Research

My main interest lies in the realm of classical ‘relativistic’ gravity as described by general relativity and its modifications, particularly in its relation to Galilei-relativistic physics in terms of post-Newtonian expansions.

I believe that for a proper understanding of such relations, one needs to work in a well-defined conceptual framework, enabling the use of systematic methods. In particular, one needs a clear geometric setting in which to analyse the problem at hand. For most of my work in (post-)Newtonian gravity, this geometric setting is given by degenerate geometry, specifically Galilei geometry—the geometry of Newton–Cartan gravity—and modifications thereof.

On a more general note, I am interested in conceptual aspects of (Poincaré-)relativistic physics in a wider sense, and of differential-geometric structures in physics.

Publications

1. P K Schwartz, A L von Blanckenburg
   Comment on ‘The Classical Limit of Teleparallel Gravity’
   arXiv:2410.02839
2. P K Schwartz, A L von Blanckenburg
   The Newtonian limit of orthonormal frames in metric theories of gravity
   arXiv:2410.01800
3. P K Schwartz
   The classification of general affine connections in Newton–Cartan geometry: Towards metric-affine Newton–Cartan gravity
   arXiv:2403.15460
4. A L von Blanckenburg, P K Schwartz
   On gauge transformations in twistless torsional Newton–Cartan geometry
   arXiv:2402.05105
5. M Werner, P K Schwartz, J-N Kirsten-Siemß, N Gaaloul, D Giulini, K Hammerer
   Atom interferometers in weakly curved spacetimes using Bragg diffraction and Bloch oscillations
   Physical Review D 109, 022008 (2024), arXiv:2310.03719
6. A Alibabaei, P K Schwartz, D Giulini
   Geometric post-Newtonian description of massive spin-half particles in curved spacetime
   Classical and Quantum Gravity 40, 235014 (2023), arXiv:2307.04743
7. P K Schwartz
   Teleparallel Newton–Cartan gravity
   Classical and Quantum Gravity 40, 105008 (2023), arXiv:2211.11796
8. D Giulini, A Großardt, P K Schwartz
   Coupling Quantum Matter and Gravity
   in: C Pfeifer, C Lämmerzahl (eds.), Modified and Quantum Gravity, Lecture Notes in Physics 1017 (Springer, Cham, 2023), arXiv:2207.05029
9. P K Schwartz, D Giulini
   Classical perspectives on the Newton–Wigner position observable
   International Journal of Geometric Methods in Modern Physics 17, 2050176 (2020), arXiv:2004.09723
10. P K Schwartz, D Giulini
    Post-Newtonian Hamiltonian description of an atom in a weak gravitational field
    Physical Review A 100, 052116 (2019), arXiv:1908.06929
11. P K Schwartz, D Giulini
    Post-Newtonian corrections to Schrödinger equations in gravitational fields
    Classical and Quantum Gravity 36, 095016 (2019), arXiv:1812.05181

Thesis