Exact radiative spacetimes: some recent developments

Bičák, Jiřı́

doi:10.1002/(sici)1521-3889(200005)9:3/5<207::aid-andp207>3.0.co;2-l

Cited by 8 publications

(6 citation statements)

References 53 publications

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“…[63]- [70], [31], [57]. He has also summarized these results in many inspiring reviews [71]- [76], [1]. Altogether, the contributions concerning boost-rotation symmetric solutions represent almost a quarter of all Bičák's original publications.…”

Section: Expanding Impulsive Wavesmentioning

confidence: 99%

Exact Impulsive Gravitational Waves in Spacetimes of Constant Curvature

Podolský

2002

Gravitation: Following the Prague Inspiration

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Exact solutions exist which describe impulsive gravitational waves propagating in Minkowski, de Sitter, or anti-de Sitter universes. These may be either nonexpanding or expanding. Both cases in each background are reviewed here from a unified point of view. All the main methods for their construction are described systematically: the Penrose "cut and paste" method, explicit construction of continuous coordinates, distributional limits of sandwich waves, embedding from higher dimensions, and boosts of sources or limits of infinite accelerations.Attention is concentrated on the most interesting specific solutions. In particular, the nonexpanding impulsive waves that are generated by null multipole particles are described. These generalize the well-known Aichelburg-Sexl and Hotta-Tanaka monopole solutions. Also described are the expanding spherical impulses that are generated by snapping and colliding strings. Geodesics and some other properties of impulsive wave spacetimes are also summarized. *

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Section: Expanding Impulsive Wavesmentioning

confidence: 99%

Exact Impulsive Gravitational Waves in Spacetimes of Constant Curvature

Podolský

2002

Gravitation: Following the Prague Inspiration

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“…This makes plausible our interpretation of the KN (Λ) and RT N (Λ, ǫ) metrics as exact gravitational waves propagating on the constant curvature backgrounds. (3) The wave propagates in the space-like direction of e (3) and has a transverse character since only motions in the perpendicular directions of e (1) and e (2) are affected. The propagation direction given by e (3) coincides with the projection of the Debever-Penrose vector k on the hypersurface orthogonal to the observer's velocity u.…”

Section: On Physical Interpretation Of Non-twisting Type N Solutions mentioning

confidence: 99%

Radiative Fields in Spacetimes With Minkowski and De Sitter Asymptotics

Bičák

Krtouš

2003

Recent Developments in Gravity

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The classical Bondi-Penrose approach to the gravitational radiation theory in asymptotically flat spacetimes is recalled and recent advances in the proofs of the existence of such spacetimes are briefly reviewed. We then mention the unique role of the boost-rotation symmetric spacetimes, representing uniformly accelerated objects, as the only explicit radiative solutions known which are asymptotically flat; they are used as test beds in numerical relativity and approximation methods. The main part of the review is devoted to the examples of radiative fields in the vacuum spacetimes with positive cosmological constant. Type N solutions are analyzed by using the equation of geodesic deviation. Both these and RobinsonTrautman solutions of type II are shown to approach de Sitter universe asymptotically. Recent work on the the radiative fields due to uniformly accelerated charges in de Sitter spacetime ("cosmological Born's solutions") is reviewed and the properties of these fields are discussed with a perspective to characterize general features of radiative fields near a de Sitter-like infinity. IntroductionAfter several important contributions to the gravitational radiation theory in the late 1950's and early 1960's by Pirani, Bondi, Robinson, Trautman and others, a landmark paper by Bondi et al 4 appeared in which radiative properties of isolated (spatially bounded) axisymmetric systems were studied along outgoing null hypersurfaces u = constant, with u representing a retarded time function. An ansatz was made that the asymptotically Minkowski metric along u = constant can be expanded in inverse powers * An extended version of the invited talk given by J. B. at the 10th Greek Relativity Meeting in Kallithea, Chalkidiki, May 2002. Secs. 1, 2, 4 and 6 are in part based on the reviews quoted as Refs. 1, 2 and 3.

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“…Considerable work has been done on two classes of such models:

The mini-superspace cosmological solutions, in which so much symmetry is imposed that only functions of one parameter (the “time”) are subject to dynamical equations (see, e.g., Ashtekar et al , 1993a,b; Ashtekar, 2010). Quantization here resembles more the quantization of a system of particles than of waves, and does not seem likely to shed too much light on the generic case.

The midi-superspace (see Torre, 1999) solutions, notably the cylindrical wave metrics (see Ashtekar and Pierri, 1996; Ashtekar et al , 1997a,b; Bičák, 2000). Here, sufficient freedom remains to include both degrees of freedom of the gravitational field.…”

Section: Current Discussion: Physical Issues90mentioning

confidence: 95%

“…The midi-superspace (see Torre, 1999) solutions, notably the cylindrical wave metrics (see Ashtekar and Pierri, 1996; Ashtekar et al , 1997a,b; Bičák, 2000). Here, sufficient freedom remains to include both degrees of freedom of the gravitational field.…”

Section: Current Discussion: Physical Issues90mentioning

confidence: 99%

The Hole Argument and Some Physical and Philosophical Implications

Stachel

2014

Living Rev. Relativ.

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This is a historical-critical study of the hole argument, concentrating on the interface between historical, philosophical and physical issues. Although it includes a review of its history, its primary aim is a discussion of the contemporary implications of the hole argument for physical theories based on dynamical, background-independent space-time structures.The historical review includes Einstein's formulations of the hole argument, Kretschmann's critique, as well as Hilbert's reformulation and Darmois' formulation of the general-relativistic Cauchy problem. The 1970s saw a revival of interest in the hole argument, growing out of attempts to answer the question: Why did three years elapse between Einstein's adoption of the metric tensor to represent the gravitational field and his adoption of the Einstein field equations?The main part presents some modern mathematical versions of the hole argument, including both coordinate-dependent and coordinate-independent definitions of covariance and general covariance; and the fiber bundle formulation of both natural and gauge natural theories. By abstraction from continuity and differentiability, these formulations can be extended from differentiable manifolds to any set; and the concepts of permutability and general permutability applied to theories based on relations between the elements of a set, such as elementary particle theories.We are closing with an overview of current discussions of philosophical and physical implications of the hole argument.

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Exact radiative spacetimes: some recent developments

Cited by 8 publications

References 53 publications

Exact Impulsive Gravitational Waves in Spacetimes of Constant Curvature

Exact Impulsive Gravitational Waves in Spacetimes of Constant Curvature

Radiative Fields in Spacetimes With Minkowski and De Sitter Asymptotics

The Hole Argument and Some Physical and Philosophical Implications

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