Related papers: A synthetic Gannon-Lee incompleteness theorem
The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net positive expansion must be geodesically incomplete. We derive a new version of the theorem using the fluid flow formalism of General Relativity. The theorem is purely…
We prove that under a generic asymptotic condition on the charge, the small data solutions to the Vlasov-Maxwell system do not verify linear scattering. In other words, we show the non-$L^1$ asymptotic completeness of the system. The proof…
A recent paper \cite{Bousso:2022cun} put forward a theorem showing that hyperentropic surface would result in incomplete null generators for a null hypersurface emanating from the surface provided it satisfies the null curvature condition…
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, "hyperbolic". We show that for a sufficiently regular one-dimensional map satisfying a weak hyperbolicity assumption,…
The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable…
We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are both asymptotic to the same ideal boundary, there is a new one…
It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the…
We investigate the stability of timelike Ricci curvature lower bounds under low-regularity limits of Lorentzian metrics. Specifically, we prove that the synthetic curvature-dimension condition $TCD^e_p(K,N)$, which provides an optimal…
We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known…
In this work, we study self-gravitating objects that obey a polytropic equation of state in hyperbolic symmetry. Specifically, we describe in detail the steps to derive the Lane-Emden equation from the structure equations of the system. To…
Penrose's quasi-local mass construction is carried through for two-surfaces at infinity in asymptotically anti-de Sitter space-times. A modification of the Witten argument is given to prove a positivity property of the resulting conserved…
We present a systematic method for constructing static, spherically symmetric regular spacetimes in general relativity satisfying the weak energy condition. Our approach relies on physically reasonable assumptions on the matter energy…
Certain equations with integral constraints have as solutions time-periodic pulses of a field-like unknown while a current-like unknown oscillates periodically with time. A general asymptotic theory of this phenomenon, the generalized Gunn…
In this paper, we extend the definition of qx-asymptotic function, for extended real-valued function that define on an infinite dimensional topological normed space without lower semicontinuity or quasi-convexity condition. As the main…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…
We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for…
We discuss the limit of vanishing $G$ (Newton's constant of universal gravitation) of the maximal analytically extended Kerr--Newman electrovacuum spacetimes {represented in Boyer--Lindquist coordinates}. We investigate the topologically…
In this paper we study space-times which evolve out of Cauchy data $(\Sigma,{}^3g,K)$ invariant under the action of a two-dimensional commutative Lie group. Moreover $(\Sigma,{}^3g,K)$ are assumed to satisfy certain completeness and…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the…