Abstract
In this paper, we present a special Lorentzian metric to solve the vacuum Einstein's field equation with cosmological constant Λ and get a general form of solution. By some proper coordinate transformations, a degenerate static vacuum solution of class A with cosmological constant is obtained, and the corresponding one of class B can also be obtained by the complex transformation. We show that this is a constructive and effective new method to extend the degenerate static vacuum solution to the case with cosmological constant.
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