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  • 1.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Dunsby, Peter K S
    Dept. of Mathematics and Applied Mathematics, University of Cape Town.
    Forsberg, Mats
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Keresztes, Zoltán
    Dept. of Experimental Physics, University of Szeged.
    Density growth in Kantowski-Sachs cosmologies with cosmological constant2012In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 29, no 9, p. 095023-Article in journal (Refereed)
    Abstract [en]

    In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically andnumerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered.We find that typically the density gradient in the bouncing direction experiences a local maximum at or slightly after the bounce.

  • 2.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edgar, S. B.
    Machado Ramos, M. P.
    Classification of a class of conformally flat pure radiation metrics with cosmological constant2012In: TOWARDS NEW PARADIGMS: PROCEEDING OF THE SPANISH RELATIVITY MEETING 2011 / [ed] Jimenez, JB; Cembranos, JAR; Dobado, A; Maroto, AL; Dombriz, AD, American Institute of Physics (AIP), 2012, p. 331-334Conference paper (Refereed)
    Abstract [en]

    A comparison between the Cartan-Karlhede classification of the conformally flat pure radiation metrics with a negative cosmological constant, satisfying Lambda + tau(tau) over bar = 0, and the construction of them in terms of the Generalised Invariant Formalism (GIF) is made.

  • 3.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edgar, S. Brian
    Mathematics, Linköping University.
    Ramos, M.P. Machado
    Mathematics, Universidade do Minho.
    Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics2010In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 42, no 1, p. 155-182Article in journal (Refereed)
    Abstract [en]

    Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras–McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras–McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we obtain complete agreement with the results obtained in intrinsic coordinates. We have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.

  • 4.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Rotating cosmological models of Bianchi type V2005In: Proceedings of the tenth Marcel Grossmann meeting on General Relativity, 2005, p. 1957-1959Conference paper (Refereed)
  • 5.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Rotating Cosmological Models of Bianchi-type V - first results2004In: Relativity Today: Proceedings of Seventh Hungarian Relativity Workshop, 2004, p. 143-156Conference paper (Refereed)
  • 6.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Tilted cosmological models of Bianchi type V2006In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 73, no 4, p. 044008-044019Article in journal (Refereed)
    Abstract [en]

    Cosmological models of Bianchi types Vand I containing a perfect fluid with a linear equation of state plus cosmological constant are investigated. In general, these spacetimes are tilted and describe fluids with expansion, shear, and vorticity. We use a tetrad approach where our variables are the Riemann tensor, the Ricci rotation coefficients, and a subset of the tetrad vector components. This set, called S, describes a spacetime when its elements are constrained by certain integrability conditions and due to a theorem by Cartan S gives a complete local description of the spacetime. With the help of the Lie algebra, the full line element is constructed up to quadratures in terms of the elements in S. The system obtained by imposing the integrability conditions and Einstein’s equations on the elements in S can be reduced to an integrable system of five coupled first order ordinary differential equations. In general, exact solutions to this system are hard to find, but the linearized equations around the open Friedmann models are easily integrated. The full system is also studied numerically and the perturbative solutions agree well with the numerical ones in the appropriate domains. We also give some examples of numerical solutions in the nonperturbative regime.

  • 7.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Fodor, Gyula
    Rácz, István
    Slowly rotating fluid balls of Petrov type D2007In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 75, no 2, p. 024013-024026Article in journal (Refereed)
    Abstract [en]

    The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order, irrespective of Petrov type, may be matched to a possibly nonasymptotically flat stationary axisymmetric vacuum exterior. The Petrov type D interior solutions are characterized by five integration constants, corresponding to density and pressure of the zeroth order configuration, the magnitude of the vorticity, one more second order constant, and an independent spherically symmetric second order small perturbation of the central pressure. A four-dimensional subspace of this five-dimensional parameter space is identified for which the solutions can be matched to an asymptotically flat exterior vacuum region. Hence these solutions are completely determined by the spherical configuration and the magnitude of the vorticity. The physical properties, like equation of state, shape, and speed of sound, are determined for a number of solutions.

  • 8.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Fodor, Gyula
    Rácz, István
    Some results on rotating fluid balls of Petrov type D2007In: Journal of Physics: Conference Series 66: XXIXTH Spanish Relativity Meeting (ERE 2006), 2007, p. 012010-Conference paper (Refereed)
  • 9.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Eriksson, Daniel
    Umeå University, Faculty of Science and Technology, Physics.
    Fodor, Gyula
    Rácz, Isván
    Slowly and rigidly rotating perfect fluid balls of Petrov type D2008In: Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, 2008, p. 795-806Conference paper (Refereed)
  • 10.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Physics.
    Fodor, Gyula
    KFKI Research Institute for Particle and Nuclear Physics, Budapest.
    Quadrupole moment of slowly rotating fluid balls2009In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 79, no 4, p. 044018-1-044018-13Article in journal (Refereed)
    Abstract [en]

    In this paper we use the second order formalism of Hartle to study slowly and rigidly rotating stars with focus on the quadrupole moment of the object. The second order field equations for the interior fluid are solved numerically for different classes of possible equations of state and these solutions are then matched to a vacuum solution that includes the general asymptotically flat axisymmetric metric to second order, using the Darmois-Israel procedure. For these solutions we find that the quadrupole moment differs from that of the Kerr metric, as has also been found for some equations of state in other studies. Further we consider the post-Minkowskian limit analytically.  In the paper we also illustrate how the relativistic multipole moments can be calculated from a complex gravitational potential.

  • 11.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Fodor, Gyula
    KFKI Research Institute for Particle and Nuclear Physics.
    The quadrupole moment of slowly rotating stars2012In: Proceedings of the twelfth Marcel Grossman meeting on General Relativity / [ed] Thibault Damour, Robert T Jantzen, Remo Ruffini, Singapore: World Scientific, 2012, p. 1883-1886Conference paper (Refereed)
  • 12.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Fodor, Gyula
    KFKI Research Institute for Particle and Nuclear Physics, Budapest.
    The quadrupole moment of slowly rotating stars2010In: / [ed] Ruth Lazkoz and Raül Vera, IOPScience , 2010, Vol. 229, no 1, p. 012025-Conference paper (Refereed)
    Abstract [en]

    The second order field equations for the interior of slowly and rigidly rotating stars are solved numerically for different classes of possible equations of state and these solutions are then matched to the general asymptotically flat axisymmetric vacuum metric to second order in the rotational parameter. For these solutions we find that the quadrupole moment differs from that of the Kerr metric. Further we consider the post-Minkowskian limit analytically.

  • 13.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Forsberg, Mats
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Keresztes, Zoltán
    Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies2017In: Universe, ISSN 2218-1997, Vol. 3, no 4, article id 69Article in journal (Refereed)
    Abstract [en]

    In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed.                

  • 14.
    Bradley, Michael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Forsberg, Mats
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Keresztes, Zoltán
    University of Szeged.
    Gergely, László A´
    University of Szeged.
    Dunsby, Peter K S
    University of Cape Town.
    Perturbations of Kantowski-Sachs models2015In: Proceedings of the Thirteenth Marcel Grossman Meeting on General Relativity / [ed] Robert T Jantzen, Kjell Rosquist, Remo Ruffini, Singapore: World Scientific, 2015, p. 2547-2549Conference paper (Refereed)
    Abstract [en]

    Perturbations of Kantowski-Sachs models with a positive cosmological constant are considered in a harmonic decomposition, in the framework of gauge invariant 1+3 and 1+1+2covariant splits of spacetime. Scalar, vector and tensor modes are allowed, however they remain vorticity-free and of perfect fluid type. The dynamics is encompassed in six evolution equations for six harmonic coefficients.

  • 15.
    Edgar, S Brian
    et al.
    Linköpings Universitet.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Machado Ramos, M Piedade
    Universidade do Minho, Guimarães.
    Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism2014In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 46, no 10, p. 1797-Article in journal (Refereed)
    Abstract [en]

    A complete and simple invariant classification of the conformally flat pure radiation metrics with a negative cosmological constant that were obtained by integration using the generalised invariant formalism is presented. We show equivalence between these metrics and the corresponding type O subclass of the more general spacetime studied by Siklos. The classification procedure indicates that the metrics possess a one degree of null isotropy freedom which has very interesting repercussions in the symmetry analysis. The Killing and homothetic vector analysis in GHP formalism is then generalised to this case were there is only one null direction defined geometrically. We determine the existing Killing vectors for the different subclasses that arise in the classification and compare these results to those obtained in the symmetry analysis performed by Siklos for a larger class of metrics with Ricci tensor representing a pure radiation field and a negative cosmological constant. It is also shown that there are no homothetic Killing vectors present.

  • 16.
    Forsberg, Mats
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Dunsby, Peter K.S.
    University of Cape Town, South Africa.
    Density perturbations in Kantowski-Sachs models with a cosmological constant2011In: Spanish Relativity Meeting (ERE 2010): Gravity as a Crossroad in Physics / [ed] Víctor Aldaya, Carlos Barceló and José Luis Jaramillo, Institute of Physics (IOP), 2011Conference paper (Refereed)
    Abstract [en]

    The growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number a closed system for eight scalars is obtained. These are formed from quantities that are zero on the background and hence are gauge invariant. As an example a numerical solution describing the evolution of density perturbations on a background that experiences a bounce is presented. Typically the density gradient in the bouncing directions experiences a local maxium at or slightly after the bounce.

  • 17. Keresztes, Zoltán
    et al.
    Forsberg, Mats
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Dunsby, Peter K S
    Gergely, László Á
    Gravitational, shear and matter waves in Kantowski-Sachs cosmologies2015In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 11, article id 042Article in journal (Refereed)
    Abstract [en]

    A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by pi/2 and share the same speed of sound.

  • 18.
    Keresztes, Zoltán
    et al.
    University of Szeged.
    Forsberg, Mats
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Dunsby, Peter K S
    University of Cape Town.
    Gergely, László Á
    University of Szged.
    Perturbations of Kantowski-Sachs Models with a Cosmological Constant2014In: Progress in Mathematical Relativity, Gravitation and Cosmology: Proceedings, Spanish Relativity Meeting ERE2012, University of Minho, Guimarães, Portugal, September 3-7, 2012 / [ed] Alfonso García-Parrado, Filipe C. Mena, Filipe Moura, Estelita Vaz, Heidelberg: Springer Berlin/Heidelberg, 2014, p. 289-293Conference paper (Refereed)
    Abstract [en]

    We investigate perturbations of Kantowski–Sachs models with a positive cosmological constant, using the gauge invariant 1 + 3 and 1 + 1 + 2 covariant splits of spacetime together with a harmonic decomposition. The perturbations are assumed to be vorticity-free and of perfect fluid type, but otherwise include general scalar, vector and tensor modes. In this case the set of equations can be reduced to six evolution equations for six harmonic coefficients.

  • 19. Källberg, A.
    et al.
    Brodin, Gert
    Umeå University, Faculty of Science and Technology, Physics.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Physics.
    Nonlinear coupled Alfvén and gravitational waves2004In: Physical Review D, Vol. 70, no 4, p. 044014-Article in journal (Refereed)
  • 20.
    Machado Ramos, Maria P
    et al.
    Departamento de Matemática e Aplicações, Universidade do Minho, Guimarães, Portugal .
    Edgar, S Brian
    Department of Mathematics, Linköping Universitet.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Invariant classification of metrics using invariant formalism2010In: Journal of Physics: Conference Series, Volume 229, 2010: M P Machado Ramos et al 2010 J. Phys.: Conf. Ser. 229 012049 / [ed] Ruth Lazkoz and Raül Vera, 2010Conference paper (Refereed)
    Abstract [en]

    Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates. By performing this classification we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.

  • 21. Törnkvist, Robin
    et al.
    Bradley, Michael
    Umeå University, Faculty of Science and Technology, Department of Physics.
    General perfect fluid perturbations of homogeneous and orthogonal locally rotationally symmetric class II cosmologies2019In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. 100, article id 124043Article in journal (Refereed)
    Abstract [en]

    First-order perturbations of homogeneous and hypersurface orthogonal locally rotationally symmetric class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime. The perturbations, which are of perfect fluid type, include general scalar, vector, and tensor modes and extend some previous works in which vorticity perturbations were excluded. A harmonic decomposition is performed, and the field equations are then reduced to a set of eight evolution equations for eight harmonic coefficients, representing perturbations in density, shear, vorticity, and the Weyl tensor, in terms of which all other variables can be expressed algebraically. This system decouples into two subsystems, one for five and one for three coefficients. As previously known, vorticity perturbations cannot be generated to any order in a barotropic perfect fluid. Hence, the time development of existing first-order vorticity perturbations is seen to be completely determined by the background. However, an already existing vorticity will act as source terms in the evolution equations for the other quantities. In the high-frequency approximation, the four independent Weyl tensor harmonics evolve as gravitational waves on the anisotropic background in the same manner as in the case without vorticity, whereas vorticity gives a first-order disturbance of sonic waves.

1 - 21 of 21
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