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A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two parts, tangent to the embedded hypersurface and orthogonal to it; only the second ones are relevant, the tangent ones being equivalent to coordinate transformations in the embedded manifold. The geometrical quantities can be then expressed in terms of embedding functions $z^A$ and their infinitesimal deformations $v^A z^A to {tilde{z}}^A = z^A + epsilon v^A$. The deformations are called Einsteinian if they keep Einstein equations satisfied up to a given order in $epsilon$. The system so obtained is then analyzed in particular in the case of the Schwarzschild metric taken as the starting point, and some solutions of the first-order deformation of Einsteins equations are found. We discuss also second and third order deformations leading to wave-like solutions and to the departure from spherical symmetry towards an axial one (the approximate Kerr solution)
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any ar
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in details: the perihelion shift of the planet Mercu
This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of General Rela
We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship hypothesis and the Penrose inequality, the uniquene
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detectio