Abstract: In this talk, I will present a construction of new SU(2)-invariant complete negative Einstein metrics on the complex line bundle O(-4) over CP^1. The metrics are conformally compact and generically neither Kähler nor self-dual. The proof involves using rigorous numerical techniques (Chebyshev polynomials and arbitrary-precision interval arithmetic) to produce an approximate Einstein metric in a bounded region near the singular orbit, then perturbing it to a genuine Einstein metric using fixed-point methods. At the boundary of this region, we show that the latter metric is sufficiently close to hyperbolic space so that it extends to a complete, asymptotically hyperbolic Einstein metric. Our construction is based on previous work of Buttsworth?Hodgkinson.