# Mass in Newtonian gravity and general relativity

Isolated gravitating systems such as stars, black holes, and galaxies play an important role both in Newton's theory of gravity and in Einstein's theory of general relativity. While the definition of mass and center of mass via the mass density is straightforward in Newtonian gravity, there is no definitive corresponding notion in general relativity. Instead, there are several alternative approaches in general relativity to defining the center of mass of an isolated system. We will discuss these different approaches and present some explicit examples. Moreover, we will introduce the notion of Newtonian limit and use it to relate the Newtonian and the relativistic centers in the case of static systems.