Infinite-derivative linearized gravity in convolutional form. (21st April 2022)

• Record Type: Journal Article
• Authors: Heredia, Carlos; Kolář, Ivan; Llosa, Josep; Maldonado Torralba, Francisco José; Mazumdar, Anupam
• Is Part Of: Classical and quantum gravity. Volume 39:Number 8(2022)
• Publication Date: 2022-04-21
• Subjects: Fourier transfom -- convolution -- infinite derivative gravity -- distributions; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/ac5a14
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local form. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions S ′ . We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all R 3 and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in S ′ .