Gravitational Fields in Finite and Conformal Bondi Frames

Tamburino, Louis A.; Winicour, Jeffrey

doi:10.1103/physrev.150.1039

Cited by 236 publications

(298 citation statements)

References 15 publications

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“…Moreover, the Penrose covariant approach can be naturally applied also to spacetimes which include the cosmological constant [28,29,33,51]. This is quite remarkable, since there is no analogue of the news function in the presence of Λ [52,53] (for a comparison of the Bondi-Sachs and Penrose approaches see, e.g., [50,[54][55][56][57][58][59]). …”

Section: On Studies Of Asymptotic Behaviour Of Radiative Fields In Gementioning

confidence: 99%

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

Krtouš¹,

Podolský²

2004

Class. Quantum Grav.

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Abstract. We analyze the directional properties of general gravitational, electromagnetic, and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of I. The standard peelingoff property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for Λ > 0) or timelike (for Λ < 0), and the radiative component of each field depends substantially on the null direction along which P is approached.The directional dependence of asymptotic fields near such de Sitter-like or anti-de Sitterlike I is explicitly found and described. We demonstrate that the corresponding directional structure of radiation has a universal character that is determined by the algebraic (Petrov) type of the field. In particular, when Λ > 0 the radiation vanishes only along directions which are opposite to principal null directions. For Λ < 0 the directional dependence is more complicated because it is necessary to distinguish outgoing and ingoing radiation. Near such anti-de Sitterlike conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to I.The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This characterization offers a better understanding of the asymptotic behaviour of the fields near conformal infinity under the presence of a cosmological constant.

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Section: On Studies Of Asymptotic Behaviour Of Radiative Fields In Gementioning

confidence: 99%

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

Krtouš¹,

Podolský²

2004

Class. Quantum Grav.

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“…Different definitions should give the same result for the total field energy-momentum vector in asymptotically flat spacetimes, but independence of the choice of coordinates in specific computations is not obvious due to the lack of manifest covariance. This has in fact motivated the formulation of more abstract global geometric 4-momentum definitions in asymptotically flat spacetimes [6][7][8].…”

Section: Jhep09(2017)145mentioning

confidence: 99%

On the ‘simple’ form of the gravitational action and the self-interacting graviton

Tomboulis¹

2017

J. High Energ. Phys.

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The so-called ΓΓ-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General Relativity as a theory of the selfinteracting graviton. A straightforward but general method of converting to a covariant formulation by the introduction of a reference metric is given. It is used to recast the Einstein field equation as the equation of motion of a spin-2 particle interacting with the canonical energy-momentum tensor symmetrized by the standard Belinfante method applicable to any field carrying nonzero spin. This represents the graviton field equation in a form complying with the precepts of standard field theory. It is then shown how representations based on other, at face value completely unrelated definitions of energymomentum (pseudo)tensors are all related by the addition of appropriate superpotential terms. Specifically, the superpotentials are explicitly constructed which connect to: i) the common definition consisting simply of the nonlinear part of the Einstein tensor; ii) the Landau-Lifshitz definition.

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“…Let us remark that, unlike the Tamburino-Winicour's quasi-local conservation equations [7] which are "weak" conservation equations since they assumed in the derivation the Ricci flat conditions (i.e. the full Einstein's equations), our quasi-local conservation equations are "strong" conservation equations since we used the four Einstein's "constraint" equations only.…”

Section: A Set Of Quasi-local Conservation Equationsmentioning

confidence: 99%

Quasi-Local Conservation Equations in General Relativity

Yoon

2002

The Ninth Marcel Grossmann Meeting

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A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted as quasi-local energy, momentum, and angular momentum conservation equations. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local energy and energy-flux integral reduce to the Bondi energy and energy-flux, respectively. In spherically symmetric spacetimes, the quasi-local energy becomes the Misner-Sharp energy. Moreover, on the event horizon of a general dynamical black hole, the quasi-local energy conservation equation coincides with the conservation equation studied by Thorne et al. We discuss the remaining quasi-local conservation equations briefly.

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Gravitational Fields in Finite and Conformal Bondi Frames

Cited by 236 publications

References 15 publications

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

On the ‘simple’ form of the gravitational action and the self-interacting graviton

Quasi-Local Conservation Equations in General Relativity

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