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Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures…

We obtain an exact solution of Einstein's equations for a charged, static and spherically symmetric body, surrounded by a fluid of strings and with a cosmological constant. This corresponds to the Reissner-Nordstr\"om (de Sitter)-Anti de…

We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…

We are interested in the evolution of a compressible fluid under its self-generated gravitational field. Assuming here Gowdy symmetry, we investigate the algebraic structure of the Euler equations satisfied by the mass density and velocity…

Optical reference geometry and related concept of inertial forces are investigated in Kerr-de Sitter spacetimes. Properties of the inertial forces are summarized and their typical behaviour is illustrated. The intuitive 'Newtonian'…

A rigid body, with an interior cavity entirely filled with a Navier-Stokes liquid, moves in absence of external torques relative to the center of mass of the coupled system body-liquid (inertial motions). The only steady-state motions…

We investigate light propagation in self-gravitating systems composed of an axially symmetric, stationary, rotating dust fluid. These configurations are intrinsically relativistic, sustained entirely by their rotation, since no compact or…

We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian…

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…

We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we use the (3+1) formalism to formulate the post-Newtonian approximation for the perfect…

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…

In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…

Exploring the characterization of singular black hole spacetimes, we study the relation between energy density, curvature invariants, and geodesic completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic fluid. Working…

This work is devoted to study the analytical and regular solutions of a particular self-gravitating object (i.e., gravastar) in a particular theory of gravity. We derive the corresponding field equations in the presence of effective energy…

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. In this paper we extend this duality to a new magnetohydrodynamics/gravity correspondence, which…

This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…

In an $n$-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any analytical theory of gravity $f(R,{\cal G})$, where $R$ is the curvature scalar and $\cal G$ is the Gauss-Bonnet topological invariant, can be…

We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of…

The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…

A exact de Sitter-like cosmological solution of quadratic gravitation with torsion has been found. In the limit of constant energy and pressure, it becomes a exact de Sitter spacetime. It exists in a wide class of quadratic gravity theories…