Eleanor Knox (London) gives a talk in the colloquium “On the split between gravity and inertia in different spacetime theories” at the 17th UK and European meeting on the foundations of physics (29-31 July, 2013)
Abstract: Relative to Newton-Cartan theory, Newtonian gravitation involves the splitting of a single curved connection into gravitational and inertial parts. I examine the prospects for imposing an analogous division of the connection in general relativity. It’s well well-known one cannot split the Levi-Civita connection in quite the same way as one does the Newton-Cartan connection, into a symmetric connection and gravitational field. However, it is possible to divide the Levi-Civita connection into a non-symmetric connection and a part that has sometimes been held (in Teleparallel theories) to represent the gravitational field. I’ll argue that non-symmetric connections are not candidates for representing full inertial structure, and hence that general relativity unites the gravitational and inertial field in a particularly profound sense.