arXiv subjects

Selim Amar

Publications and source records attributed to Selim Amar.

3 recordsLinked to original sources

arXiv2026

Feynman Propagators on Exponentially Decaying Perturbations of Stationary Spacetimes with Compact Cauchy Surface

In this paper, we construct Feynman propagators on exponentially decaying perturbations of stationary spacetime with compact Cauchy surface. The propagators are defined as parametrices of the wave operator on exponentially weighted Sobolev spaces defined by complex contours $Γ$. We then apply this theory to the computation of indexes of Dirac operators using a continuous Wick-like rotation to relate it to the Riemannian case.

math.AP↗

arXiv2025

Fredholm Theory of Non-Elliptic Operators in the Presence of Normally Hyperbolic Trapping

We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic Sobolev spaces with weak regularity at the backward trapped set $Γ_u$, which are roughly speaking made of distributions $v \in H^s$ satisfying $Φ_u v \in H^{s+1}$ for some quantization $Φ_u$ of the defining function $ϕ_u$ of $Γ_u$. We then apply it to the case of wave operators on spacetimes.

math.AP↗

arXiv2021

A peeling theorem for the Weyl tensor in higher dimensions

A peeling theorem for the Weyl tensor in higher dimensional Lorentzian manifolds is presented. We obtain it by generalizing a proof from the four dimensional case. We derive a generic behavior, discuss interesting subcases and retrieve the four dimensional result.

math-ph↗