Dynamical Instability of Self-Gravitating Membranes

Area of Science:

• Theoretical physics
• General relativity
• Compact object astrophysics

Background:

• Exotic compact objects are theoretical constructs that mimic black holes.
• Relativistic membranes are used to model the structure of these objects.
• Understanding their stability is crucial for their physical viability.

Purpose of the Study:

• To investigate the stability of generic relativistic membranes.
• To determine the instability criteria for exotic compact objects.
• To analyze specific models like gravastars and wormholes.

Main Methods:

• Analysis of warping mode instabilities.
• Examination of high wave number perturbations.
• Application of energy conditions to compact object models.

Main Results:

• Generic relativistic membranes with positive or negative in-plane pressure and surface density are unstable.
• Gravastars satisfying the weak energy condition are dynamically unstable.
• Thin-layer black hole mimickers require opposing signs for pressure and density to be stable.

Conclusions:

• The presence of in-plane pressure and surface density with the same sign leads to instability in relativistic membranes.
• Many exotic compact object models, including some gravastars, are dynamically unstable.
• Stability of black hole mimickers depends critically on the relationship between pressure and density.