相关论文: Elliptic orbits with a non-Newtonian eccentricity
We obtain rotation laws for axially symmetric, selfgravitating and stationary fluids around spinning black holes. They reduce --- in the Newtonian limit --- to monomial rotation curves. For spinless black hole, one obtains in the first…
Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…
The non-abelian symmetry of a lagrangian invalidates the principle of superposition for the field described by this lagrangian. A consequence in QCD is that non-linear effects occur, resulting in the quark-quark linear potential that…
We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in…
Historically, the eccentricity of Sommerfeld orbits from quantization conditions in either parabolic or spherical coordinates was found to differ in almost all cases. To do the orbit comparison correctly, one must use amended instead of…
We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can only…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting…
We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are…
Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
In this paper we prove a H\"older partial regularity result for weak solutions $u:\Omega\to \mathbb{R}^N$, $N\geq 2$, to non-autonomous elliptic systems with general growth of the type: \begin{equation*} -\rm{div}\, a(x, u, Du)= b(x, u, Du)…
We prove a general fusion theorem for complete orientable minimal surfaces in $\mathbb{R}^3$ with finite total curvature. As a consequence, complete orientable minimal surfaces of weak finite total curvature with exotic geometry are…
Higher-order corrections of Einstein-Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where Ricci scalar R and its d'Alembertian $\Box R$ are present. In…
The vectorial velocity is given as a function of the position of a particle in orbit when a Newtonian central force is supplemented by an inverse cubic force as in Newton's theorem on revolving orbits. Such expressions are useful in fitting…
For a class of linear elliptic equations of general type with rapidly oscillating coefficients, we use the sigma-convergence method to prove the homogenization result and a corrector-type result. In the case of asymptotic periodic…
The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.
The post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an isolated, oblate spheroid of constant density that is rigidly and uniformly rotating on the motion of a test particle are analytically worked…
In the case of nonspinning compact binary systems on quasi-elliptic orbits, I obtain the conservative map between the constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) frequencies at the fourth…