Thermodynamics of viscoelastic rate-type fluids with stress diffusion

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.Comment: The benefits of the knowledge of the thermodynamical background of the derived models are now documented in the study of nonlinear stability of equilibrium rest state

Graviton propagators in AdS beyond GR: heat kernel approach

We present a new covariant method of construction of the (position space) graviton propagators in the $N$-dimensional (Euclidean) anti-de Sitter background for any gravitational theory with the Lagrangian that is an analytic expression in the metric, curvature, and covariant derivative. We show that the graviton propagators (in Landau gauge) for all such theories can be expressed using the heat kernels for scalars and symmetric transverse-traceless rank-2 tensors on the hyperbolic $N$-space. The latter heat kernels are constructed explicitly and shown to be directly related to the former if an improved bi-scalar representation is used. Our heat kernel approach is first tested on general relativity, where we find equivalent forms of the graviton propagators. Then it is used to obtain explicit expressions for graviton propagators for various higher-derivative as well as infinite-derivative/nonlocal theories of gravity. As a by-product, we also provide a new derivation of the equivalent action (correcting a mistake in the original derivation) and an extension of the quadratic action to arbitrary ${N\geq 3}$ dimensions.Comment: 35 page

Infinite derivative gravity resolves nonscalar curvature singularities

We explicitly demonstrate that the nonlocal ghost-free ultraviolet modification of general relativity (GR) known as the infinite derivative gravity (IDG) resolves nonscalar curvature singularities in exact solutions of the full theory. We analyze exact pp-wave solutions of GR and IDG describing gravitational waves generated by null radiation. Curvature of GR and IDG solutions with the same energy-momentum tensor is compared in parallel-propagated frames along timelike and null geodesics at finite values of the affine parameter. While the GR pp-wave solution contains a physically problematic nonscalar curvature singularity at the location of the source, the curvature of its IDG counterpart is finite.Comment: 5 pages, 1 figur