Related papers: Einstein-Klein-Gordon system via Cauchy-characteri…
This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan…
Self-accelerating backgrounds in massive gravity provide an arena to explore the Cauchy problem for derivatively coupled fields that obey complex constraints which reduce the phase space degrees of freedom. We present here an algorithm…
The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group…
Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity.…
Bose-Einstein condensation is usually modeled by nonlinear Schroedinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For…
A well-known open problem in general relativity, dating back to 1972, has been to prove Price's law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux on…
We study the Cauchy problem for the one-dimensional wave equation with an inverse square potential. We derive dispersive estimates, energy estimates, and estimates involving the scaling vector field, where the latter are obtained by…
We propose an efficient semi-Lagrangian Characteristic Mapping (CM) method for solving the three-dimensional (3D) incompressible Euler equations. This method evolves advected quantities by discretizing the flow map associated with the…
In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
We present a unified description of the matter and dark energy epochs, using a class of scalar-torsion theories. We provide a Hamiltonian description, and by applying Noether's theorem and by requiring the field equations to admit…
Complex scalar fields described by a novel Klein-Gordon equation derived from gauge and group theories are considered at the Schwarzschild's black hole singularities. It is shown that the field is well-behaved in the vicinity of these…
We compute tail contributions to the conservative dynamics of a generic self-gravitating system, for every multipole order, of either electric and magnetic parity. Such contributions arise when gravitational radiation is backscattered by…
We analyze the initial value problem for scalar fields obeying the Klein-Gordon equation. The standard Cauchy initial value problem for second order differential equation is to construct a solution function in a neighborhood of space and…
We study analytically the initial value problem for a charged massless scalar-field on a Reissner-Nordstr\"om spacetime. Using the technique of spectral decomposition we extend recent results on this problem. Following the no-hair theorem…
We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at 4PN order in the dynamics of a binary system. The computation entails a subtle interplay between the near…
We study the vacuum Cauchy problem for K-essence, i.e. cosmologically relevant scalar-tensor theories that involve first-order derivative self-interactions, and which pass all existing gravitational wave bounds. We restrict to spherical…
Using the late-time expansion we calculate the leading-order coefficients describing the evolution of a massless scalar field inside a Reissner-Nordstrom black hole. These coefficients may be interpreted as the reflection and transmission…
The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum…