Algebraic classification of higher dimensional spacetimes

Coley, A. A.; Pelavas, Nicos

doi:10.1007/s10714-006-0232-2

Cited by 25 publications

(58 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, the black ring is a typical higher dimensional solution preventing the extension of 4 dimensional uniqueness theorems [23]. 4 Regarding solution generating methods (see [25] for work on classification of higher dimensional solutions), Emparan and Reall [26] extended Weyl's work to higher dimensions while a cosmological constant was included in the analysis of [27]. Recently Harmark et al [28,29] analysed stationary and axisymmetric metrics for Λ = 0, giving the relevant mappings of solutions in multiple coordinate systems.…”

Section: Jhep02(2007)064mentioning

confidence: 99%

Rotating spacetimes with a cosmological constant

Charmousis¹,

Langlois²,

Steer³

et al. 2007

J. High Energy Phys.

View full text Add to dashboard Cite

We develop solution-generating techniques for stationary metrics with one angular momentum and axial symmetry, in the presence of a cosmological constant and in arbitrary spacetime dimension. In parallel we study the related lower dimensional EinsteinMaxwell-dilaton static spacetimes with a Liouville potential. For vanishing cosmological constant, we show that the field equations in more than four dimensions decouple into a four dimensional Papapetrou system and a Weyl system. We also show that given any four dimensional "seed" solution, one can construct an infinity of higher dimensional solutions parametrised by the Weyl potentials, associated to the extra dimensions. When the cosmological constant is non-zero, we discuss the symmetries of the field equations, and then extend the well known works of Papapetrou and Ernst (concerning the complex Ernst equation) in four-dimensional general relativity, to arbitrary dimensions. In particular, we demonstrate that the Papapetrou hypothesis generically reduces a stationary system to a static one even in the presence of a cosmological constant. We also give a particular class of solutions which are deformations of the (planar) adS soliton and the (planar) adS black hole. We give example solutions of these techniques and determine the four-dimensional seed solutions of the 5 dimensional black ring and the Myers-Perry black hole.

show abstract

Section: Jhep02(2007)064mentioning

confidence: 99%

Rotating spacetimes with a cosmological constant

Charmousis¹,

Langlois²,

Steer³

et al. 2007

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…The mathematics and physics communities have been engaged not only in generalising known four-dimensional solutions such as pp-waves [CMP + 03], the Kerr black hole [GLPP05,CLP06] or the Kerr-Schild ansatz [OPP09b,OPP09a] to higher dimensions, but also in investigating the broader geometrical properties of higher-dimensional spacetimes [CMPP04b,CMPP04a]. To this effect, Coley, Milson, Pravdá, and Pravdová have proposed a spacetime classification purporting to generalise the Petrov classification [CMPP04a,MCPP05,CP06,Col08]. In this setting, various attempts have been made to generalise classical results of general relativity to higher dimensions, with some measure of success [PPCM04,PP05,Pra06,PPO07,OPP07,PP08].…”

Section: Introductionmentioning

confidence: 99%

Optical structures, algebraically special spacetimes, and the Goldberg–Sachs theorem in five dimensions

Taghavi-Chabert¹

2011

Class. Quantum Grav.

112

View full text Add to dashboard Cite

Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the Goldberg-Sachs theorem to five dimensions. To be precise, we find a new algebraic condition on the Weyl tensor, which generalises the Petrov type II condition, in the sense that it ensures the existence of such congruences on a five-dimensional spacetime, vacuum or under weaker assumptions on the Ricci tensor. This results in a significant simplification of the field equations. We discuss possible degenerate cases, including a five-dimensional generalisation of the Petrov type D condition. We also show that the vacuum black ring solution is endowed with optical structures, yet fails to be algebraically special with respect to them. We finally explain the generalisation of these ideas to higher dimensions, which has been checked in six and seven dimensions.

show abstract

“…Now, we shall discuss the models for two cases depending upon the values of n as defined in Eqs. (25) and (26).…”

Section: Case (I): Solution Without Heat Conductionmentioning

confidence: 99%

“…(19) and (20) in the following two subsections, depending on the values of n as defined in Eqs. (25) and (26).…”

Section: Case Ii: Solution With Heat Conduction (Hmentioning

confidence: 99%

“…Vanleeumen et al [17], Novello and Reboucas [18],Reboucas [19],Coley and Tupper [20,21] Sviestins [22], Mukherjee [23], Banerjee and Sanyal [24], Deng [25] all have studied the cosmological models with heat conduction. Coley [26] and Coley and Hoogen [27] investigated LRS Bianchi -V imperfect fluid cosmology with and without heat conduction in which the equation of state are completely 'dimensionless'. Chan [28] developed an analytical solution for a collapsing radiating body consisting of an isotropic fluid with shear undergoing radial heat flow with outgoing radiation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

LRS Bianchi type -V cosmology with heat flow in scalar: tensor theory

Singh¹

2009

Braz. J. Phys.

View full text Add to dashboard Cite

In this paper we present a spatially homogeneous locally rotationally symmetric (LRS) Bianchi type -V perfect fluid model with heat conduction in scalar tensor theory proposed by Saez and Ballester. The field equations are solved with and without heat conduction by using a law of variation for the mean Hubble parameter, which is related to the average scale factor of metric and yields a constant value for the deceleration parameter. The law of variation for the mean Hubble parameter generates two types of cosmologies one is of power -law form and second the exponential form. Using these two forms singular and non -singular solutions are obtained with and without heat conduction. We observe that a constant value of the deceleration parameter is reasonable a description of the different phases of the universe. We arrive to the conclusion that the universe decelerates for positive value of deceleration parameter where as it accelerates for negative one. The physical constraints on the solutions of the field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions are discussed in some detail.The behavior of the observationally important parameters like expansion scalar, anisotropy parameter and shear scalar is considered in detail.

show abstract

Algebraic classification of higher dimensional spacetimes

Abstract: We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.

Cited by 25 publications

References 50 publications

Rotating spacetimes with a cosmological constant

Rotating spacetimes with a cosmological constant

Optical structures, algebraically special spacetimes, and the Goldberg–Sachs theorem in five dimensions

LRS Bianchi type -V cosmology with heat flow in scalar: tensor theory

Contact Info

Product

Resources

About