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  • 1
    Electronic Resource
    Electronic Resource
    Symmetries of cosmological Cauchy horizons (1983)
    Springer
    Communications in mathematical physics 89 (1983), S. 387-413 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider analytic vacuum and electrovacuum spacetimes which contain a compact null hypersurface ruled byclosed null generators. We prove that each such spacetime has a non-trivial Killing symmetry. We distinguish two classes of null surfaces, degenerate and non-degenerate ones, characterized by the zero or non-zero value of a constant analogous to the “surface gravity” of stationary black holes. We show that the non-degenerate null surfaces are always Cauchy horizons across which the Killing fields change from spacelike (in the globally hyperbolic regions) to timelike (in the acausal, analytic extensions). For the special case of a null surface diffeomorphic toT 3 we characterize the degenerate vacuum solutions completely. These consist of an infinite dimensional family of “plane wave” spacetimes which are entirely foliated by compact null surfaces. Previous work by one of us has shown that, when one dimensional Killing symmetries are allowed, then infinite dimensional families of non-degenerate, vacuum solutions exist. We recall these results for the case of Cauchy horizons diffeomorphic toT 3 and prove the generality of the previously constructed non-degenerate solutions. We briefly discuss the possibility of removing the assumptions of closed generators and analyticity and proving an appropriate generalization of our main results. Such a generalization would provide strong support for the cosmic censorship conjecture by showing that causality violating, cosmological solutions of Einstein's equations are essentially an artefact of symmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214662
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  • 2
    Electronic Resource
    Electronic Resource
    The existence of constant mean curvature foliations of Gowdy 3-torus spacetimes (1982)
    Springer
    Communications in mathematical physics 86 (1982), S. 485-493 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the class of smooth, maximally extended, globally hyperbolic, vacuum, Gowdy spacetimes onT 3×R and prove that these spacetimes are globally foliated by space-like, constant mean curvature hypersurfaces. Our results can easily be extended to cover electrovac solutions of the same symmetry type and can probably be extended to cover other spacetime topologies as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214884
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  • 3
    Electronic Resource
    Electronic Resource
    The well-posedness of (N=1) classical supergravity (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 329-333 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we investigate whether classical (N=1) supergravity has a well-posed locally causal Cauchy problem. We define well-posedness to mean that any choice of initial data (from an appropriate function space) which satisfies the supergravity constraint equations and a set of gauge conditions can be continuously developed into a space-time solution of the supergravity field equations around the initial surface. Local causality means that the domains of dependence of the evolution equations coincide with those determined by the light cones. We show that when the fields of classical supergravity are treated as formal objects, the field equations are (under certain gauge conditions) equivalent to a coupled system of quasilinear nondiagonal second-order partial differential equations which is formally nonstrictly hyperbolic (in the sense of Leray–Ohya). Hence, if the fields were numerical valued, there would be an applicable existence theorem leading to well-posedness. We shall observe that well-posedness is assured if the fields are taken to be Grassmann (i.e., exterior algebra) valued, for then the second-order system decouples into the vacuum Einstein equation and a sequence of numerical valued linear diagonal strictly hyperbolic partial differential equations which can be solved successively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526663
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  • 4
    Electronic Resource
    Electronic Resource
    Symmetries of cosmological Cauchy horizons with exceptional orbits (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1024-1027 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show here that if an analytic space-time satisfying the vacuum (or electrovacuum) Einstein equations contains a compact null hypersurface with closed generators, then the space-time must have a nontrivial Killing vector field. This result is an extension of an earlier theorem, which required that the generators of the hypersurface must not only be closed, but in addition must satisfy a local product bundle (LPB) condition. This LPB condition (which is known to be violated in certain of the Kerr–Taub–NUT space-time models) is equivalent to the requirement that the generators must all be ordinary fibers of a Seifert fibration. We prove here that the LPB condition can be dropped. Thus we have stronger support for our conjecture that causality violations (as evidenced by Cauchy horizons) in cosmological solutions of the Einstein equations are essentially an artifact of symmetry, and are therefore nongeneric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526587
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  • 5
    Electronic Resource
    Electronic Resource
    Singularity formation in 2+1 wave maps (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 678-683 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1418717
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  • 6
    Electronic Resource
    Electronic Resource
    Asymptotic behavior in polarized T2-symmetric vacuum space–times (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 340-352 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We use the Fuchsian algorithm to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy space–times, but their twist does not vanish. The space–times are also polarized in the sense that one of the "gravitational degrees of freedom" is turned off. Examining an analytic family of solutions with the maximum number of arbitrary functions, we find that they are all asymptotically velocity-term dominated as one approaches the singularity. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532775
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  • 7
    Electronic Resource
    Electronic Resource
    Evolution of the Bel–Robinson energy in Gowdy T 3×R space-times (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 517-519 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528885
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  • 8
    Electronic Resource
    Electronic Resource
    On the determination of Cauchy surfaces from intrinsic properties (1978)
    Springer
    Communications in mathematical physics 61 (1978), S. 87-95 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the problem of determining from intrinsic properties whether or not a given spacelike surface is a Cauchy surface. We present three results relevant to this question. First, we derive necessary and sufficient conditions for a compact surface to be a Cauchy surface in a spacetime which admits one. Second, we show that for a non-compact surface it is impossible to determine whether or not it is a Cauchy surface without imposing some restriction on the entire spacetime. Third, we derive conditions for an asymptotically flat surface to be a Cauchy surface by imposing the global condition that it be imbedded in a weakly asymptotically simple and empty spacetime.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609469
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  • 9
    Electronic Resource
    Electronic Resource
    Quantum cosmology and geometric quantization (1981)
    Springer
    General relativity and gravitation 13 (1981), S. 301-306 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Kostant-Souriau method of geometric quantization is applied to homogeneous and isotropic cosmological models with positive intrinsic curvature and a massless Klein-Gordon scalar field. These models are studied because classically they collapse to a singularity. It is rigorously shown that the quantized models collapse as well (so that there is no “quantum bounce”). This work demonstrates the practical usefulness of geometric quantization for the study of physical systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01025465
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  • 10
    Electronic Resource
    Electronic Resource
    Steering the universe (1986)
    Springer
    Foundations of physics 16 (1986), S. 651-665 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We discuss the present status of the Cauchy problem for Einstein's classical field theory of gravity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01889627
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