Related papers: The Case Against Smooth Null Infinity IV: Linearis…
Starting from Post-Newtonian predictions for a system of $N$ infalling masses from the infinite past, we formulate and solve a scattering problem for the system of linearised gravity around Schwarzschild as introduced in [DHR19]. The…
This paper initiates a series of works dedicated to the rigorous study of the precise structure of gravitational radiation near infinity. We begin with a brief review of an argument due to Christodoulou [1] stating that Penrose's proposal…
We construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We build on the results of Part I \cite{Mas20}, where we used the energy conservation enjoyed by the Regge--Wheeler…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
Using a set of field equations in the null surface formulation we obtain the linearized coupling between the gravitational and matter fields. We first derive a formula for the metric of the space time and then we use this formula to study…
We construct a scattering theory for the spin $\pm2$ Teukolsky equations on the exterior of the Schwarzschild spacetime, as a first step towards developing a scattering theory for the linearised Einstein equations in double null gauge. This…
An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the `outside' is then…
We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order ($O[(v/c)^4] \sim O[(Gm/rc^2)^2]$)…
We present the first numerical simulations of asymptotically flat space-times whose computational domain includes past and future null-infinity. As an application, we explore the scattering of a gravitational wave in a black hole…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
The existence of gravitational radiation arriving at null infinity -- i.e. escaping from the physical system -- is addressed in the presence of a non-negative cosmological constant $\Lambda\geq 0$. The case with vanishing $\Lambda$ is well…
We study both of the scattering and Cauchy problems for the semilinear wave equation with null quadratic form on the Schwarzschild background. Prescribing the scattering data that are given by the short pulse data on the future null…
A novel criterion to determine the presence of gravitational radiation arriving to, or departing from, null infinity of any weakly asymptotically-simple space-time with vanishing cosmological constant is given. The quantities involved are…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…
We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which…
Quadratic gravity constitutes a prototypical example of a perturbatively renormalizable quantum theory of the gravitational interactions. In this work, we construct the associated phase space of static, spherically symmetric, and…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…