Gravity from the extension of spatial diffeomorphisms

The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential term which can be a general (not necessarily local) functional of the metric. From the perspective of the foundation of Einstein's gravity our results are positive: The extended constraint algebra is either that of Einstein's gravity, or ultralocal gravity. If our goal is a simple modification of Einstein's gravity that for example makes it perturbatively renormalizable, as has recently been suggested, then our results show that there is no such theory within this class.Comment: 34 page

A generalized variational principle in b-metric spaces

In this paper we establish and prove a generalized variational principle for b-metric spaces. As a consequence, we obtain a weak Zhong-type variational principle in b-metric spaces. We show the applicability of the mentioned generalized variational principle by presenting a Caristi-type fixed point theorem and an extension of the main result for bifunctions - both of them stated in b-metric spaces