Gravitational mass in asymptotically de Sitter spacetimes

Nakao, Ken Ichi; Shiromizu, Tetsuya; Maeda, Kei Ichi

doi:10.1088/0264-9381/11/8/012

Cited by 22 publications

(43 citation statements)

References 12 publications

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“…For Q ξ to be finite, we see that F must generically be independent of r, and that |β| fall off like 1/r, as r goes to infinity. From equation (12) we see that the only CKV for which Q ξ will be generically finite is the generator of conformal time translations ζ a given in equation (13). Further, we see that in general none of the charges generated by the KV's are finite.…”

Section: Convergence Of Q ψ and Q ξ For Ckv'smentioning

confidence: 93%

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A positive energy theorem for asymptotically de Sitter spacetimes

Kastor

Traschen

2002

Class. Quantum Grav.

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We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of deSitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarilly positive and hence may provide a useful definition of energy for these spacetimes. A similar spinor construction shows that the charge associated with the time translation Killing vector of deSitter in static coordinates has both positive and negative definite contributions. For Schwarzshild-deSitter the conformal energy we define is given by the mass parameter times the cosmological scale factor. The time dependence of the charge is a consequence of a non-zero flux of the corresponding conserved current at spatial infinity. For small perturbations of deSitter, the charge is given by the total comoving mass density.

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Section: Convergence Of Q ψ and Q ξ For Ckv'smentioning

confidence: 93%

“…We note that the particular linear combination of CKV's, ζ = ξ (0) − ξ (4) , is given simply by ζ = e Ht ∂ ∂t (13) and is everywhere timelike and future directed. The CKV ζ generates translations in the conformal time parameter η defined by dη = exp (−Ht)dt.…”

Section: Conformal Killing Vectorsmentioning

confidence: 99%

A positive energy theorem for asymptotically de Sitter spacetimes

Kastor

Traschen

2002

Class. Quantum Grav.

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“…So we remember that the flat chart of de Sitter space-time has boundary and its spatial metric is conformally flat(See Fig. 2 in ref [10]). Thus, we realize that the most natural condition is given by…”

Section: In the Case Thatξmentioning

confidence: 99%

“…Thus, there is not contradiction with the existence of non-trivial solution which has zero ADM mass and is given in ref. [10].…”

Section: Positive Energy Theorem Elementary Fermion and Stabilitymentioning

confidence: 99%

“…In the next section we give the definition of gravitational mass in asymptotically de Sitter space-time with extra dimensions and write down the expression in terms of canonical quantities on the hypersurfaces. Since a part of this is straightforward extension of work by Nakao et al [10] based on [12] [13], we give the brief discussion. We will point out that the expression is a special case of the gravitational Hamiltonian defined by Hawking & Horowitz [14].…”

Section: Introductionmentioning

confidence: 99%

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Gravitational mass in asymptotically de Sitter space-times with compactified dimensions

Shiromizu

1999

Phys. Rev. D

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to be published in Phys. Rev. DWe define gravitational mass in asymptotically de Sitter space-times with compactified dimension. It was shown that the mass can be negative for space-time with matter spreading beyond the cosmological horizon scale or large outward 'momentum' in four dimension. We give simple examples with negative energy in higher dimensions even if the matter is not beyond horizon or system does not have large 'momentum'. They do not have the lower bound on the mass. We also give a positive energy argument in higher dimensions and realise that elementary fermion cannot exist in our examples.

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Towards a cosmic no hair theorem for higher‐order gravity

Kluske¹,

Schmidt²

1996

Astron Nachr

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We use gravitational Lagrangians RakRJ-s and linear combinations of them motivated from trials how to overcome the non-renormalizability of Einstein's theory. We ask under which circumstances the de Sitter space-time represents an attractor solution in the set of spatially flat Friedman models. This property ensures the inflationary model to be a typical solution; nowadays, this property is called cosmic no hair theorem because it is analogous to the no hair theorem for black holes.Results are: for arbitrary k, i.e., for arbitrarily large order 2k + 4 of the field equation, one can always find examples where the attractor property takes place. Such examples necessarily need a non-vanishing R2-term. T h e main formulas do not depend on the dimension, so one gets similar results also for l+l-dimensional gravity and for Kaluza-Klein cosmology.K e y words: cosmology -unified field theories and other theories of gravitation AAA subject ctasszfication: 161 IntroductionOver the years, the notion "no hair conjecture" drifted to "no hair theorem" without possessing a generally accepted formulation or even a complete proof. Several trials have been made to formulate and prove it at least for certain special cases. They all have the overall structure: "For a geometrically defined class of space-times and physically motivated properties of the energy-momentum tensor, all the solutions of the gravitational field equation asymptotically converge to a space of constant curvature." The paper of Weyl (1927) is cited in Barrow and Gotz (1989) with the phrase "The behaviour of every world satisfying certain natural homogeneity conditions in the large follows the de Sitter solution asymptotically" to be the first published version of the no hair conjecture. Barrow and Gotz (1989) apply the formulation "All ever-expanding universes with A > 0 approach the de Sitter space-time locally." The first proof of the stability of the de Sitter solution (here: within the steady-state theory), is due to Hoyle and Narlikar (1963).In the papers of Price (1972a,b) perturbations of scalar fields have been considered for the no hair theorem. The probability of inflation is large, if the no hair theorem is valid, cf. Altshuler (1990). Peter et al. (1994) and Kofman et al. (1996) compared the double-inflationary models with cosmological observations. Barrow and Gotz (1989) and Brauer et al. (1994) discussed the no hair conjecture within Newtonian cosmological models. Hiibner and Ehlers (1991) and Burd (1993) considered inflation in an open Friedman universe and have noted that inflationary models need not to be spatially flat. Gibbons and Hawking (1977) have found two of the earliest strict results on the no hair conjecture for Einstein's theory, cf. also Hawking and Moss (1982) and Demianski (1984). Barrow (1986) gave examples that the no hair conjecture fails if the energy condition is relaxed and points out, that this is necessary to solve the graceful exit problem. He uses the formulation of the no hair conjecture "in the presence of an effect...

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Gravitational mass in asymptotically de Sitter spacetimes

Cited by 22 publications

References 12 publications

A positive energy theorem for asymptotically de Sitter spacetimes

A positive energy theorem for asymptotically de Sitter spacetimes

Gravitational mass in asymptotically de Sitter space-times with compactified dimensions

Towards a cosmic no hair theorem for higher‐order gravity

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