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We analyze a class of linear wave equations for odd half spin that have a well posed initial value problem. We demonstrate consistency of the equations in curved space-times. They generalize the Weyl neutrino equation. We show that there…
We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…
We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the…
Gravitational wave (GW) oscillations occur whenever there are additional tensor modes interacting with the perturbations of the metric coupled to matter. These extra modes can arise from new spin-2 fields (as in e.g. bigravity theories) or…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
A study of the linearised gravitational field (spin 2 zero-rest-mass field) on a Minkowski background close to spatial infinity is done. To this purpose, a certain representation of spatial infinity in which it is depicted as a cylinder is…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
Numerical evolutions of a system of equations close to null infinity in the geometric background of the inversion-Minkowski spacetime are performed. The evolved equations correspond to the linearisation of a second order metric formulation…
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the…
We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the…
Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields…
A discretized massless wave equation in two dimensions, on an appropriately chosen square lattice, exactly reproduces the solutions of the corresponding continuous equations. We show that the reason for this exact solution property is the…
We derive the tensor gravitational waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to second post-Newtonian order…
In order to extract physical parameters from the waveform of an extreme-mass-ratio binary, one requires a second-order--accurate description of the motion of the smaller of the two objects in the binary. Using a method of matched asymptotic…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
We present a new particle model that generalize for constant curvature space an infinite spin particle in flat space. The model is described by commuting Weyl spinor additional coordinates. It proved that such a model is consistent only in…
In addition to the usual linear gravitational waves in transverse-traceless coordinates, higher-order gravitational field equations, as well as their corresponding solutions, are explicitly obtained. It is found that higher-order waves do…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We study gravitational waves to first and second order in amplitude in vacuum asymptotically flat spacetimes. The Einstein equations are solved to first order and these solutions are superposed to form a time-symmetric ingoing and then…
We consider a Klein-Gordon-Wave system, describing the evolution of a massive field and a massless one interacting through a Yukawa-like coupling, and we explicitly derive its Hamiltonian normal form to first and second order. To the…