Related papers: Corrected Newtonian potentials in the two-body pro…
The potential energy problem in an electrostatically bound two-body system is studied in the framework of a recently proposed impact model of the electrostatic force and in analogy to the potential energy in a gravitationally bound system.…
The effect of the recently obtained 2nd post-Newtonian corrections on the accuracy of estimation of parameters of the gravitational-wave signal from a coalescing binary is investigated. It is shown that addition of this correction degrades…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively…
We calculate the leading quantum and semi-classical corrections to the Newtonian potential energy of two widely separated static masses. In this large-distance, static limit, the quantum behaviour of the sources does not contribute to the…
We revisit the decay of the orbital period in binary systems that occurs due to the emission of gravitational waves in the context of modified gravity models where the coupling $G_{gw}$ between matter and on-shell gravitons is allowed to…
In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let the orbit of a particle moving in a central force field be an off-center circle. How…
Chiral EFT yields singular potentials that require regularization and renormalization when implemented in a dynamical equation such as the Lippmann--Schwinger equation. We employ two different approaches, renormalization with contact terms…
Geodesy in a Newtonian framework is based on the Newtonian gravitational potential. The general-relativistic gravitational field, however, is not fully determined by a single potential. The vacuum field around a stationary source can be…
We consider the secular dynamics of a binary and a planet in terms of non-restricted, hierarchical three-body problem, including the general relativity corrections to the Newtonian gravity. We determine regions in the parameter space where…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable…
In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We…
Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential. In…
We study the Jeans instability of a self-gravitating fluid in the context of alternative gravitational theories. Our formulation accommodates arbitrary corrections to the Newtonian potential, providing a versatile approach to analyzing a…
We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice…
We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
The two full body problem concerns the dynamics of two spatially extended rigid bodies (e.g. rocky asteroids) subject to mutual gravitational interaction. In this note we deduce the Euler-Poincare and Hamiltonian equations of motion using…
We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…