Coupling Constants as Conserved Charges in Black Hole Thermodynamics

Area of Science:

• Theoretical physics
• Gravitational physics
• Black hole thermodynamics

Background:

• The Smarr formula for black holes is essential for understanding their thermodynamics.
• Coupling constants in gravity theories are typically fixed parameters, limiting their role in solutions.
• Existing methods do not adequately incorporate these constants into black hole thermodynamics.

Purpose of the Study:

• To develop a robust method for treating coupling constants as free parameters in gravity theories.
• To systematically extend the first law and Smarr formula for black holes.
• To apply the method to a quadratic gravity theory as a case study.

Main Methods:

• Introducing auxiliary scalar and gauge fields for each coupling constant.
• Identifying couplings as conserved charges of implemented gauge symmetry.
• Defining conjugate chemical potentials as electric potentials on the black hole horizon.

Main Results:

• A generalized framework for black hole thermodynamics that incorporates variable coupling constants.
• The derived conserved charges and their conjugate potentials systematically extend the first law and Smarr formula.
• Successful application to a quadratic gravity theory, demonstrating the method's efficacy.

Conclusions:

• The presented method provides a powerful tool for analyzing black hole thermodynamics in generic gravity theories.
• Treating coupling constants as dynamical parameters offers new insights into black hole solutions.
• This approach unifies the treatment of constants and variables in gravitational theories.