Gravitational interactions of finite thickness global topological defects with black holes
Abstract
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 (Schwarzschildde Sitter (SdS) 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 field configurations are embedded in nontrivial gravitational backgrounds. In the context of the above stated question, we consider three global defect configurations: a finite thickness spherical domain wall with a central SdS black hole, a global string loop with a SdS black hole in the center and a global monopole near a SdS black hole. Using an analytical model, numerical simulations of the evolving spherical wall and energetic arguments 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 SdS metric where it develops ghost instabilities (the kinetic term changes sign). 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.
 Publication:

Physical Review D
 Pub Date:
 June 2018
 DOI:
 10.1103/PhysRevD.97.124035
 arXiv:
 arXiv:1804.08098
 Bibcode:
 2018PhRvD..97l4035P
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Physics  Computational Physics
 EPrint:
 13 pages, 9 Figures. The Mathematica file used for the numericala analysis and the construction of the Figures of the paper may be downloaded from http://leandros.physics.uoi.gr/defectsgravity/