The Possibility of a Non-Lagrangian Theory of Gravity

TL;DR

This paper explores the potential for a non-Lagrangian theory of gravity, motivated by the limitations and issues of traditional Lagrangian-based General Relativity, aiming to extend the theory with principles from classical and quantum physics.

Contribution

It proposes investigating a non-Lagrangian approach to gravity inspired by fundamental classical and quantum principles, challenging the traditional Lagrangian framework.

Findings

Identifies limitations of Lagrangian-based gravity theories.

Suggests non-Lagrangian extensions could address unresolved issues.

Provides theoretical motivation for alternative gravity models.

Abstract

General Relativity resembles a very elegant crystal glass: If we touch its principles, that is, its Lagrangian, there is a risk of breaking everything. Or, if we will, it is like a short blanket: Curing some problems creates new problems. This paper is devoted to bring to light the reasons why we pursue the possibility of a non-Lagrangian theory of gravity under the hypothesis of an extension of the original general relativity with an ansatz inspired in the fundamental principles of classical and quantum physics.