6 papers
Group Contractions via Infinite-Dimensional Lie Theory
David Prinz, Alexander Schmeding, Philip K. Schwartz
Contractions are a procedure to construct a new Lie algebra out of a given one via a singular limit. Specifically, the Ä°nönü--Wigner construction starts with a Lie algebra $\mat…
The trace-free Einstein tensor is not variational for the metric as field variable
Arian L. von Blanckenburg, Domenico Giulini, Philip K. Schwartz
It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse…
The Newtonian limit of orthonormal frames in metric theories of gravity
Philip K. Schwartz, Arian L. von Blanckenburg
We extend well-known results on the Newtonian limit of Lorentzian metrics to orthonormal frames. Concretely, we prove that, given a one-parameter family of Lorentzian metrics that…
On gauge transformations in twistless-torsional Newton--Cartan geometry
Arian L. von Blanckenburg, Philip K. Schwartz
Twistless-torsional Newton--Cartan (TTNC) geometry exists in two variants, type I and type II, which differ by their gauge transformations. In TTNC geometry there exists a specific…
The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity
Philip K. Schwartz
We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsi…
Comment on `The Classical Limit of Teleparallel Gravity'
Philip K. Schwartz, Arian L. von Blanckenburg
We critically discuss the claims of a recent article regarding the Newtonian limit of the teleparallel equivalent of general relativity (TEGR) in pure-tetrad formulation (arXiv:240…