Levi-Civita cylinders with fractional angular deficit

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.Comment: 5 figure

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components--the ingoing and outgoing dusts--are assumed to interact only through gravitation. Different kinds of singularities, naked or "clothed", that can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bicak and Kuchar is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).Comment: 15 pages, 3 figures, submitted to Phys. Rev.

Null dust in canonical gravity

We present the Lagrangian and Hamiltonian framework which incorporates null dust as a source into canonical gravity. Null dust is a generalized Lagrangian system which is described by six Clebsch potentials of its four-velocity Pfaff form. The Dirac--ADM decomposition splits these into three canonical coordinates (the comoving coordinates of the dust) and their conjugate momenta (appropriate projections of four-velocity). Unlike ordinary dust of massive particles, null dust therefore has three rather than four degrees of freedom per space point. These are evolved by a Hamiltonian which is a linear combination of energy and momentum densities of the dust. The energy density is the norm of the momentum density with respect to the spatial metric. The coupling to geometry is achieved by adding these densities to the gravitational super-Hamiltonian and supermomentum. This leads to appropriate Hamiltonian and momentum constraints in the phase space of the system. The constraints can be rewritten in two alternative forms in which they generate a true Lie algebra. The Dirac constraint quantization of the system is formally accomplished by imposing the new constraints as quantum operator restrictions on state functionals. We compare the canonical schemes for null and ordinary dust and emhasize their differences.Comment: 25 pages, REVTEX, no figure

Cauchy-characteristic Evolution And Waveforms

We investigate a new methodology for the computation of waves generated by isolated sources. This approach consists of a global spacetime evolution algorithm based on a Cauchy initial-value formulation in a bounded interior region and based on characteristic hypersurfaces in the exterior; we match the two schemes at their common interface. The characteristic formulation allows accurate description of radiative infinity in a compactified finite coordinate interval, so that our numerical solution extends to infinity and accurately models the free-space problem. The matching interface need not be situated far from the sources, the wavefronts may have arbitrary nonspherical geometry, and strong nonlinearity may be present in both the interior and the exterior regions. Stability and second-order convergence of the algorithms (to the exact solution of the infinite-domain problem) are established numerically in three space dimensions. The matching algorithm is compared with examples of both local and nonlocal radiation boundary conditions proposed in the literature. For linear problems, matching outperformed the local radiation conditions chosen for testing, and was about as accurate (for the same grid resolution) as the exact nonlocal conditions. However, since the computational cost of the nonlocal conditions is many times that of matching, this algorithm may be used with higher grid resolutions, yielding a significantly higher final accuracy. For strongly nonlinear problems, matching was significantly more accurate than all other methods tested. This seems to be due to the fact that currently available local and nonlocal conditions are based on linearizing the governing equations in the far field, while matching consistently takes nonlinearity into account in both interior and exterior regions. © 1997 Academic Press.1361140167Lindman, E., (1975) J. Comput. Phys., 18, p. 66Israeli, M., Orszag, S.A., (1981) J. Comput. Phys., 41, p. 115Higdon, R., (1986) Math. Comput., 47, p. 437Renaut, R., (1992) J. Comput. Phys., 102, p. 236Givoli, D., (1991) J. Comput. Phys., 94, p. 1Tsynkov, S.V., Artificial Boundary Conditions Based on the Difference Potentials Method (1996) NASA Technical Memorandum No. 110265Ryaben'kii, V., Tsynkov, S.V., An application of the difference potentials method to solving external problems in CFD (1997) NASA Technical Memorandum No. 110338Engquist, B., Majda, A., (1977) Math. Comput., 31, p. 629Bayliss, A., Turkel, E., (1980) Commun. Pure Appl. Math., 33, p. 707Trefethen, L., Halpern, L., (1986) Math. Comput., 47, p. 421Blaschak, J., Kriegsmann, G., (1988) J. Comput. Phys., 77, p. 109Jiang, H., Wong, Y.S., (1990) J. Comput. Phys., 88, p. 205Ting, L., Miksis, M., (1986) J. Acoust. Soc. Am., 80, p. 1825De Moerloose, J., De Zutter, D., (1993) IEEE Trans. Antennas Propagation, 41, p. 890Thompson, K.W., (1987) J. Comput. Phys., 68, p. 1Hedstrom, G.W., (1979) J. Comput. Phys., 30, p. 222Hagstrom, T.M., Hariharan, S., (1988) Math. Comput., 581, p. 51Friedlander, F.G., (1975) The Wave Equation on a Curved Space-Time, , Cambridge: Cambridge Univ. Press. p. 193-Gómez, R., Winicour, J., Isaacson, R., (1992) J. Comput. Phys., 98, p. 11Penrose, R., (1963) Phys. Rev. Lett., 10, p. 66Friedrich, H., Stewart, J.M., (1983) Proc. R. Soc. A, 385, p. 345Bishop, N., (1992) Approaches to Numerical Relativity, , Cambridge: Cambridge Univ. PressBishop, N., (1993) Class. Quantum Grav., 10, p. 333Clarke, C., D'Inverno, R., (1994) Class. Quantum Grav., 11, p. 1463Bishop, N.T., (1996) Phys. Rev. Lett., 76, p. 4303Anderson, J., (1988) J. Comput. Phys., 75, p. 288Anderson, J.L., Hobill, D.W., (1986) Dynamical Spacetimes and Numerical Relativity, , J.M. Centrella. Cambridge: Cambridge Univ. PressGómez, R., Laguna, P., Papadopoulos, P., Winicour, J., (1996) Phys. Rev. D, 54, p. 4719Clarke, C., D'Inverno, R., Vickers, J., (1995) Phys. Rev. D, 52, p. 6863Dubal, M., D'Inverno, R., Clarke, C., (1995) Phys. Rev. D, 52, p. 6868Gómez, R., Lehner, L., Papadopoulos, P., Winicour, J., (1997) Class. Quantum Grav., 14, p. 977Papadopoulos, P., (1994), University of PittsburghHardy, R., (1990) Comput. Math. Appl., 19, p. 163Franke, R., (1982) Math. Comput., 38, p. 381Kansa, E., (1990) Comput. Math. Appl., 19, p. 147Dubal, M., (1992) Phys. Rev. D, 45, p. 1178Cook, G., (1993) Phys. Rev. D, 47, p. 1471Buhmann, M., Dyn, N., (1991) Curves and Surfaces, , P.-J. Laurent, A. Le Méhauté, & L. Schumaker. New York: Academic PressPowell, M., (1991) Curves and Surfaces, , P.-J. Laurent, A. Le Méhauté, & L. Schumaker. New York: Academic PressCarlson, R., Foley, T., (1991) Comput. Math. Appl., 21, p. 29Mitchell, A., Griffiths, D., (1980) The Finite Difference Method in Partial Differential Equations, , Chichester: WileyRichardson, L., (1910) Philos. Trans. R. Soc., 210, p. 307Zwillinger, D., (1992) Handbook of Differential Equations, , San Diego: Academic PressBishop, N., (1996) 3rd Texas Workshop on 3-Dimensional Numerical Relativity, , R. Matzner, Univ. of Texas, AustinBishop, N., Gómez, R., Lehner, L., Winicour, J., (1996) Phys. Rev. D, 54, p. 6153Shampine, L., Gordon, M., (1975) Computer Solution of Ordinary Differential Equations: The Initial Value Problem, , San Francisco: Freema

Cauchy-characteristic matching: A new approach to radiation boundary conditions

We investigate a new methodology for computing wave generation, using Cauchy evolution in a bounded interior region and characteristic evolution in the exterior. Matching the two schemes eliminates usual difficulties such as backreflection from the outer computational boundary. Mapping radiative infinity into a finite grid domain allows a global solution. The matching interface can be close to the sources, the wave fronts can have arbitrary geometry, and strong nonlinearity can be present. The matching algorithm dramatically outperforms traditional radiation boundary conditions.76234303430

2017 UA43

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2016 EK85

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2016 EK85

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2017 WC14

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2016 EK85

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