Junction conditions in infinite derivative gravity

Abstract

The junction conditions for the infinite derivative gravity theory R þ RFð□ÞR are derived under the assumption that the conditions can be imposed by avoiding the "ill-defined expressions" in the theory of distributions term by term in infinite summations. We find that the junction conditions of such nonlocal theories are much more restrictive than in local theories, since the conditions comprise an infinite number of equations for the Ricci scalar. These conditions can constrain the geometry far beyond the matching hypersurface. Furthermore, we derive the junction field equations which are satisfied by the energymomentum tensor on the hypersurface. It turns out that the theory still allows some matter content on the hypersurface (without external flux and external tension) but with a traceless energy-momentum tensor. We also discuss the proper matching condition where no matter is concentrated on the hypersurface. Finally, we explore the possible applications and consequences of our results to the braneworld scenarios and star models. Particularly, we find that the internal tension is given purely by the trace of the energy-momentum tensor of the matter confined to the brane. Consequences of the junction conditions are illustrated on two simple examples of static and collapsing stars. It is demonstrated that, even without solving the field equations, the geometry on one side of the hypersurface can be determined to a great extent by the geometry on the other side if the Ricci scalar is analytic. We further show that some usual star models in the general relativity are no longer solutions of the infinite derivative gravity.

Fate of the false vacuum in string-inspired nonlocal field theory

“…One can compute numerically the convolution of the exact soliton profile (4.1) with the Gaussian function (4.7), where one can see in figures 2 and 3 that nonlocality (σ = 0) smears the behavior of the local soliton near the kink when σ increases: the soliton width is increased by the smearing effect of nonlocality. This effect is already known for zero-thickness topological defects [51,[74][75][76][77][78][79]. Far from the wall, the nonlocal soliton smoothly recovers the asymptotic behavior of the local one.…”

“…In context to gravity theories, i.e. string-inspired nonlocal extensions of the Einstein gravity, it has been shown that one can get rid of classical singularities, such as black hole singularities [19,24,[57][58][59][60][61][62][63][64][65][66], cosmological singularities [67][68][69][70][71][72][73], and topological defects [74][75][76][77][78][79][80].…”

Topological defects in nonlocal field theories

“…This type of transcendental operators with some entire function γ(− ) have been intensely studied in the past years not only in the context of quantum field theories in flat space [29-32, 36, 37], but also to formulate ghost-free infinite-derivative theories of gravity [29,[38][39][40][41][42][43][44][45][46][47][48][49][50][51].…”