Introduction

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement.

An Ermakov-Pinney-like equation associated with the scalar wave equation in curved space-time is here studied. The example of Schwarzschild space-time considered in the present work shows that this equation can be viewed more as a "model equation," with interesting applications in black hole physics. Other applications studied involve cosmological space-times (de Sitter) and pulse of plane gravitational waves: in all these cases the evolution of the Ermakov-Pinney field seems to be consistent with a rapid blow-up, unlike the Schwarzschild case where spatially damped oscillations are allowed.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants.

We compute the first-order self-force contribution to Detweiler's redshift invariant for extended bodies endowed with both dipolar and quadrupolar structure (with spin-induced quadrupole moment) moving along circular orbits on a Schwarzschild background. Our analysis includes effects which arc second order in spin, generalizing previous results for purely spinning particles. The perturbing body is assumed to move on the equatorial plane, the associated spin vector being orthogonal to it.

Dissipative kinetic models inspired by neutron transport are studied in a (1+1)-dimensional context: first, in the two-stream approximation, then in the general case of continuous velocities. Both are known to relax, in the diffusive scaling, toward a damped heat equation. Accordingly, it is shown that "uniformly accurate" L-splines discretizations of this parabolic asymptotic equation emerge from well-balanced schemes involving scattering S-matrices for the kinetic models.

We investigate the motion of uncharged particles scattered by a binary system consisting of extremely charged black holes in equilibrium as described by the Majumdar-Papapetrou solution. We focus on unbound orbits confined to the plane containing both black holes. We consider the two complementary situations of particles approaching the system along a direction parallel to the axis where the black holes are displaced and orthogonal to it.

TEOBResumS and SEOBNRv4 are the two existing semianalytical gravitational waveform models for spin-aligned coalescing black hole binaries based on the effective-one-body (EOB) approach. They are informed by numerical relativity simulations and provide the relative dynamics and waveforms from early inspiral to plunge, merger, and ringdown. The central building block of each model is the EOB resummed Hamiltonian. The two models implement different Hamiltonians that are both deformations of the Hamiltonian of a test spinning black hole moving around a Kerr black hole.

The post-Minkowskian approach to gravitationally interacting binary systems (i.e., perturbation theory in G, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the fast post-Minkowskian order.