Speaker
Description
Within the framework of general relativity, the concept of local mass (or quasi-local mass) aims to quantify the amount of mass contained within a particular region of space-time. Nevertheless, the precise definition of such mass in accordance with the theory of general relativity continues to be an unresolved matter. Over the past few decades, numerous proposals have emerged in an attempt to address this issue. One particular proposal that has garnered significant attention from the scientific community in recent years is Bartnik's mass proposal, which builds upon a specific instance of the well-established ADM-mass concept. Unfortunately, performing numerical calculations of this mass for specific situations using conventional numerical methods presents a formidable challenge due to the inherent complexity of the coupled system of partial differential equations that must be solved. Motivated by this challenge, our presentation aims to introduce a deep learning approach for approximating Bartnik's mass for a two-dimensional hypersurface. We will showcase several numerical results and discuss the advantages and disadvantages associated with this method.
