The claim states a foundational textbook fact of general relativity: the vacuum Einstein field equations (R_mu_nu = 0) admit non-trivial solutions that describe gravitational waves (such as linearized plane waves or exact pp-waves) and black holes (such as the Schwarzschild and Kerr metrics). Because this is a standard textbook definition and direct consequence of the theory, it is common knowledge within physics and does not need to be proved by a specific primary research citation from the retrieved list (papers like [0], [2], and [9] study specific aspects of these solutions, but the fundamental premise is foundational knowledge).