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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…
In this article we perform a detailed theoretical analysis for a class of new exact solutions with anisotropic fluid distribution of matter for compact objects in hydrostatic equilibrium. To achieve this we call the relation between the…
The Tolman--Oppenheimer--Volkoff (TOV) equations are a partially uncoupled system of nonlinear and non-autonomous ordinary differential equations which describe the structure of isotropic spherically symmetric static fluids. Nonlinearity…
Relativistic fluid dynamics finds application in astrophysics, cosmology and the physics of high-energy heavy-ion collisions. In this thesis, we present our work on the formulation of relativistic dissipative fluid dynamics within the…
This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide…
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…
This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In this third paper we elevate the Newtonian theory of the…
The TOV equation appears as the relativistic counterpart of the classical condition for hydrostatic equilibrium. In the present work we aim at showing that a generalised TOV equation also characterises the equilibrium of models endowed with…
We present a formalism to describe the motion of a fluid that is fully covariant with respect to arbitrary observers. To achieve full covariance, we write prognostic equations for quantities that belong to the graded exterior algebra of the…
We investigate the existence of analytic solutions for the field equations in the Einstein-\ae ther theory for a static spherically symmetric spacetime and provide a detailed dynamical system analysis of the field equations. In particular,…
We have developed a theoretical model and a numerical code for stationary rotating superfluid neutron stars in full general relativity. The underlying two-fluid model is based on Carter's covariant multi-fluid hydrodynamic formalism. The…
A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are…
This paper is the first in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian and relativistic gravity. In this first paper we set the stage, place our work in the context of…
For a static, perfect fluid sphere with a general equation of state, we obtain the relativistic equation of hydrostatic equilibrium, namely the Tolman-Oppenheimer-Volkov equation, as the thermodynamical equilibrium in the microcanonical, as…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
We discuss two different approaches to synthesise holographic non-relativistic fluid from its relativistic counterpart. In the first approach we obtain the non-relativistic fluid by light-cone reduction of a relativistic conformal fluid. In…
Non-local $f(R)$ gravity was proposed as a powerfull alternative to general relativity (GR) . This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolent(UV) early epochs. However, there are a lot of…
We discuss the construction of perfect fluid stellar objects having optical geometries with multiple necks corresponding to spatially closed unstable lightlike geodesics. We prove that there exist physically reasonable models with…
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular…
We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating…