Classical gauge theories and gravity

It is well-known that electromagnetic, electroweak, and strong interactions are interpreted as gauge theories. In contrast, the situation regarding gravitational interaction is often considered more complex. Since the 1950s, this complexity has prompted extensive research into whether gravity can be understood as a gauge theory. The goal of this work is to provide an introduction to a framework for describing classical gauge theories developed by Andrzej Trautman in the 1970s and discuss its consequences for the gauge interpretation of gravity. This framework utilizes the theory of (Ehresmann) connections on principal G-bundles. Within the framework, gravity is interpreted as a classical gauge theory, where the metric tensor field is treated as a classical Higgs field. One significant advantage of this framework is that it enables the description of gravity and gauge theories of internal symmetries using the same mathematical formalism. This unification leads to a deeper understanding of the crucial geometric similarities and differences between these two distinct classes of classical gauge theories.