Asymptotically Euclidean and asymptotically hyperbolic manifolds have mass invariants computed at infinity. These invariants have the interpretation as the total mass of the manifold as a slice of spacetime in general relativity. One can ask if there are other geometric invariants at infinity of such manifolds.
In this talk we will consider the asymptotically hyperbolic case and we will formulate a definition of mass-like invariants at infinity for such metrics. Further, we will classify the set of mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is one example among two families of invariants.
This is joint work in progress with Julien Cortier and Romain Gicquaud.