[Paper Review] Thermodynamics with pressure and volume of 4D Gauss-Bonnet AdS Black Holes under the scalar field

Benrong Mu, Jing Liang+1 more|arXiv (Cornell University)|Oct 31, 2020

Black Holes and Theoretical Physics69 references8 citations

TL;DR

This paper investigates the thermodynamics and overcharging of 4D Gauss-Bonnet AdS black holes under scalar field scattering in both normal and extended phase spaces. It finds that while the first law holds in both cases, the second law is indefinite in the extended phase space, and near-extremal black holes can be overcharged, rendering the weak cosmic censorship conjecture invalid under certain conditions.

ABSTRACT

By using the scattering of a scalar field, we discuss the thermodynamics and overcharging problem in a 4D Gauss-Bonnet AdS black hole in both the normal phase space and extended phase space. In the normal phase space, where the cosmological constant and Gauss-Bonnet parameter are fixed, the first law and the second law of thermodynamics are valid. In addiction, the black hole cannot be overcharged and the weak cosmic censorship conjecture is valid. In the extended phase space, where the cosmological constant and Gauss-Bonnet parameter are treated as the thermodynamic variables, the first law is still valid. However, the second law is indefinite. Moreover, after the scattering of the scalar field, the extremal black hole cannot be overcharged and the near-extremal black hole can be overcharged.

Motivation & Objective

• To analyze the thermodynamic behavior of 4D Gauss-Bonnet AdS black holes under scalar field scattering.
• To test the validity of the first and second laws of thermodynamics in both normal and extended phase spaces.
• To investigate the overcharging problem and the status of the weak cosmic censorship conjecture (WCCC) in different thermodynamic frameworks.
• To compare results with RN-AdS black holes and clarify the role of pressure, volume, and Gauss-Bonnet coupling in black hole thermodynamics.

Proposed method

• Uses scalar field scattering as a Gedanken experiment to probe black hole evolution and thermodynamic stability.
• Applies the first law of thermodynamics in both normal phase space (fixed cosmological constant and Gauss-Bonnet parameter) and extended phase space (where Λ and α are thermodynamic variables).
• Defines thermodynamic pressure as P = -Λ/(8π) and volume as V = (∂M/∂P)_{S,Q}, enabling PdV work terms in the first law.
• Evaluates entropy and energy variations via infinitesimal time evolution under scalar field interaction.
• Analyzes the extremality condition and horizon structure to determine overcharging potential.
• Compares results with RN-AdS black holes to highlight differences due to Gauss-Bonnet gravity in four dimensions.

Experimental results

Research questions

• RQ1 Does the first law of thermodynamics hold for 4D Gauss-Bonnet AdS black holes under scalar field scattering in both normal and extended phase spaces?
• RQ2 Is the second law of thermodynamics valid in the extended phase space, where pressure and volume are dynamical variables?
• RQ3 Can the black hole be overcharged via scalar field absorption, and does this violate the weak cosmic censorship conjecture?
• RQ4 How does the behavior of extremal and near-extremal black holes differ in the extended phase space compared to the normal phase space?
• RQ5 What is the role of the Gauss-Bonnet parameter α in modifying thermodynamic laws and overcharging dynamics?

Key findings

• The first law of thermodynamics is satisfied in both normal and extended phase spaces after scalar field scattering.
• The second law of thermodynamics is valid in the normal phase space but indefinite in the extended phase space.
• Extremal 4D Gauss-Bonnet AdS black holes cannot be overcharged in either phase space, preserving the weak cosmic censorship conjecture.
• Near-extremal black holes can be overcharged in the extended phase space, indicating that the weak cosmic censorship conjecture is not universally valid under these conditions.
• The thermodynamic behavior of the 4D Gauss-Bonnet AdS black hole differs significantly from RN-AdS black holes in the extended phase space, particularly in the validity of the second law and overcharging potential.
• The first law in the extended phase space includes an additional term involving dα, reflecting the dependence of mass on the Gauss-Bonnet coupling parameter: dM = TdS + φdQ + VdP + [1/(2r+) + 2πT(1 - 2ln(r+/√α))]dα.