Illustration of the topologically distinct global solutions in quadratic gravity. The solutions are obtained from solving (11) numerically with initial conditions given in Table 2. The top line displays the radial dependence of lnf (blue curve) and lnh (orange curve) for the solutions of (a) Type I, (b) Type II, and (c) Type III. The Schwarzschild solution with M = 10 and an event horizon at r/M = 2 is superimposed as the dashed line. The lower row shows the scaling behavior of the solutions as r → 0 (Type I and Type II) as well as for r − r₀ → 0 (Type III) in a double logarithmic presentation. The scaling behaviors are (s, t)₀ = ( − 2, 2)₀ for Type I, (s, t)₀ = ( − 1, −1)₀ for Type II, and (s, t)_r0 = (1, 0)_r0 for Type III. Graphs of the respective power law are superimposed as dashed lines (black for h and orange for f). This links the asymptotically flat, global solutions to the classification of local scaling behaviors identified in Table 1.