Related papers: On Variational Principles for Gravitating Perfect …
This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt's relativistic elastic media and that the velocity--potential formalism for…
In the context of $f(R,T)$ gravity and other modified theories of gravity, the knowledge of the first order variation of the trace $T$ of the energy-momentum tensor with respect to the metric is essential for an accurate characterization of…
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…
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that…
A connection between linearized Gauss-Bonnet gravity and classical electrodynamics is found by developing a procedure which can be used to derive completely gauge invariant models. The procedure involves building the most general Lagrangian…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
Principles of successful Hamiltonian approaches, which were developed to describe free gravitational field(s) in the metric gravity, are formulated and discussed. By using the standard $\Gamma-\Gamma$ Lagrangian ${\cal L}_{\Gamma-\Gamma}$…
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for…
We present a new complete set of Lagrangian relativistic hydrodynamical equations describing the transfer of energy and momentum between a standard fluid and a radiation fluid in a general non-stationary spherical flow. The new set of…
The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints…
In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…
We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of…
We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties…
For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces…
We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter action is considered. In this case, we show the existence of nontrivial scalar…
We use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid whose constituent degrees of freedom have microscopic polarization. We discuss the meaning of such a system, and argue…
We compute cosmological perturbations for a generic self-gravitating media described by four derivatively- coupled scalar fields. Depending on the internal symmetries of the action for the scalar fields, one can describe perfect fluids,…
The restriction of hydrodynamics to non-viscous, potential (gradient, irrotational) flows is a theory both simple and elegant; a favorite topic of introductory textbooks. It is known that this theory can be formulated as an action principle…
We apply the stochastic variational method to the action of the ideal fluid and showed that the Navier-Stokes equation is derived. In this variational method, the effect of dissipation is realized as the direct consequence of the…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…