Abstract:

A remarkable feature of general relativity is the presence of spacetime singularities. One of the central aims of a complete theory of (quantum) gravity is to resolve these singularities. In this talk, I will describe ongoing work—building upon pioneering results by Aron Wall—to define a precise notion of "geometric singularity resolution." Roughly speaking, geometric singularity resolution occurs when non-perturbative effects arising at an ultraviolet scale modify a singular spacetime metric into one without singularities. I will propose a conjecture that provides a simple criterion to determine when such singularity resolution is possible. To motivate this, I will discuss a class of theories in which the conjecture has been proved, thus providing concrete realizations of these ideas. Finally, I will present explicit examples illustrating scenarios where singularities are resolved, as well as cases where they are not.