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Thermodynamics of Asymptotically Conical Geometries
Mirjam Cvetič1, Gary W Gibbons2, Zain H Saleem3
1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia.
Physical Review Letters
|July 22, 2015
Summary
This study explores thermodynamic properties of subtracted geometries, confirming mass and angular momentum calculations and demonstrating the validity of the Smarr formula and the first law of thermodynamics.
Area of Science:
- Theoretical Physics
- Thermodynamics
- General Relativity
Background:
- Asymptotically conical geometries present unique challenges in defining physical properties.
- Previous methods for calculating mass and angular momentum in these spacetimes lacked unified approaches.
Purpose of the Study:
- To investigate the thermodynamical properties of subtracted geometries.
- To establish a consistent method for deriving mass and angular momentum.
- To verify fundamental thermodynamic relations and propose new inequalities.
Main Methods:
- Utilizing the regulated Komar integral for mass and angular momentum derivation.
- Applying the Hawking-Horowitz prescription for comparison.
- Calculating asymptotic charges to verify thermodynamic laws.
Main Results:
- Equivalence shown between Komar integral and Hawking-Horowitz methods for mass and angular momentum.
- Smarr formula and the first law of thermodynamics are confirmed to hold.
- An analog of the Christodulou-Ruffini inequality is proposed.
Conclusions:
- The study provides a robust framework for analyzing thermodynamic properties of subtracted geometries.
- The findings are generalizable to other asymptotically conical spacetimes.
- This work contributes to a deeper understanding of black hole thermodynamics and related inequalities.
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