Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form

Understand

Some sixty years ago Buchdahl pioneered a program in search of static spherically symmetric vacua for pure $R^{2}$ gravity (Nuovo Cimento, Vol 23, No 1, pp 141-157 (1962); [https://link.springer.com/article/10.1007/BF02733549]).

• Surpassing several obstacles, his work culminated in a non-linear second-order ordinary differential equation (ODE) which required being solved.
• However Buchdahl deemed the ODE intractable and prematurely abandoned his pursuit for an analytical solution.
• We have finally managed to break this six-decades-old impasse and accomplish his goal.