Reissner–Nordstrom–anti–de Sitter nontopological solitons in broken Einstein-Maxwell-Higgs theory

Abstract

Results are presented from numerical simulations of the Einstein-Maxwell-Higgs equations with a broken U(1) symmetry. Coherent nontopological soliton solutions are shown to exist that separate an anti--de Sitter (AdS) true vacuum interior from a Reissner-Nordstrom (RN) false vacuum exterior. The stability of these bubble solutions is tested by perturbing the charge of the coherent solution and evolving the time-dependent equations of motion. In the weak gravitational limit, the short-term stability depends on the sign of $(\ensuremath{\omega}/Q){\ensuremath{\partial}}_{\ensuremath{\omega}}Q$, similar to $Q$-balls. The long-term end state of the perturbed solutions demonstrates a rich structure and is visualized using ``phase diagrams.'' Regions of both stability and instability are shown to exist for ${\ensuremath{\kappa}}_{g}\ensuremath{\lesssim}0.015$, while solutions with ${\ensuremath{\kappa}}_{g}\ensuremath{\gtrsim}0.015$ were observed to be entirely unstable. Threshold solutions are shown to demonstrate time-scaling laws, and the space separating true and false vacuum end states is shown to be fractal in nature, similar to oscillons. Coherent states with superextremal charge-to-mass ratios are shown to exist and observed to collapse or expand, depending on the sign of the charge perturbation. Expanding superextremal bubbles induce phase transitions to the true AdS vacuum, while collapsing superextremal bubbles can form nonsingular strongly gravitating solutions with superextremal RN exteriors.