From Asymptotically Flat Gravity to Finite Causal Diamonds.

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• The soft sector of asymptotically flat gravity describes low-energy gravitational interactions.
• Understanding the phase space of gravity is crucial for unifying quantum mechanics and general relativity.

Purpose of the Study:

• To identify the phase space of the soft sector of asymptotically flat gravity in four spacetime dimensions.
• To establish a geometric interpretation for soft graviton and Goldstone modes.

Main Methods:

• Phase space identification between gravitational soft sector and causal diamond.
• Geometric interpretation of soft graviton and Goldstone modes.

Main Results:

• The phase space of the soft sector of gravity is identified with a spherically symmetric finite causal diamond in Minkowski spacetime.
• The leading soft graviton mode corresponds to the radial fluctuation of the causal diamond size.
• The Goldstone mode is related to both radial fluctuations and its symplectic partner.

Conclusions:

• Radial fluctuations of the causal diamond are linked to asymptotic transverse fluctuations via soft modes.
• This work provides a novel geometric perspective on gravitational soft modes.