The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources.

The kinetics of neutral particles diluted in a gas or plasma and reacting with a catalytic surface can be calculated accurately only by taking into account the finite value of the mean free path. In reactor models, this problem is usually solved by using reaction-diffusion equations, but this approximation is not always appropriate. As an alternative, Monte Carlo (MC) simulations are used, but they are affected by the noxious problem of statistical error. We propose to address this problem by using the formalism of radiative transfer. A system of integral equations is formulated by generalizing the Schwarzschild-Milne one, in order to take into account several chemical species interacting with a partially catalytic surface, including any kind of backscattering angular distribution. We show that the generalized equations can be easily solved in a computer model using a standard relaxation technique; an excellent agreement with MC simulations is obtained. Applications are discussed.

We study the so-called Gravitational Wave luminosity distance-redshift relation  d L GW(z) during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term δ(z) with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio d L GW/d L EM which tends to a constant value when the sources are at z ≳ 1, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of Ω m0. According to our final discussion, the predicted redshift dependence δ(z) provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity.

We study the so-called Gravitational Wave luminosity distance-redshift relation d GW L (z) during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term δ(z) with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio d GW L /d EM L which tends to a constant value when the sources are at z 1, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of Ω m0 . According to our final discussion, the predicted redshift dependence δ(z) provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity.