Within Newtonian gravity, the term “mass” refers to a measure of the power of gravitational attraction of an object. It can be quantified by computing the monopole term for the gravitational field. Mass is also the sole way of interacting with the Newtonian gravitational field, and thus this concept plays a very prominent role in any description of gravitational phenomena.

Despite this, defining “mass” in general relativity is a much more subtle task. Since the gravitational field and spacetime are now two facets of the same physical entity, it is not as straightforward to compute what we would like to call a monopole. Furthermore, time is no longer absolute, which means evaluating a monopole moment at a fixed time may have an ambiguous meaning.

In The Measure of a Mass, Bruno and I discuss the difficulties in defining mass and how to address them in a few different scenarios for asymptotically flat spacetimes. These different notions of mass are compared and interpreted to pursue a deeper understanding of what “mass” means in relativistic contexts.

Once a few possible definitions of mass have been agreed upon, we shift our focus to discussing a key physical property of mass: its positivity. Different possible arguments lead to the conclusion that a suitably defined notion of mass should be nonnegative. One of the main routes is to assume microscopic masses are always positive in a suitable sense (i.e., an energy condition is obeyed) and this is used to conclude that macroscopic masses are always positive as well. A second route, recently considered by the authors in collaboration with Landulfo, uses stability arguments to show that negative masses need to be short-lived.