Conserved charges for gravity with locally anti-de sitter asymptotics

Area of Science:

• Theoretical Physics
• General Relativity
• Quantum Gravity

Background:

• Conserved charges in gravity are crucial for understanding spacetime dynamics.
• Existing methods often require a reference background, limiting applicability.
• Anti-de Sitter (AdS) asymptotic geometries present unique challenges for charge definitions.

Purpose of the Study:

• To propose a new, background-independent formula for conserved charges in 3+1 gravity.
• To apply this formula to spacetimes with local anti-de Sitter asymptotic geometry.
• To investigate the implications for mass, angular momentum, and specific spacetime geometries.

Main Methods:

• Derivation of a new formula for conserved charges.
• Extremization of the gravitational action with a specific boundary term (Euler density).
• Association of Noether charges with asymptotic Killing vectors.

Main Results:

• A new formula for conserved charges in 3+1 gravity for AdS asymptotic spacetimes is presented.
• The Euler density with a fixed weight factor is identified as the necessary boundary term for action extremization.
• Mass and angular momentum are derived as Noether charges without needing a reference background.
• Spacetimes with negative constant curvature are shown to have vanishing Noether charges.

Conclusions:

• The proposed formula provides a consistent and background-independent method for calculating conserved charges in specific gravitational contexts.
• The results offer new insights into the nature of mass and angular momentum in spacetimes with AdS asymptotics.
• The vanishing of charges for negative curvature spacetimes is a significant consequence of this formulation.