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Sep 22, 2013
09/13

by
Jacek Jezierski

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A complete description of the linearized gravitational field on a flat background is given in terms of gauge-independent quasilocal quantities. This is an extension of the results from gr-qc/9801068. Asymptotic spherical quasilocal parameterization of the Weyl field and its relation with Einstein equations is presented. The field equations are equivalent to the wave equation. A generalization for Schwarzschild background is developed and the axial part of gravitational field is fully analyzed....

Source: http://arxiv.org/abs/gr-qc/0111030v1

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108

Jul 20, 2013
07/13

by
Jacek Jezierski

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A twenty--dimensional space of charged solutions of spin--2 equations is proposed. The relation with extended (via dilatation) Poincar\'e group is analyzed. Locally, each solution of the theory may be described in terms of a potential, which can be interpreted as a metric tensor satisfying linearized Einstein equations. Globally, the non--singular metric tensor exists if and only if 10 among the above 20 charges do vanish. The situation is analogous to that in classical electrodynamics, where...

Source: http://arxiv.org/abs/gr-qc/9411066v1

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47

Sep 18, 2013
09/13

by
Jacek Jezierski

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Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitter spacetimes. Properties of asymptotic conformal Yano--Killing tensors are examined for asymptotic anti-de Sitter spacetimes. Explicit asymptotic forms of them are derived. The results are used to construct asymptotic charges in asymptotic AdS spacetime. Well...

Source: http://arxiv.org/abs/0705.4370v1

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44

Sep 19, 2013
09/13

by
Jacek Jezierski

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We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein equations are analyzed around null infinity. It is shown how the dynamics can be reduced to gauge invariant quanitities in a quasi-local way. The quasi-local gauge-invariant ``density'' of the hamiltonian is derived on the hyperboloid and on the future null...

Source: http://arxiv.org/abs/gr-qc/9703083v1

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46

Sep 18, 2013
09/13

by
Jacek Jezierski

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It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus $\mathbf{g} \geq 2$ is excluded by vacuum Einstein equations. The so-called {\em basic equation} (resulting from Einstein equations) is examined. This is a non-linear PDE for unknown covector field and unknown Riemannian structure on the two-dimensional manifold. It...

Source: http://arxiv.org/abs/0806.0518v1

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65

Sep 20, 2013
09/13

by
Jacek Jezierski

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We review some basic natural geometric objects on null hypersurfaces. Gauss-Codazzi constraints are given in terms of the analog of canonical ADM momentum which is a well defined tensor density on the null surface. Bondi cones are analyzed with the help of this object.

Source: http://arxiv.org/abs/gr-qc/0405108v1

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106

Jul 20, 2013
07/13

by
Jacek Jezierski

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The energy at null infinity is presented with the help of a simple example of a massless scalar field in Minkowski spacetime. It is also discussed for Einstein gravity. In particular, various aspects of the loss of the energy in the radiating regime are shown.

Source: http://arxiv.org/abs/gr-qc/9910085v1

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49

Sep 19, 2013
09/13

by
Jacek Jezierski

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It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the gauge-invariant quantities. Both degrees of freedom fulfill generalized scalar wave equation. For the axial degree of freedom the radial part of the equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069 (1957)) and for the polar one we get...

Source: http://arxiv.org/abs/gr-qc/9801068v1

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77

Jul 20, 2013
07/13

by
Jacek Jezierski

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New geometric objects on null thin layers are introduced and their importance for crossing null-like shells are discussed. The Barrab\`es--Israel equations are represented in a new geometric form and they split into decoupled system of equations for two different geometric objects: tensor density ${\bf G}^a{_b}$ and vector field $I$. Continuity properties of these objects through a crossing sphere are proved. In the case of spherical symmetry Dray--t'Hooft--Redmount formula results from...

Source: http://arxiv.org/abs/gr-qc/0406084v1

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8.0

Jun 30, 2018
06/18

by
Jacek Jezierski; Szymon Migacz

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The "fully charged" spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the "non-waving" part of the spin-2 field theory. Basic facts and definitions of the spin--2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3+1 decomposition leads to the construction of the momentary gravitational charges on...

Topics: Mathematics, Mathematical Physics, General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1404.6629

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65

Sep 23, 2013
09/13

by
Jacek Jezierski; Maciej Łukasik

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Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel--Robinson tensor and is examined in Kerr...

Source: http://arxiv.org/abs/gr-qc/0510058v2

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Jun 28, 2018
06/18

by
Jacek Jezierski; Piotr Waluk

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Here we present an alternative approach, requiring only basic tools of differential geometry. This method was conceived by Kijowski and first presented during the IV Marcel Grossman Meeting on General Relativity in Rome (1986). It was later published in a generalized form by J. Jezierski, J. Kijowski in 1987 (Positivity of total energy in general relativity, Physical Review D {\bf 36} (1987), 1041-4). We summarize these results briefly and present a new foliation gauge.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1508.05795

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Jun 26, 2018
06/18

by
Jacek Jezierski; Tomasz Smołka

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We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Kiling tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1502.00599

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Sep 22, 2013
09/13

by
Jacek Jezierski; Jerzy Kijowski

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A new parameterization of unconstrained degrees of freedom for gravitational field, used in Classical and Quantum Gravity {\bf 11}, 1055-1068 (1994), has been generalized to one-parameter family of such parameterizations, depending on a real parameter $\beta \in [0,2]$. The description introduced in CQG 11, 1055 corresponds to the special choice $\beta=0$. The method is closely related to the proof of the positivity of the energy presented in Phys. Rev. D {\bf 36}, 1041-1044 (1987) where...

Source: http://arxiv.org/abs/gr-qc/0501073v1

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78

Sep 23, 2013
09/13

by
Jacek Jezierski; Jerzy Kijowski

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The field theoretical description of thermo-hydrodynamics is given. It is based on the duality between the physical space--time and the "material space-time" which we construct here. The material space appearing in a natural way in the canonical formulation of the hydrodynamics is completed with a material time playing role of the field potential for temperature. Both Lagrangian and Hamiltonian formulations, the canonical structure, Poisson bracket, N\"other theorem and...

Source: http://arxiv.org/abs/1112.5842v1

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Sep 19, 2013
09/13

by
Jacek Jezierski; Maciej Łukasik

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Symmetric conformal Killing tensors and (skew-symmetric) conformal Yano-Killing tensors for Euclidean Taub-NUT metric are given in explicit form. Relations between Yano and CYK tensors in terms of conformal rescaling are discussed.

Source: http://arxiv.org/abs/gr-qc/0610090v1

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45

Sep 19, 2013
09/13

by
Piotr T. Chruściel; Jacek Jezierski

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We provide a simple explicit parameterization of free general relativistic data on the light cone.

Source: http://arxiv.org/abs/1010.2098v1

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113

Sep 18, 2013
09/13

by
Jacek Jezierski; Jerzy Kijowski; Ewa Czuchry

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A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities. For this purpose the notion of an extrinsic curvature for a null-like hypersurface is discussed and the corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi identities for spacetimes with null-like, singular curvature. Energy-momentum tensor-density of a light-like matter shell is unambiguously...

Source: http://arxiv.org/abs/gr-qc/0110018v1

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58

Sep 18, 2013
09/13

by
Tomasz Pawlowski; Jerzy Lewandowski; Jacek Jezierski

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It seems to be expected, that a horizon of a quasi-local type, like a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighborhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the...

Source: http://arxiv.org/abs/gr-qc/0306107v1

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61

Sep 21, 2013
09/13

by
Jacek Jezierski; Jerzy Kijowski; Szymon Leski

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An attempt to construct the ``ground state'' vacuum initial data for the gravitational field surrounding two black holes is presented. The ground state is defined as the gravitational initial data minimizing the ADM mass within the class of data for which the masses of the holes and their distance are fixed. To parameterize different geometric arrangements of the two holes (and, therefore, their distance) we use an appropriately chosen scale factor. A method for analyzing the variations of the...

Source: http://arxiv.org/abs/0706.0129v2

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15

Jun 28, 2018
06/18

by
Piotr T. Chruściel; Jacek Jezierski; Jerzy Kijowski

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We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out.

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1507.03868

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71

Sep 23, 2013
09/13

by
Piotr T. Chrusciel; Jacek Jezierski; Jerzy Kijowski

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We derive the Hamiltonian mass for general relativistic initial data sets with asymptotically Schwarzschild-de Sitter ends.

Source: http://arxiv.org/abs/1305.1014v2

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13

Jun 28, 2018
06/18

by
Hans-Peter Gittel; Jacek Jezierski; Jerzy Kijowski

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This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and introduce conditions on external curvature and torsion, which lead to a definition of a {\em rigid sphere}. The main result is a local existence theorem concernig such spheres. For this purpose we apply the surjective implicit function theorem. The proof is based...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1508.07872

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Sep 23, 2013
09/13

by
Piotr Dzierzak; Jacek Jezierski; Przemyslaw Malkiewicz; Wlodzimierz Piechocki

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The appearance of the big bounce (BB) in the evolution of the universe is analyzed in the setting of loop quantum cosmology (LQC). Making use of an idea of a minimum length turns classical Big Bang into BB. We argue why the spectrum of the kinematical area operator of loop quantum gravity cannot be used for the determination of this length. We find that the fundamental length, at the present stage of development of LQC, is a free parameter of this model.

Source: http://arxiv.org/abs/0810.3172v3

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61

Sep 18, 2013
09/13

by
Piotr T. Chruściel; Jacek Jezierski; Malcolm A. H. MacCallum

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It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri, are those depending on the metric only through a specific combination of the Bondi `mass aspect' and other next--to--leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman--Bondi energy....

Source: http://arxiv.org/abs/gr-qc/9803010v1

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49

Sep 19, 2013
09/13

by
Piotr T. Chrusciel; Jacek Jezierski; Malcolm A. H. MacCallum

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The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a...

Source: http://arxiv.org/abs/gr-qc/9801073v1