Double Copy Root of Hawking Thermality

Area of Science:

• Theoretical Physics
• Quantum Gravity
• High-Energy Physics

Background:

• Hawking radiation describes particle emission from black holes.
• The double copy prescription relates gravity to gauge theories.
• Null shell collapse offers a simplified model for Hawking radiation studies.

Purpose of the Study:

• To derive the Hawking radiation spectrum from a collapsing null shell.
• To analyze the thermal properties of the radiation in the context of gauge theory.
• To explore the duality between gravitational and gauge theory descriptions.

Main Methods:

• Utilizing the double copy method to relate gauge theory to gravity.
• Analyzing the non-Abelian Yang-Mills theory underlying the process.
• Considering the SU(N_{c}) gauge theory in the large N_{c} limit.
• Modeling the color phase space density using random matrix theory (Wigner semicircle).

Main Results:

• The Hawking radiation spectrum is demonstrated to be thermal in the color charge eigenvalue (λ), not energy.
• The differential spectrum (dN/dλ) is a product of a Planck-like factor and the color phase space density.
• Apparent energy thermality in gravity is shown to be dual to charge thermality in non-Abelian gauge theory.

Conclusions:

• The study reveals a fundamental connection between thermal properties in gravity and gauge theory.
• The non-Abelian Yang-Mills theory provides a direct explanation for the thermal spectrum of Hawking radiation.
• This work deepens the understanding of the double copy and its implications for quantum gravity.