. G. Boulware andS. Deser:Phys. Rev. D,6, 3368 (1972).
See the appendix.
Hamiltonians form≠0 are obtainable from these by making the symmetrical replacementsp 1 p 2→p *1 p 2+p 1 p *2 in each term.
Variation with respect ton 0 apparently yields one constraint. In order for this to be compatible with the equation of motion, a second constraint which is the time derivative of the first must also be satisfied. The pair of constraints would then serve to eliminate oneq and onep. This is what happens in the linearized system with Fierz-Pauli mass term in flat space-time and it seems plausible that it will occur here as well, but we have not investigated the matter.
L. A. Edelstein andC. V. Vishveshwara:Phys. Rev. D,1, 3514 (1970).
Author information
Authors and Affiliations
Additional information
Work supported in part by the Scientific and Technical Research Council of Turkey, TBTAK.
Traduzione a cura della Redazione.
Перебедено редакцией.
Rights and permissions
About this article
Cite this article
Baran, S.A. Multipole expansions in strong-gravity theory. Nuov Cim B 52, 69–89 (1979). https://doi.org/10.1007/BF02743570
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02743570