Birkhoff's theorem for stable torsion theories

Understand

We present a novel approach to establish the Birkhoff's theorem validity in the so-called quadratic Poincar\'e 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.