arXiv subjects
Publications and source records attributed to Roy Maartens.
We find a simple inflationary solution in an inhomogeneous spacetime with heat flux. The heat flux obeys a causal transport equation, and counteracts the inflationary decrease of energy density. At late times, the heat flux tends to zero and the fluid approaches the equation of state $p=-ρ$.
We find a simple exact model of radiating stellar collapse, with a shear-free and non-accelerating interior matched to a Vaidya exterior. The heat flux is subject to causal thermodynamics, leading to self-consistent determination of the temperature $T$. We solve for $T$ exactly when the mean collision time $τ_{c}$ is constant, and perturbatively in a more realistic case of variable $τ_{c}$. Causal thermodynamics predicts temperature behaviour that can differ significantly from the predictions of non-causal theory. In particular, the causal theory gives a higher central temperature and greater temperature gradient.
We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, equivalent to the usual density perturbations, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viscous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases. A companion paper uses the general formalism to analyze damping of density perturbations before last scattering.
One of the necessary covariant conditions for gravitational radiation is the vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab} itself is nonzero. We complete a recent analysis by showing that in irrotational dust spacetimes, the condition div H=0 evolves consistently in the exact nonlinear theory.
In a cosmological context, the electric and magnetic parts of the Weyl tensor, E_{ab} and H_{ab}, represent the locally free curvature - i.e. they are not pointwise determined by the matter fields. By performing a complete covariant decomposition of the derivatives of E_{ab} and H_{ab}, we show that the parts of the derivative of the curvature which are locally free (i.e. not pointwise determined by the matter via the Bianchi identities) are exactly the symmetrised trace-free spatial derivatives of E_{ab} and H_{ab} together with their spatial curls. These parts of the derivatives are shown to be crucial for the existence of gravitational waves.
We develop a nonlinear generalisation of the causal linear thermodynamics of bulk viscosity, incorporating positivity of the entropy production rate and the effective specific entropy. The theory is applied to viscous fluid inflation (which is necessarily far from equilibrium), and we find thermodynamically consistent inflationary solutions, both exponential and power-law.
The reheating process in inflationary universe models is considered as an out-of-equilibrium mixture of two interacting and reacting fluids, and studied within the framework of causal, irreversible thermodynamics. The evolution of the temperature and the decay rate as determined by causal thermodynamics are estimated at different stages of the process. A simple model is also used to find the perturbations of the expansion rate, including the possibility of damped oscillations.
We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.
Gravity waves in irrotational dust spacetimes are characterised by nonzero magnetic Weyl tensor $H_{ab}$. In the linearised theory, the divergence of $H_{ab}$ is set to zero. Recently Lesame et al. [Phys. Rev. D {\bf 53}, 738 (1996)] presented an argument to show that, in the exact nonlinear theory, $div H=0$ forces $H_{ab}=0$, thus implying a linearisation instability for gravity waves interacting with matter. However a sign error in the equations invalidates their conclusion. Bianchi type V spacetimes are shown to include examples with $div H=0\neq H_{ab}$. An improved covariant formalism is used to show that in a generic irrotational dust spacetime, the covariant constraint equations are preserved under evolution. It is shown elsewhere that $\mbox{div} H=0$ does not generate further conditions.
I review the causal relativistic thermodynamics developed by Israel and Stewart, and discuss some applications in cosmology and astrophysics. The lectures begin with an overview of relativistic fluid dynamics (in a covariant formalism) and equilibrium thermodynamics. Causal bulk viscosity in cosmology is considered in detail, including some new results.
By imposing natural geometrical and kinematical conditions on a conformal Killing vector in Bianchi I spacetime, we show that a class of axisymmetric metrics admits a conformal motion. This class contains new exact solutions of Einstein's equations, including anisotropic radiation universes that isotropise at late times.
We calculate the off--center observational relations in a spherically symmetric dust universe that is inhomogeneous at small redshifts. In contrast to the usual model, in which the CMBR dipole is interpreted as a Doppler effect due to peculiar velocity, our model explores an alternative interpretation, in which the CMBR dipole is non--Doppler, and the observer is comoving with the mean matter flow. We do not assume a background frame relative to which peculiar velocities are calculated. Our analysis is fully nonlinear and the density contrast is not assumed to be small. We obtain exact expressions for the Hubble and deceleration parameters, and find that both parameters have quadrupole anisotropies, but no dipoles. A simple numerical procedure for calculating the CMBR dipole anisotropy in our model is presented, and the observed 0.1% dipole is shown to be reproducible with a reasonable choices of parameters.
The integrability properties of the field equation $L_{xx} = F(x)L^2$ of a spherically symmetric shear--free fluid are investigated. A first integral, subject to an integrability condition on $F(x)$, is found, giving a new class of solutions which contains the solutions of Stephani (1983) and Srivastava (1987) as special cases. The integrability condition on $F(x)$ is reduced to a quadrature which is expressible in terms of elliptic integrals in general. There are three classes of solution and in general the solution of $L_{xx} = F(x)L^2$ can only be written in parametric form. The case for which $F=F(x)$ can be explicitly given corresponds to the solution of Stephani (1983). A Lie analysis of $L_{xx} = F(x) L^2$ is also performed. If a constant $α$ vanishes, then the solutions of Kustaanheimo and Qvist (1948) and of this paper are regained. For $α\neq 0$ we reduce the problem to a simpler, autonomous equation. The applicability of the Painlevé analysis is also briefly considered.
We consider quantum effects of an electromagnetic field in a radiation-dominated almost FRW spacetime. The dominant non-local quantum correction to the photon distribution is a quadrupole moment, corresponding to an effective anisotropic pressure in the energy-momentum tensor.
In the $R+αR^2$ gravity theory, we show that if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (FRW). This extends the result proved recently in general relativity ($α=0$), which is applicable to the microwave background after photon decoupling. The higher-order result is in principle applicable to a massless species that decouples in the early universe, such as a relic graviton background. Any future observations that show small anisotropies in such a background would imply that the geometry of the early universe were almost FRW.
Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observer's galactic worldline. The field equations are reduced to a single first--order {\sc ode} in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. {\sc frw}), but at larger redshift develops inhomogeneity. New observational characterisations of homogeneity ({\sc frw} universes) are also given.
A recent paper (Martinez--Gonzalez & Sanz 1995) showed that if the universe is homogeneous but anisotropic, then the small quadrupole anisotropy in the cosmic microwave background radiation implies that the spacetime anisotropy is very small. We point out that more general results may be established, without assuming a priori homogeneity. We have proved that small anisotropies in the microwave background imply that the universe is almost Friedmann--Robertson--Walker. Furthermore, the quadrupole and octopole place direct and explicit limits on the degree of anisotropy and inhomogeneity, as measured by the shear, vorticity, Weyl tensor and density gradients. In the presence of inhomogeneity, it is only possible to set a much weaker limit on the shear than that given by Martinez--Gonzalez & Sanz.
We consider directly the equations by which matter imposes anisotropies on freely propagating background radiation, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but they are more model-independent. We also give new results about combined matter-radiation perturbations in an almost-FRW universe, and a new exact solution of the linearised equations.