Related papers: Global Hyperbolicity and Self-adjointness

We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold $M$ as part of the construction of quantum geodesics on the algebra $D(M)$ of differential operators. Geodesic motion arises here as an…

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$\hat{i}$tre-Robertson-Walker model of the…

We consider the Klein-Gordon equation on analytic spacetimes with an analytic Cauchy surface. In this setting, we prove the existence of pure analytic Hadamard states. The proof is based on considering an elliptic operator obtained by Wick…

The open Milne cosmological spacetime has a 3-dimensional Cauchy surface isometric to the (non-compact) hyperbolic space. We prove the globally nonlinear stability of the open Milne spacetime for both massive and massless Einstein-scalar…

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 consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a…

Let $M$ be a globally hyperbolic manifold with complete spacelike Cauchy hypersurface $\Sigma$. We prove well-posedness of the Cauchy problem for the Dirac operator on globally hyperbolic manifolds with complete Cauchy hypersurfaces. This…

Several uniqueness results for non-compact complete stationary spacelike surfaces in an $n(\geq 3)$-dimensional Generalized Robertson Walker spacetime are obtained. In order to do that, we assume a natural inequality involving the Gauss…

We consider the massive Klein-Gordon equation on short-range asymptotically Minkowski spacetimes. Extending our results in [GW1], we show that the Klein-Gordon operator with Feynman type boundary conditions at infinite times is invertible…

This paper deals with the Klein-Gordon equation on the Poincar\'e chart of the 5-dimensional Anti-de Sitter universe. When the mass $\mu$ is larger than $-{1}{4}$, the Cauchy problem is well posed despite the loss of global hyperbolicity…

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof…

Uniqueness (up to isometries) and existence of limits are studied in the context of Cheeger-Gromov convergence of spacetimes. To address the non-compactness of the vector isometry group in the semi-Riemannian setting, standard pointed…

Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic"…

We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other…

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced…

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…

Given a globally hyperbolic spacetime endowed with a complete lightlike Killing vector field and a complete Cauchy hypersurface, we characterize the points which can be connected by geodesics. A straightforward consequence is the geodesic…

Generalized parity (P), time-reversal (T), and charge-conjugation (C)operators were initially definedin the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show…

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter and Kerr-Kruskal spacetimes. In this setup, we give…

Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…