Abstract
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of gravity being traced in rendering the equation for the scalar field nonlinear. We obtain regular (in the mass-less case) and asymptotic (in the massive case) solutions for the resulting matter field and discuss their ensuing finite time blowup in the light of earlier findings. Finally, some potentially interesting connections of these blowups with features of focusing in the theory of nonlinear partial differential equations are outlined, suggesting the potential relevance of a nonlinear theory of quantum cosmology.
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References
E. Witten, Nucl. Phys. B 311, 46 (1988).
M. Bañados, C. Teitelboim and J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992); M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Phys. Rev. D 48, 1506 (1993).
S. Giddings, J. Abbott and K. Kuchar, Gen. Rel. Grav. 16, 751 (1984).
J.D. Barrow, A.B. Burd and D. Lancaster, Class. Quantum. Grav. 3, 551 (1986).
N.J. Cornish and N.E. Frankel, Phys. Rev. D 43, 2555 (1991).
M.W. Choptuik, gr-qc/9803075.
N. Cruz and C. Martínez, Class. Quantum Grav. 17, 2867 (2000).
F. Williams and P.G. Kevrekidis, Class. Quantum Grav. 20, L177 (2003).
T. Koike, T. Hara and S. Adachi, Phys. Rev. Lett. 74, 5170 (1995).
A.M. Abrahams and C.R. Evans, Phys. Rev. Lett. 70, 2980 (1993).
C. Gundlach, gr-qc/9712084.
M.J. Landman, G.C. Papanicolaou, C. Sulem and P.L. Sulem, Phys. Rev. A 38, 3837 (1988).
C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger equation, Springer-Verlag (New York, 1999).
C.I. Siettos, I.G. Kevrekidis and P.G. Kevrekidis, Nonlinearity 16, 497 (2003).
B.J. Carr and A.A. Coley, Class. Quantum Grav. 16, R31 (1999).
S.W. Hawking and R. Penrose, Proc. R. Soc. A 314, 529 (1969).
S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press (Cambridge, 1973).
F.J. Tipler, G.F.R. Ellis and C. Clarke, General Relativity and Gravitation, ed. A Held, pp 97–206, Plenum (New York, 1978).
C. Clarke, Commun. Math. Phys. 41, 65 (1975); C. Clarke and J. Isenberg, Proc. 9th Int. Conf. on General Relativity and Gravitation ed. E Schmutzer, Cambridge University Press (Cambridge, 1982).
T. Christodoulakis et al. (in preparation).
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Christodoulakis, T., Helias, C., Kevrekidis, P., Kevrekidis, I., Papadopoulos, G. (2004). On 3+1 Dimensional Friedman-Robertson-Walker Universes with Matter. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_11
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DOI: https://doi.org/10.1007/1-4020-2190-9_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2188-6
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