Abstract
The metric of an arbitrary-dimensional Schwarzschild black hole in the background of a Friedmann–Robertson–Walker universe is presented in the cosmic coordinates system. In particular, the arbitrary-dimensional Schwarzschild–de Sitter metric is rewritten in the Schwarzschild coordinates system, based on which the even more generalized higher dimensional Schwarzschild–de Sitter metric with other extra dimensions is found. The generalized solution shows that the cosmological constant may root in the extra dimensions of space.
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