Revisiting Some Leibnizian Concepts in Einstein's Gravitational Theory

We will discuss the analogies between principles and concepts established by G. Leibniz and their potential repercussions on Einstein's Theory of Gravitation. Our focus is on a formulation of Einstein's Equivalence Principle, specifically, the infinitesimal [strong] formulation of Einstein's principle. We will discuss Leibnizian concepts relevant to the technique of infinitesimal parallel transport of vectors, including the so-called "Schild ladder". To this end, we will address the Principle of Identity of Indiscernibles and other pertinent Leibnizian ideas, particularly those related to infinitesimals. We will point out that it is possible to establish connections between Leibniz's fundamental contributions and the framework of General Relativity. Although there are extensive debates in the literature on these topics, we identify new issues within General Relativity that deserve attention.