Journal ArticleDOI
Static and stationary multiple soliton solutions to the Einstein equations
TLDR
In this article, the problem of finding stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal, and the possibility of having real odd number soliton solutions is investigated.Abstract:
The application of the Belinsky–Zakharov solution‐generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd‐number soliton solutions is investigated. These solutions represent solitonic perturbations of Euclidean metrics. The possibility of using instantons as seed solutions is also investigated. The one‐ and two‐soliton solutions generated from a diagonal seed solution are studied. As an application, a unified derivation of some well‐known static solutions, like the Schwarzschild metric and the Chazy–Curzon metric, as well as other new metrics is presented. By using these metrics as seed solutions, some known stationary solutions, like the Kerr‐NUT metric, the double Kerr metric, and the rotating Weyl C‐metric, as well as other new metrics are also derived in a unified way.read more
Citations
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Multipole Moments in General Relativity —Static and Stationary Vacuum Solutions—
TL;DR: In this paper, the most important properties of the axisymmetric and stationary solutions of Einstein's vacuum field equations, the solution generating techniques developed in the last few years the relativistic definitions of multipole moments, and their use for obtaining and investigating static and stationary axisymetric vacuum solutions are reviewed.
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Exact self‐gravitating disks and rings: A solitonic approach
TL;DR: In this article, the Belinsky-Zakharov version of the inverse scattering method is used to generate a large class of solutions to the vacuum Einstein equations representing uniformly accelerating and rotating disks and rings.
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Soliton solutions in spacetimes with two spacelike killing fields
TL;DR: A review of the solutions to Einstein's equations generated by the soliton transform when the spacetime admits two commuting spacelike Killing fields is given in this paper, where the properties and physical meaning of these solutions are discussed and emphasis is given to those solutions which may have some physical significance.
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Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method. II. Production of the black ring solution
Shinya Tomizawa,Masato Nozawa +1 more
TL;DR: In this article, the authors reproduce the black ring solution which was found by Emparan and Reall by taking the Euclidean Levi-Civita metric plus one-dimensional flat space as a seed.
Journal ArticleDOI
Uniformly accelerated black holes
TL;DR: In this paper, the static and stationary C metric are examined in a generic framework and their interpretations studied in some detail, especially those with two event horizons, one for the black hole and another for the acceleration.
References
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Book
Exact Solutions of Einstein's Field Equations
TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
Journal ArticleDOI
Rotating, charged, and uniformly accelerating mass in general relativity
Jerzy F. Plebański,M Demianski +1 more
TL;DR: In this paper, a new general class of solutions of the Einstein-Maxwell equations is presented, which is based on seven arbitrary parameters that group in a natural way into three complex parameters m + in, a + ib, e + ig, and the cosmological constant λ.