Sumio Yamada

Soliton solutions to the Einstein equation

The Einstein equation with time symmetry has been regarded as an elliptic variational problem, ever since H. Weyl in 1916 described the Schwarzschild metric using a single harmonic function. In a series of collaborative work with Marcus Khuri, Martin Reiris and Gilbert Weinstein, we constructed 5-dimensional gravitational solitons, and consequently 4-dimensional gravitational (Riemannian) instantons. In 3+1 spacetime dimensions, there are known to be no nontrivial solitons, and our new construction seems to indicate that the higher dimensional Einstein equation is geometrically more fertile.