Junction conditions in infinite derivative gravity

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