Related papers: Double Null Data and the Characteristic Problem in…
The characteristic Cauchy problem of the Einstein field equations has been recently addressed from a completely abstract viewpoint by means of hypersurface data and, in particular, via the notion of double null data. However, this…
This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
The formalism of hypersurface data is a framework to study hypersurfaces of any causal character abstractly (i.e. without the need of viewing them as embedded in an ambient space). In this paper we exploit this formalism to study the…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
A hypersurface formed of two null sheets, or "light fronts", swept out by the future null normal geodesics emerging from a common spacelike 2-disk can serve as a Cauchy surface for a region of spacetime. Already in the 1960s free…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…
We show that the maximal globally hyperbolic solution of the initial-value problem for the higher-dimensional vacuum Einstein equations on two transversally intersecting characteristic hypersurfaces contains a future neighborhood of the…
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…
From Einstein's theory we know that besides the electromagnetic spectrum, objects like quasars, active galactic nuclei, pulsars and black holes also generate a physical signal of purely gravitational nature. The actual form of the signal is…
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the…
Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…
In the spirit of the Newtonian theory, we characterize spherically symmetric empty space in general relativity in terms of energy density measured by a static observer and convergence density experienced by null and timelike congruences. It…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem, due…
We study the Cauchy problem in a special case of non-linear massive gravity: the two-tensor "f-g" theory. Despite being ghost-free, it has recently been argued that the theory is inherently problematic due to the existence of superluminal…
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due…
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…