Related papers: Bound-Unbound Universality and the All-Order Semi-…
A novel method for calculation of the motion and radiation reaction for the two-body problem (body plus particle, the small parameter m/M being the ratio of the masses) is presented. In the background curvature given by the Schwarzschild…
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 recently reported compactified hyperboloidal method has found wide use in the numerical computation of quasinormal modes, with implications for fields as diverse as gravitational physics and optics. We extend this intrinsically…
For a Schwarzchild black hole of mass $M$, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius $r=4GM/c^2$. When the particle is endowed with a small mass,…
The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…
We describe a special class of ballistic geodesics in Schwarzschild space-time, extending to the horizon in the infinite past and future of observer time, which are characterized by the property that they are in 1-1 correspondence, and…
The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic…
A unified equation is employed to analytically investigate the scattering of massless spin particles by a Schwarzschild-type medium black hole. It is found that for spin particles, curved spacetime induces an effective complex potential…
Nonstandard analysis and electromagnetic propagation properties are used to derive all of the fundamental results for the Special Theory of Relativity. Infinitesimal modeling via infinitesimal light-clocks is used to derive two general…
We analyze the gravitational radiation emitted from a particle in circular motion around a Schwarzschild black hole using the framework of quantum field theory in curved spacetime at tree level. The gravitational perturbations are written…
General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the…
When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should…
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus…
Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding c/2^0.5 are observed to be accelerated in the gravitational field by a distant…
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated…
Global existence and boundedness of classical solutions are shown for a parabolic-elliptic chemotaxis system with local sensing when the motility function is assumed to be unbounded at infinity. The cornerstone of the proof is the…
We derive the functional Schrodinger equation for quantum fields in curved spacetime in the semiclassical limit of quantum geometrodynamics with a Gaussian incoherent dust acting as a clock field. We perform the semiclassical limit using a…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT…
We propose a quantum experiment to measure with high precision the Schwarzschild space-time parameters of the Earth. The scheme can also be applied to measure distances by taking into account the curvature of the Earth's space-time. As a…