Stationary stars are axisymmetric in higher curvature gravity

Abstract

The final equilibrium stage of stellar evolution can result in either a black hole or a compact object, such as a white dwarf or neutron star. In general relativity, both stationary black holes and stationary stellar configurations are known to be axisymmetric, and black hole rigidity has been extended to several higher curvature modifications of gravity. In contrast, no comparable result had previously been established for stationary stars beyond general relativity. In this work, we extend the stellar axisymmetry theorem to a broad class of diffeomorphism-invariant metric theories. Assuming asymptotic flatness and standard smoothness requirements, we show that the Killing symmetry implied by thermodynamic equilibrium inside the star uniquely extends to the exterior region, thereby enforcing rotational invariance. This demonstrates that axisymmetry of stationary stellar configurations is not a feature peculiar to Einstein gravity but a universal property of generally covariant gravitational theories, persisting even in the presence of higher curvature corrections.