Gravity between Newton and Einstein

The quest for a consistent theory of quantum gravity is one of the most important outstanding problems in theoretical physics. In the landscape of physical theories, quantum gravity sits at the corner where all the physical constants (speed of light, Newton’s and Planck’s constant) are finite. A region that is often overlooked is the nonrelativistic gravity regime. Contrary to common lore, it is becoming clear that the theory of nonrelativistic gravity is much richer than was so far appreciated, containing much more than just Newtonian gravity. Thus, this offers an entirely unexplored potential as a new route towards quantum gravity. Central to this development is the formulation of non-relativistic gravity in terms of Newton–Cartan type geometries, originally introduced by Cartan in 1923 to geometrize Newton’s law of gravitation. Moreover, a wide range of recent applications of Newton-Cartan Geometry, spanning from string theory and holography to condensed matter and biophysical systems, have spurred further interest and insights into Newton-Cartan geometry and related non-relativistic geometries.
In this talk, I will present an overview of these developments and their future perspectives.