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For slowly-varying initial data, solutions to the Ablowitz-Ladik system have been proven to converge to solutions of the cubic Schr\"odinger equation. In this paper we show that in the continuum limit, solutions to the Ablowitz-Ladik system…
In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…
We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces near static vacuum $n$-dimensional backgrounds, $n\ge 3$, with any finite $k$, with…
A theorem providing a characterisation of Schwarzschildean initial data sets on slices with an asymptotically Euclidean end is proved. This characterisation is based on the proportionality of the Weyl tensor and its D'Alambertian that holds…
Complete constant positive scalar curvature metrics on S^n - {p_1, ..., p_k} admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific S^{n-1}-invariant metric near the puncture points. This allows one to glue…
The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions…
We investigate f(R)-gravity models performing the ADM-slicing of standard General Relativity. We extract the static, spherically-symmetric vacuum solutions in the general case, which correspond to either Schwarzschild de-Sitter or…
We obtain a general class of time-dependent, asymptotically de Sitter backgrounds which solve the first order bosonic equations that extremize the action for supergravity with gauged non-compact $R$-symmetry. These backgrounds correspond…
We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak…
We generalize the Galileon symmetry and its relativistic extension to a de Sitter background. This is made possible by studying a probe-brane in a flat five-dimensional bulk using a de Sitter slicing. The generalized Lovelock invariants…
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we constructed in Part I a family…
The general theory of relativity is currently the accepted theory of gravity and as such, a large repository of test results has been obtained since its inception in 1915. However, in this paper we only focus on what are considered as the…
Generalizing previous work we propose how to superpose spinning black holes in a Kerr-Schild initial slice. This superposition satisfies several physically meaningful limits, including the close and the far ones. Further we consider the…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
We establish probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency…
Recent technical and conceptual advancements in the asymptotic safety approach to quantum gravity have enabled studies of the UV completion of Lorentzian Einstein gravity, emphasizing the role of the state dependence. We present here the…
We present a non-perturbative quantization of gravitational null initial data. Our starting point is the characteristic null initial problem for tetradic gravity with a parity-odd Holst term in the bulk. After a basic review about the…
We construct high-frequency initial data for the Einstein vacuum equations in dimension 3+1 by solving the constraint equations on $\mathbb{R}^3$. Our family of solutions $(\bar{g}_\lambda,K_\lambda)_{\lambda\in(0,1]}$ is defined through a…
In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…