2018/11/30 by Álvaro de la Cruz-Dombriz, Francisco José Maldonado Torralba, Francisco J. Maldonado Torralba
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Deriving the Schwarzschild solution #Field equation #Fixed-point theorem #Formalism (music) #Gauge theory #Geometry #Kerr metric #Mathematical physics #Mathematics #No-go theorem #Physics #Picard–Lindelöf theorem #Pulsars and Gravitational Waves Research #Pure mathematics #Quadratic equation #Quantum mechanics #Schwarzschild radius #Spacetime #Theoretical physics #Torsion (gastropod) #gr-qc
paper · pdf · doi:10.1088/1475-7516/2019/03/002
published as JCAP 1903 (2019) 002 · 39 pages, 5 figures, minor corrections, conclusions unchanged. It matches the version published in JCAP
openalex publication_date 2019/03/01 · arxiv created 2019/03/04 · arxiv updated 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present a novel approach to establish the Birkhoff's theorem validity in the so-called quadratic Poincaré Gauge theories of gravity. By obtaining the field equations via the Palatini formalism, we find paradigmatic scenarios where the theorem applies neatly. For more general and physically relevant situations, a suitable decomposition of the torsion tensor also allows us to establish the validity of the theorem. Our analysis shows rigorously how for all stable cases under consideration, the only solution of the vacuum field equations is a torsionless Schwarzschild spacetime, although it is possible to find non-Schwarzschild metrics in the realm of unstable Lagrangians. Finally, we study the weakened formulation of the Birkhoff's theorem where an asymptotically flat metric is assumed, showing that the theorem also holds.