Related papers: Some global results for asymptotically simple spac…
We prove in this note that local geometric uniqueness holds true without loss of regularity for Einstein equations coupled with a large class of matter models. We thus extend the Planchon-Rodnianski uniqueness theorem for vacuum spacetimes.…
Within the general class of Asymptotically Anti-de Sitter spacetimes that are asymptotic to the A-de-S Schwarzschild metric, we give a simple positive mass theorem based on arguments from causal structure. A general result for all…
In this work we investigate some non-Newtonian effects in exact solutions of the Einstein equations, which describe stationary and axisymmetric configurations of self-gravitating dust. A distinctive feature of these solutions is the…
Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic sym- metries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism,…
We compute the physical graviton two-point function in de Sitter spacetime with three-sphere spatial sections. We demonstrate that the large-distance growth present in the corresponding two-point function in spatially flat de Sitter…
We present some sufficient conditions for the global in time existence of solutions of the semilinear Klein-Gordon equation of the self-interacting scalar field with complex mass. The coefficients of the equation depend on spatial variables…
We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which…
Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting…
Birkhoff's theorem is a classic result that characterizes locally spherically symmetric solutions of the Einstein equations. In this paper, we illustrate the consequences of its local nature for the cases of vacuum and positive cosmological…
A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background…
We prove that the Minkowski spacetime is stable at nonlinear level and to all perturbative orders in the gravitational perturbation in a general class of nonlocal gravitational theories that are unitary and finite at quantum level.
The Minkowski inequality is a classical inequality in differential geometry, giving a bound from below, on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving…
We discuss some recent results in the quest to implement the holographic principle in asymptotically flat spacetimes. In particular we introduce the key ingredients of the candidate dual theory which lives at null infinity and it is…
We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends…
Pure gauge theories for de Sitter, anti de Sitter and orthogonal groups, in four-dimensional Euclidean spacetime, are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective…
The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity. Bondi,…
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric…
We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-$0$ fields (solutions to the wave equation) on $n$-dimensional Minkowski spacetimes in a neighbourhood of…
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that…
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…