3,093 research outputs found
Obtaining a class of Type N pure radiation metrics using invariant operators
We develop further the integration procedure in the generalised invariant
formalism, and demonstrate its efficiency by obtaining a class of Petrov type N
pure radiation metrics without any explicit integration, and with comparatively
little detailed calculations. The method is similar to the one exploited by
Edgar and Vickers when deriving the general conformally flat pure radiation
metric. A major addition to the technique is the introduction of non-intrinsic
elements in generalised invariant formalism, which can be exploited to keep
calculations manageable.Comment: This work was presented in July 2004, in the Gr17 meeting held in
Dublin-Irelan
Relativistic Elasticity: recent developments.
The theory of elasticity in the context of general relativity was developed in the mid twentieth century. The need for such a theory came in the late 1950s with Weber´s bar antenna for gravitational waves in order to explain how these waves interact with elastic solids. In 1973, a fully developed nonlinear theory of elasticity adapted to general relativity was given in a paper by Carter and Quintana, which, to a certain extent, remains as the standard reference of this theory. In this paper the concept of elasticity is formulated within the framework of general relativity. In this talk, the theory of elastic matter within the context of general relativity is presented, following the formulation of Carter and Quintana. The latest developments within this theory will be discussed; in particular, recent work on conformally flat spacetimes associated to an elastic stress energy tensor will be analysed
Dynamical properties of a cosmological model with diffusion
The description of the dynamics of particles undergoing diffusion in general relativity has been an object of interest in the last years. Most recently a new cosmological model with diffusion has been studied in which the evolution of the particle system is described by a Fokker-Planck equation. This equation is then coupled to a modified system of Einstein equations, in order to satisfy the energy conservation condition. Continuing with this work, we study in the present paper a spatially
homogeneous and isotropic spacetime model with diffusion velocity. We write the system of ordinary differential equations of this particular model and obtain the solutions for which the scale factor in the RobertsonWalker metric is linear in time. We analyse the asymptotic behavior of the subclass of spatially flat solutions. The system representing the homogeneous and isotropic model with diffusion is rewritten using dynamical variables. For the subclass of spatially flat solutions we were able to determine all equilibrium points and analyse their local stability properties.http://www.springer.com/gp/book/9783319166360#otherVersion=9783319166377Fundação para a Ciência e a Tecnologia (FCT
Using the generalised invariant formalism: a class of conformally flat pure radiation metrics with a negative cosmological constant
We demonstrate an integration procedure for the generalised invariant formalism by obtaining a subclass of conformally flat pure radiation spacetimes with a negative cosmological constant. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. This subclass of spacetimes turns out to have one degree of isotropy freedom, so in this paper we have extended the integration procedure for the generalised invariant formalism to spacetimes with isotropy freedom,SBE wishes to thank Officina Mathematica for supporting a visit to Universidade do Minhoand the Department of Mathematics for Science and Technology for their hospitality. MPMRwishes to thank Vetenskapsr ̊adet (Swedish Research Council) for supporting a visit to Link ̈opingsuniversitet and the Mathematics Department for their hospitality. SBE wishes to thankStiftelsen G S Magnusons fond, K.V.A. (The Royal Swedish Academy of Sciences) for supportto attend the Spanish General Relativity Meeting (ERE 2006) in Mallorca
Double warped spacetimes
An invariant characterization of double warped space–times is given in terms of
Newman-Penrose formalism and a classification scheme is proposed. A detailed
study of the conformal algebra of these space–times is also carried out and some
remarks are made on certain classes of exact solutions
Type O pure radiation metrics with a cosmological constant
In this paper we complete the integration of the conformally flat pure
radiation spacetimes with a non-zero cosmological constant , and , by considering the case . This is a
further demonstration of the power and suitability of the generalised invariant
formalism (GIF) for spacetimes where only one null direction is picked out by
the Riemann tensor. For these spacetimes, the GIF picks out a second null
direction, (from the second derivative of the Riemann tensor) and once this
spinor has been identified the calculations are transferred to the simpler GHP
formalism, where the tetrad and metric are determined. The whole class of
conformally flat pure radiation spacetimes with a non-zero cosmological
constant (those found in this paper, together with those found earlier for the
case ) have a rich variety of subclasses with zero,
one, two, three, four or five Killing vectors
Modelling and analysis of time dependent processes in a chemically reactive mixture
In this paper, we study the propagation of sound waves and the dynamics of local wave disturbances
induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat
conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in themodel in a proper way. For both time-dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen–Chlorine system as reference. Several numerical computations are included illustrating the behavior of the phase velocity and attenuation coefficient in a low-frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.The paper is partially supported by the Research Centre of Mathematics of the University of Minho, with the Portuguese Funds from the Foundation for Science and Technology (FCT) through the Project UID/MAT/00013/2013. We wish to thank the anonymous Referees for their valuable comments and suggestions that helped us to improve the paper.info:eu-repo/semantics/publishedVersio
The type N Karlhede bound is sharp
We present a family of four-dimensional Lorentzian manifolds whose invariant
classification requires the seventh covariant derivative of the curvature
tensor. The spacetimes in questions are null radiation, type N solutions on an
anti-de Sitter background. The large order of the bound is due to the fact that
these spacetimes are properly , i.e., curvature homogeneous of order 2
but non-homogeneous. This means that tetrad components of are constant, and that essential coordinates first appear as
components of . Covariant derivatives of orders 4,5,6 yield one
additional invariant each, and is needed for invariant
classification. Thus, our class proves that the bound of 7 on the order of the
covariant derivative, first established by Karlhede, is sharp. Our finding
corrects an outstanding assertion that invariant classification of
four-dimensional Lorentzian manifolds requires at most .Comment: 7 pages, typos corrected, added citation and acknowledgemen
Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant
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
are able to obtain complete agreement with the results obtained in intrinsic
coordinates. In particular, 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.Comment: Extended version of GRG publication, with some typos etc correcte
Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators
Using the generalised invariant formalism we derive a class of conformally
flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar
component. The method used is a development of the methods used earlier for
pure radiation spacetimes of Petrov types O and N respectively. In this paper
we demonstrate how to handle, in the generalised invariant formalism,
spacetimes with isotropy freedom and rich Killing vector structure. Once the
spacetimes have been constructed, it is straightforward to deduce their
Karlhede classification: the Karlhede algorithm terminates at the fourth
derivative order, and the spacetimes all have one degree of null isotropy and
three, four or five Killing vectors.Comment: 29 page
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