Empty Space Metrics Containing Hypersurface Orthogonal Geodesic Rays

Newman, Ezra T.; Tamburino, Louis A.

doi:10.1063/1.1724304

Cited by 62 publications

(41 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…' g9A 2 P -ee(w) , ImT it =o (5)(6)(7)(8)(9)(10)(11) and the only freedom remaining in the choice of ~ is Then from [4] …”

Section: -mentioning

confidence: 99%

See 1 more Smart Citation

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Lind

1974

Gen Relat Gravit

View full text Add to dashboard Cite

The problem of finding algebraically special solutions to the vacuum Einstein-Maxwell equations is investigated using the spin coefficient formalism of Newman and Penrose. The general case in which the degenerate null vectors are not hypersurface orthogonal is reduced to a problem of solving five coupled differential equations that are no longer dependent on the affine parameter along the degenerate null directions.It is shown that the most general regular, shear-free, nonradiating solution to these equations is the Kerr-Newman metric. July 1972Based in part on a doctoral thesis submitted to the University of Pittsburgh (1970) while the author was a NASA Predoctoral Trainee.

show abstract

“…' g9A 2 P -ee(w) , ImT it =o (5)(6)(7)(8)(9)(10)(11) and the only freedom remaining in the choice of ~ is Then from [4] …”

Section: -mentioning

confidence: 99%

“…Xt-t X Ali tA ag (3)(4)(5)(6)(7)(8)(9)(10)(11) and we will now show that (3.9) can be used to put X' = 0 while still maintaining the form of G0 . It is clear from (3.10) and ( …”

mentioning

confidence: 99%

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Lind

1974

Gen Relat Gravit

View full text Add to dashboard Cite

show abstract

“…In the Newman-Penrose formalism this implies that Ψ 0 = κ = 0, that ρ is real and non-zero and σ = 0. In [1] Newman and Tamburino explicitly gave all such metrics and showed that they fall into two classes: the spherical, with ρ 2 = σσ and the cylindrical with ρ 2 = σσ. In [3] I gave a formalism suitable for investigating homothetic symmetries of vacuum solutions of the field equations, and this paper arose from an exercise in applying that formalism to the (algebraically general) spherical Newman-Tamburino solutions, with the purpose of checking that the obvious homothety (see section 2) came out of the analysis.…”

Section: Introductionmentioning

confidence: 99%

Symmetries in some Newman–Tamburino metrics

Steele

2004

Class. Quantum Grav.

View full text Add to dashboard Cite

The Newman-Tamburino spherical metrics are investigated using the homothety formalism of the author's previous work (2002 Class. Quantum Grav. 19 259) and shown to always admit a homothety. The analysis also reveals that these metrics always admit a Killing vector, correcting a claim by Collinson and French (1967 J. Math. Phys. 8 701). The limit form of the cylindrical Newman-Tamburino metric is also shown to admit a homothety.

show abstract

“…Results up to 1999 are summarized in chapters 26-32 of [10]. Basic papers on certain major classes of such solutions appeared very soon after the present paper: for solutions with geodesic, shearfree and non-twisting rays, Robinson and Trautman [11]; for geodesic twistfree rays, Newman and Tamburino [12]; and for twist and divergence-free rays, Kundt [13] and paper V of this series. Particularly important cases included the NUT solutions [14] and perhaps the most astrophysically important of all exact solutions which can be considered to describe an isolated body, the Kerr solution for a rotating black hole [15].…”

mentioning

confidence: 99%

“…However, reference (12) of this paper is the first of the Mainz series [1] and is therefore now readily available.…”

mentioning

confidence: 99%

Editorial note to: Pascual Jordan, Jürgen Ehlers and Rainer K. Sachs, Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

MacCallum

Kundt

2013

Gen Relativ Gravit

View full text Add to dashboard Cite

The overall arc of the 'Hamburg bible' has already been described in Ellis' editorial note to paper I in the series [1]. This second paper discusses the geometry of affinelyparametrized geodesic null congruences, reviews and develops the classification of conformal curvature using spinor techniques, and then puts the two together in studying the propagation of gravitational and electromagnetic radiation. In doing so, the authors say that they intended to address the question 'whether null fields and the other "special" fields in the sense of the Petrov classification have analytical properties, which justify their interpretation as more or less "pure" radiation fields'. Here "null fields" means what we would now refer to as fields of Petrov type N.Paper II appeared at a time of rapid evolution in the understanding and use of null congruences and of the Petrov types. Petrov's classification of conformal curvature, which had first been given (in Russian) in 1954 [2], naturally defines congruencesThe republication of the original paper can be found in this issue following the editorial note and online via

show abstract

Empty Space Metrics Containing Hypersurface Orthogonal Geodesic Rays

Cited by 62 publications

References 4 publications

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Shear-free, twisting Einstein-Maxwell metrics in the Newman-Penrose formalism

Symmetries in some Newman–Tamburino metrics

Editorial note to: Pascual Jordan, Jürgen Ehlers and Rainer K. Sachs, Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

Contact Info

Product

Resources

About