Certain Metrics on R⁴₊

We studied the pseudo-Riemannian metric on R³ × R₊, where γ² = Σ³_b=1x_bx_b and a = constant, which satisfies the Einstein condition (in [1], [2], [3] ). The purpose of this work is to find Einstein metrics including the above metric as a special one, which is analogous to the relation between the Schwarzschild metric and the Kerr one in the theory of relativity.