Cosmologically Embedded Black Holes: Schwarzschild and Kerr-Newman Solutions in the Cosmological General Theory of Relativity

The Cosmological General Theory of Relativity (CGTR) extends the Cosmological Special Theory of Relativity (CSTR) to curved spacetime byembedding a localized mass, or a rotating charged mass, within a spatially flat, spatially homogeneous Robertson-Walker background whosescale factor is denoted the cosmological expansion function τ (t0) (Yi, 2020, 2021). This paper concentrates specifically on the black-holesolutions of this framework: the cosmologically embedded Schwarzschild solution and the cosmologically embedded Kerr-Newman solution(Yi, 2021, 2025). We present the CGTR field equation and its perturbative metric ansatz, derive the Schwarzschild and Kerr-Newman metricfunctions and their horizon structure, work out the radial and circular photon and massive-particle geodesics, the ergosphere and extremalitycondition of the rotating solution, and the homogeneous (source-free) limit that recovers the background Robertson-Walker cosmology.We show that, in every case considered, the physically measured horizon radii, extremality condition, and photon-sphere radius reduce totheir ordinary, epoch-independent general-relativistic values once expressed in the physically expanded radial coordinate, even though thecorresponding local-coordinate expressions carry explicit τ (t0)-dependence. We close with a comparison to the mainstream McVittie andSchwarzschild-de Sitter embeddings of a point mass in an expanding or accelerating universe, and with the open questions raised by anindependent critical review of the underlying CSTR framework (A Critical Review, 2025).