Buchdahl Limits Beyond General Relativity

Abstract

Buchdahl’s theorem in four dimensions establishes a universal bound on the degree of compactness of a static star of radius R. The bound is saturated by constant-density stars with infinite central pressure and in terms of the stars’ Schwarzschild radius reads R ≥ 9 8 rS. We show that the theorem holds for D-dimensional Einstein gravity and that the limit becomes R ≥ h (D−1)2 4(D−2) i1/(D−3) rS. We show that the bound is modified when Einstein gravity is corrected by a quadratic higher-curvature term of the Gauss-Bonnet type. In that case, the degree of compactness can be significantly reduced with respect to the Einsteinian result.