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It is well known that global topological defects induce a repulsivegravitational potential for test particles. 'What is the gravitationalpotential induced by black holes with a cosmological constant (Schwarzschild-deSitter (S-dS) metric) on finite thickness global topological defects?'. This isthe main question addressed in the present analysis. We also discuss thevalidity of Derrick's theorem when scalar fields are embedded in non-trivialgravitational backgrounds. In the context of the above question, we considerthree global defect configurations: a finite thickness spherical domain wallwith a central S-dS black hole, a global string loop with a S-dS black hole inthe center and a global monopole near a S-dS black hole. Using an analyticalmodel and numerical simulations of the evolving spherical wall we show that thespherical wall experiences a repelling gravitational potential due to the massof the central black hole. This potential is further amplified by the presenceof a cosmological constant. For initial domain wall radius larger than acritical value, the repulsive potential dominates over the wall tension and thewall expands towards the cosmological horizon of the S-dS metric where itdevelops ghost instabilities. For smaller initial radius, tension dominates andthe wall contracts towards the black hole horizon where it also develops ghostinstabilities. We also show, using the same analytical model and energeticarguments that a global monopole is gravitationally attracted by a black holewhile a cosmological constant induces a repulsive gravitational potential as inthe case of test particles. Finally we show that a global string loop withfinite thickness experiences gravitational repulsion due to the cosmologicalconstant which dominates over its tension for a radius larger than a criticalradius leading to an expanding rather than contracting loop.

Gravitational Interactions of Finite Thickness Global Topological Defects with Black Holes