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Resonant Dynamics and the Instability of Anti-de Sitter Spacetime
Piotr Bizoń1, Maciej Maliborski2, Andrzej Rostworowski1
1Institute of Physics, Jagiellonian University, Kraków, Poland.
Physical Review Letters
|September 5, 2015
Summary
Small perturbations of five-dimensional anti-de Sitter (AdS) spacetime with a negative cosmological constant can develop an oscillatory singularity. This finding suggests potential instability in AdS spacetimes under small disturbances.
Area of Science:
- Theoretical Physics
- General Relativity
- Cosmology
Background:
- Investigating the stability of anti-de Sitter (AdS) spacetime is crucial for understanding gravitational theories.
- Five-dimensional spacetimes with negative cosmological constants are relevant in string theory and quantum gravity.
- Einstein-massless-scalar field equations describe fundamental interactions in curved spacetimes.
Purpose of the Study:
- To analyze the behavior of small perturbations in five-dimensional AdS spacetime.
- To explore the implications of a negative cosmological constant on spacetime stability.
- To investigate the applicability of the resonant approximation method to gravitational field equations.
Main Methods:
- Solving spherically symmetric Einstein-massless-scalar field equations in five dimensions.
- Applying the resonant approximation to analyze the evolution of small perturbations.
- Studying the behavior of solutions for typical initial data.
Main Results:
- The resonant system solution develops an oscillatory singularity in finite time for typical initial data.
- This singularity formation indicates a breakdown of the smooth spacetime evolution.
- The findings are derived from the analysis of Einstein-massless-scalar field dynamics.
Conclusions:
- The development of an oscillatory singularity suggests that five-dimensional AdS spacetime may be unstable.
- This instability could arise even under arbitrarily small perturbations.
- The resonant approximation provides a valuable tool for probing spacetime stability.
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