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We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic…

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of…

We describe conformally flat initial data, with explicitly given analytic extrinsic curvature solving the vacuum momentum constraints. They follow from a solution of Dain and Friedrich discovered in 2001. The cylindrically symmetric subcase…

We obtain general analytical solutions of third-order viscous hydrodynamic equations for Bjorken and Gubser flows in systems with vanishing bulk viscosity and chemical potential, and having a constant shear relaxation time. We also…

Viscous hydrodynamics is commonly used to model the evolution of the matter created in an ultra-relativistic heavy-ion collision. It provides a good description of transverse momentum spectra and anisotropic flow. These observables,…

A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…

In his PhD thesis, Einstein derived an explicit first-order expansion for the effective viscosity of a Stokes fluid with a suspension of small rigid particles at low density. His formal derivation relied on two implicit assumptions: (i)…

Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is…

We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint…

Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a…

We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…

I describe the conformal method for constructing solutions of the hyperboloidal constraint equations as well as the conditions needed on the free data in order to have regularity up to boundary for the solutions to the constraint equations.…

We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…

We show that by requiring positivity of the longitudinal pressure it is possible to constrain the initial conditions one can use in 2nd-order viscous hydrodynamical simulations of ultrarelativistic heavy-ion collisions. We demonstrate this…

We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical…

Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…