Related papers: Einstein-Klein-Gordon system via Cauchy-characteri…
The beyond-Horndeski gravity has recently been reformulated in the dark energy paradigm - which has been dubbed, Unified Dark Energy (UDE). The evolution equations for the given UDE appear to correspond to a non-conservative dark energy…
The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and…
General relativity admits a plethora of exact compact object solutions. The augmentation of Einstein's action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with…
In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor…
General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this…
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…
This article studies the Cauchy problem for the scalar conservation law \[ \partial_t u + \partial_t w + \partial_x f(u) = 0, \] where $w(x,t) = [\mathcal{F}(u)(x,t)]$ is the output of a specific hysteresis operator, namely the Play…
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…
The gravitational self-force on a point particle moving in a vacuum background spacetime can be expressed as an integral over the past worldline of the particle, the so-called tail term. In this paper, we consider that piece of the…
We prove Price's law with an explicit leading order term for solutions $\phi(t,x)$ of the scalar wave equation on a class of stationary asymptotically flat $(3+1)$-dimensional spacetimes including subextremal Kerr black holes. Our precise…
We conduct a preliminary investigation into the phenomenological implications of Einsteinian cubic gravity (ECG), a 4-dimensional theory of gravity cubic in curvature of interest for its unique formulation and properties. We find an…
We prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary,…
A new method for improving the optimization performance of a state-of-the-art differential evolution (DE) variant is proposed in this paper. The technique can increase the exploration by adopting the long-tailed property of the Cauchy…
On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the…
We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The…
The central equations in classical general relativity are the Einstein Field Equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
Recently Burrage, de Rham, Heisenberg and Tolley have constructed eternal, classical solutions with closed timelike curves (CTCs) in a Galileon model coupled to an auxiliary scalar field. These theories contain at least two distinct metrics…
The evolution of scalar, electromagnetic and gravitational fields around spherically symmetric black hole surrounded by quintessence are studied with special interest on the late-time behavior. In the ring down stage of evolution, we find…
It is well known that the scalar field Green's function in odd dimensions has a tail, i.e. a non-zero support inside the light cone, which in turn implies that the Huygens' principle is violated. However, the reason behind this behavior is…