Lagrangian Partition Functions Subject to a Fixed Spatial Volume Constraint in the Lovelock Theory

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• The quantum gravity partition function is crucial for understanding spacetime at quantum scales.
• Generalizing Einstein gravity to Lovelock gravity offers insights into more complex gravitational theories.

Purpose of the Study:

• To evaluate the quantum gravity partition function in Lovelock gravity.
• To generalize existing results from Einstein gravity.
• To analyze the implications for Hilbert space dimensions and black hole entropy.

Main Methods:

• Analysis of the quantum gravity partition function for a fixed proper volume.
• Identification and characterization of sphere saddle metrics.
• Comparison of results with those from Einstein gravity.

Main Results:

• Sphere saddle metrics were found for the partition function in Lovelock theory.
• These stationary points mirror those in Einstein gravity.
• The logarithm of the partition function (Z) relates to Bekenstein-Hawking and Wald entropies for different cosmological constants.
• Zeroth-order phase transitions between vacua were identified, a novel phenomenon in Lovelock gravity.

Conclusions:

• Lovelock gravity exhibits unique features, including distinct phase transitions, not present in Einstein gravity.
• The study provides a deeper understanding of quantum gravity partition functions and their connection to black hole thermodynamics.