The fast Newtonian limit for perfect fluids

(In)finiteness of Spherically Symmetric Static Perfect Fluids

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 perfect fluid solutions possess finite/infinite extent. In the Newtonian case, for the large class of monotonic equations of state, and in General Relativity we improve earlier results.

Post-Newtonian Approximation

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 fluid. As an application we show the method for constructing the equilibrium configuration of nonaxisymmetric uniformly rotating fluid. We also discuss the gravitational waves including tail from post-Newtonian systems.

旋转带电流体的稳定性：牛顿非导电情形下Hoiland条件的推广

Stability of Rotating, Charged Fluids: Generalization of the Hoiland Conditions in Newtonian Non-conductive Case

该研究采用拉格朗日扰动形式，在牛顿引力框架下分析旋转带电非导电理想流体环的线性稳定性，推广了Høiland判据至非零电荷情形，发现恒定角动量环面线性稳定、但对非轴对称扰动不稳定。

Averaging out Inhomogeneous Newtonian Cosmologies: I. Fluid Mechanics and the Navier-Stokes Equation

The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A special attention is paid to the analytic formulation of the definitions and equations of moving fluids and to their physical content.

Pseudo-Newtonian equations for evolution of particles and fluids in stationary space-times

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black-hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper we develop a general pseudo-Newtonian formalism which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and m…

First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals

The rotational dynamics of an $N$-body system at the first post-Newtonian order in Einstein-Cartan theory is derived. This result is achieved by performing the point-particle limit of the equations of motion of the Weyssenhoff fluid, which models the quantum spin effects residing inside the bodies. For the special case of binary systems, we determine the Lagrangian function and the resulting first integrals underlying the translational dynamics and the spin precession.

A Post-Newtonian approach to black hole-fluid systems

This work devises a formalism to obtain the equations of motion for a black hole-fluid configuration. Our approach is based on a Post-Newtonian expansion and adapted to scenarios where obtaining the relevant dynamics requires long time-scale evolutions. These systems are typically studied with Newtonian approaches, which have the advantage that larger time-steps can be employed than in full general-relativistic simulations, but have the downside that important physical effects are not accounted for. The formalism presented here provides a relatively straightforward way to incorporate those eff…

Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory

We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitating shells (or bubbles) have been used in numerous model problems especially in general relativity and cosmology. A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian gravity we show that self-gravitating static fluid shells are unstable with…

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are …

Modified Newtonian potentials for particles and fluids in permanent rotation around black holes

Modified Newtonian potentials have been proposed for the description of relativistic effects acting on particles and fluids in permanent orbital motion around black holes. Here we further discuss spherically symmetric potentials like the one proposed by Artemova, Bjornson & Novikov (1996, Astrophysical Journal, 461, 565), and we illustrate their virtues by studying the acceleration along circular trajectories. We compare the results with exact expressions in the spacetime of a rotating (Kerr) black hole.

General-relativistic rotation laws in rotating fluid bodies

We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic anti-dragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids selfgravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations, …

Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory

The generation of gravitational waves from a post-Newtonian source endowed with a quantum spin, modeled by the Weyssenhoff fluid, is investigated in the context of Einstein-Cartan theory at the first post-Newtonian level by resorting to the Blanchet-Damour formalism. After having worked out the basic principles of the hydrodynamics in Einstein-Cartan framework, we study the Weyssenhoff fluid within the post-Newtonian approximation scheme. The complexity of the underlying dynamical equations suggests to employ a discrete description via the point-particle limit, a procedure which permits the an…

First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: equations of motion

We derive the equations of motion for an $N$-body system in the Einstein-Cartan gravity theory at the first post-Newtonian order by exploiting the Weyssenhoff fluid as the spin model. Our approach consists in performing the point-particle limit of the continuous description of the gravitational source. The final equations provide a hint for the validity of the effacing principle at 1PN level in Einstein-Cartan model. The analogies with the general relativistic dynamics involving the macroscopic angular momentum are also discussed.