相关论文: Self-force and radial fall: new integration method…
A new integrability condition of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation depending on a generating function $f(x)$, the general solution of the Riccati equation can be obtained if…
We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the…
The radial neoclassical fluxes of electrons in the 1/nu regime are calculated with relativistic effects taken into account and compared with those in the non-relativistic approach. The treatment is based on the relativistic drift-kinetic…
Extreme mass-ratio inspirals are among the key sources of gravitational waves for the Laser Interferometer Space Antenna space-based gravitational-wave detector. Achieving sufficient accuracy in the gravitational-wave template for these…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
We present a new method designed to avoid numerical challenges that have impeded calculation of the Lorenz gauge self-force acting on a compact object inspiraling into a Kerr black hole. This type of calculation is valuable in creating…
We present a novel perspective on gravity-induced wave function reduction using Bohmian trajectories. This study examines the quantum motion of both point particles and objects, identifying critical parameters for the transition from…
This paper considers the relativistic motion of charged particles coupled with electromagnetic fields in the higher-order theory proposed by Bopp, Land\'e--Thomas, and Podolsky. We rigorously derive a world-line integral expression for the…
The problem of the self-interaction of a quasi-rigid classical particle with an arbitrary spherically symmetric charge distribution is completely solved up to the first order in the acceleration. No ad hoc assumptions are made. It is shown…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
It is well known that supermassive black holes in the centers of galaxies are capable of accelerating charged particles to very high energies. In many cases, the particle acceleration by black holes occurs electromagnetically through an…
We consider the focusing wave equation outside a ball of $\R^3$, with Dirichlet boundary condition and a superquintic power nonlinearity. We classify all radial stationary solutions, and prove that all radial global solutions are…
The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves…
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical…
Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined.…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…
The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the…
A scalar charged particle moving in a curved background spacetime will emit a field affecting its own motion; the resolving of this resulting motion is often referred to as the self-force problem. This also serves as a toy model for the…
It is proposed in this paper that without a measurement, the wave function of a system periodically transits to a bound energy eigenfunction or the complementary wave function that is orthogonal to all the bound energy eigenfunctions.…