Analytic Discrete Self-Similar Solutions of Einstein-Klein-Gordon at Large D

Area of Science:

• Theoretical Physics
• General Relativity
• Quantum Field Theory

Background:

• Critical collapse phenomena are governed by discretely self-similar solutions.
• These solutions have historically been accessible only through numerical simulations since Choptuik's work.

Purpose of the Study:

• To construct an infinite family of analytic solutions for critical collapse.
• To explore the behavior of Einstein-massless-Klein-Gordon equations in the large spacetime dimension limit.
• To compare analytic findings with existing numerical solutions.

Main Methods:

• Application of the large-D expansion (where D is the spacetime dimension).
• Simplification of field equations in the large-D limit.
• Encoding solutions in a single time-dependent function.

Main Results:

• An infinite family of analytic solutions was constructed.
• The field equations were drastically simplified in the large-D limit.
• Comparison with finite-D numerical solutions revealed universal features and large-D specific effects.

Conclusions:

• The large-D expansion provides a powerful analytical tool for studying critical collapse.
• This approach offers new insights into the structure of self-similar solutions.
• The study bridges the gap between numerical and analytical understanding of critical phenomena.