The electron-acoustic wave, in a plasma with hot suprathermal, kappa-distributed electrons and cool, Maxwellian electrons, is investigated. This model is a generalization of those that have been investigated previously, and through its parametrization by κ, can be reduced to many previous models of the stable wave. It is found that the hot suprathermal electrons significantly increase the Landau damping of the wave at small wave numbers, i.e., in its acoustic regime. Results from a survey of parameter space, which help to identify parameters for which the stable mode will be only weakly Landau damped, are presented. The dependence of the Landau damping on the fraction of suprathermal electrons, which is related to the index, κ, of the hot electron distribution, is investigated in detail.

We investigate the form of Killing tensors, constructed from conformal Killing vectors of a given spacetime (M, g), by utilizing the Koutras algorithm. As an example we find irreducible Killing tensors in Robertson–Walker spacetimes. A number of theorems are given for the existence of Killing tensors in the conformally related spacetime [Formula: see text]. The form of the conformally related Killing tensors are explicitly determined. The conditions on the conformal factor Ω relating the two spacetimes (M, g) and [Formula: see text] are determined for the existence of the tensors. Also we briefly consider the role of recurrent vectors, inheriting conformal vectors and gradient conformal vectors in building Killing tensors.

We describe energy-momentum conservation in relativistic perturbation theory in general Friedmann-Robertson-Walker ͑FRW͒ backgrounds with causal source terms, such as the presence of cosmic defect networks. A prescription for a linear energy-momentum pseudotensor in a curved FRW universe is provided, and it is decomposed using eigenfunctions of the Helmholtz equation. Conserved vector densities are constructed from the conformal geometry of these spacetimes and related to our pseudotensor, demonstrating the equivalence of these two approaches. We also relate these techniques to the role played by residual gauge freedom in establishing matching conditions at early phase transitions, which we can express in terms of components of our pseudotensor. This formalism is concise and geometrically sound on both sub-and superhorizon scales, thus extending existing work to a physically ͑and numerically͒ useful context.