Semilinear Klein-Gordon equation in space-time of black hole, which is gaining mass in the universe with accelerating expansion

Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with relativity and gravitational theory (35Q75) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)

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