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This work concerns the dynamics of conformal cubic scalar field on aSchwarzschild--anti-de Sitter background. The main focus is on understandinghow it depends on the size of the black hole and the Robin boundary condition.We identify a critical curve in the parameter space that separates regions withdistinct asymptotic behaviours. For defocusing nonlinearity, the globalattractor undergoes a pitchfork bifurcation, whereas for the focusing case, weidentify a region of the phase space where all solutions blow up in finitetime. In the course of this study we observe an interplay between black holegeometry, boundary conditions, and the nonlinear dynamics of scalar fields inasymptotically anti-de Sitter spacetime.

Dynamics of nonlinear scalar field with Robin boundary condition on the Schwarzschild--Anti-de Sitter background