| 1. |
- Bäckdahl, Thomas, et al.
(författare)
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Calculation of, and bounds for, the multipole moments of stationary spacetimes
- 2006
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 23:20, s. 5997-6006
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on . We also give a bound on the multipole moments. This gives a proof of the 'necessary part' of a long-standing conjecture due to Geroch.
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| 2. |
- Bäckdahl, Thomas, et al.
(författare)
-
Explicit multipole moments of stationary axisymmetric spacetimes
- 2005
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:17, s. 3585-3594
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study multipole moments of axisymmetric stationary asymptotically flat spacetimes. We show how the tensorial recursion of Geroch and Hansen can be reduced to a recursion of scalar functions. We also demonstrate how a careful choice of conformal factor collects all moments into one complex-valued function on , where the moments appear as the derivatives at 0. As an application, we calculate the moments of the Kerr solution. We also discuss the freedom in choosing the potential for the moments.
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| 3. |
- Bäckdahl, Thomas, et al.
(författare)
-
Static axisymmetric spacetimes with prescribed multipole moments
- 2005
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 22:9, s. 1607-1621
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we develop a method of finding the static axisymmetric spacetime corresponding to any given set ofmultipolemoments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static spacetime for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernández-Pastora and Martín concerning the monopole–quadrupole solution.
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| 4. |
- Herberthson, Magnus, 1963-
(författare)
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Static spacetimes with prescribed multipole moments: a proof of a conjecture by Geroch
- 2009
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Ingår i: Classical and quantum gravity. - Bristol, UK : IOP Publishing. - 0264-9381 .- 1361-6382. ; 26:21, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we give sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. The proof is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. Since these sufficient conditions agree with already known necessary conditions, this completes the proof of a long standing conjecture due to Geroch.
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| 5. |
- Herberthson, Magnus, 1963-
(författare)
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The gravitational dipole and explicit multipole moments of static axisymmetric spacetimes
- 2004
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 21:22, s. 5121-5138
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Tidskriftsartikel (refereegranskat)abstract
- The multipole moments of static axisymmetric asymptotically flat spacetimes are considered. The usual set of recursively defined tensors is replaced with one real-valued function m defined on R+ ∪ {0}, where the moments are given by the derivatives of m at 0. As examples of applications, we show that the Schwarzschild spacetime is the gravitational monopole and derive the metric for the gravitational dipole.
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