Slowly rotating perfect fluids with a cosmological constant

1998

A rigidly rotating incompressible perfect fluid solution of Einstein's gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the instantaneous constantpressure surfaces is positive and they have two ring-shaped cusps.

Classical and Quantum Gravity, 2000

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work.

Astronomische Nachrichten, 2002

The dynamics of a radiating perfect fluid universe coupled with scalar field and heat flux are studied in the non-static Gödel-type universe including the cosmological constant and obtained some exact solutions of Einstein field equations. The solutions have nonzero expansion, shear, and rotating universe. Various physical and geometrical properties of the model are also discussed and the temperature distribution is also given explicitly.

Classical and Quantum Gravity, 2010

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Gödel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.

Classical and Quantum Gravity, 1999

It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker space-time. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.

Gen Relativ Gravit, 2004

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz-Senovilla and Fernández-Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.

Annalen der Physik, 1999

The various schemes for studying rigidly rotating perfect fluids in general relativity are reviewed. General conclusions one may draw from these are: (i) There is a need to restrict the scope of the possible ansatze, and (ii) the angular behaviour is a valuable commodity. This latter observation follows from a large number of analytic models exhibiting a NUT-like behaviour. A method of getting around problem (ii) is presented on a simple example. To alleviate problem (i) for rigidly rotating perfect fluids, approximation schemes based on a series expansion in the angular velocity are suggested. A pioneering work, due to Hartle, explores the global properties of matched space-times to quadratic order in the angular velocity. As a first example of the applications, it is shown that the rigidly rotating incompressible fluid cannot be Petrov type D.

Astrophysics and Space Science, 1995

An exact solution of Einstein equations representing a perfect fluid model in the presence of a zero-mass scalar field is obtained for an anisotropic metric. The effect of dissipative processes on the model is also discussed. Different physically valid forms of the scale factors in the three spatial directions give rise to some distinct models. The physical behaviour of these models is discussed in detail. Some of the perfect fluid models exhibit the 'cigar' singularity.

Classical and Quantum Gravity, 1994

Abstraft We consider self-consistent spinning fluid cosmologies in bath general relativity in Riemannh spacetimes and Einstein-theory in Riemano-CW spacetimes. First we extend slightly the cosmological calculation of Marlin eral for general relativistic self-consistent spinning Buids. The existence of spin-squared terms in the field equations in the Einstein-cutan theory shows, however, that an expanded class of meaningful cosmologies is possible. Under certain assumptions on the arbikariness of the cosmological shear and expansion the results for the ad hoc Weyssenhofl spin fluid in a spherically symmehic spacetime can be reproduced. PACS numben: 0440,0450,9880 Preprint University of Cologne p415 Wdey) p 57 density Repon 8.7.92 Univenity of Alabama in Huntsville

Journal of High Energy Physics, 2007

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 Einstein-Maxwell-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.