Gravitational Interactions of Finite Thickness Global Topological Defects with Black Holes

It is well known that global topological defects induce a repulsive gravitational potential for test particles. 'What is the gravitational potential induced by black holes with a cosmological constant (Schwarzschild-de Sitter (S-dS) metric) on finite thickness global topological defects?'. This is the main question addressed in the present analysis. We also discuss the validity of Derrick's theorem when scalar fields are embedded in non-trivial gravitational backgrounds. In the context of the above question, we consider three global defect configurations: a finite thickness spherical domain wall with a central S-dS black hole, a global string loop with a S-dS black hole in the center and a global monopole near a S-dS black hole. Using an analytical model and numerical simulations of the evolving spherical wall we show that the spherical wall experiences a repelling gravitational potential due to the mass of the central black hole. This potential is further amplified by the presence of a cosmological constant. For initial domain wall radius larger than a critical value, the repulsive potential dominates over the wall tension and the wall expands towards the cosmological horizon of the S-dS metric where it develops ghost instabilities. For smaller initial radius, tension dominates and the wall contracts towards the black hole horizon where it also develops ghost instabilities. We also show, using the same analytical model and energetic arguments that a global monopole is gravitationally attracted by a black hole while a cosmological constant induces a repulsive gravitational potential as in the case of test particles. Finally we show that a global string loop with finite thickness experiences gravitational repulsion due to the cosmological constant which dominates over its tension for a radius larger than a critical radius leading to an expanding rather than contracting loop.