[Paper Review] 4D Einstein-Gauss-Bonnet AdS Black Holes as Heat Engine

B. Eslam Panah, Kh. Jafarzade|arXiv (Cornell University)|Apr 8, 2020

Black Holes and Theoretical Physics11 citations

TL;DR

This paper investigates 4D Einstein-Gauss-Bonnet AdS black holes as heat engines, analyzing how electric and magnetic charges, along with the Gauss-Bonnet coupling, influence thermodynamic efficiency in a rectangular cycle. It finds that both charge and coupling enhance efficiency, and the ratio of engine to Carnot efficiency remains below one, consistent with the second law of thermodynamics.

ABSTRACT

Motivated by studying black hole thermodynamics in a novel theory, known as 4D Einstein Gauss-Bonnet gravity. We perform a study of holographic heat engines of AdS black holes in such a theory, obtaining efficiency of a rectangular engine cycle. First, we consider the charged AdS black hole as the working substance and analyze the effective roles of electric charge and Gauss-Bonnet coupling on the heat engine efficiency. We find that they can improve the heat engine efficiency. Then, we study the heat engine of Bardeen AdS black hole and show that how magnetic charge and Gauss-Bonnet parameter affect the heat engine efficiency. Finally, by comparing engine efficiency with the Carnot efficiency, we indicate that the ratio $\frac{\eta}{\eta_{c}}$ is less than one all the time which is consistent with the thermodynamic second law.

Motivation & Objective

• To explore black hole thermodynamics in 4D Einstein-Gauss-Bonnet gravity, a novel theory with potential implications for quantum gravity.
• To investigate the feasibility and efficiency of holographic heat engines using AdS black holes as working substances in this theory.
• To analyze the influence of electric and magnetic charges, as well as the Gauss-Bonnet coupling parameter, on engine performance.
• To compare the obtained engine efficiency with the Carnot efficiency to validate thermodynamic consistency.

Proposed method

• Modeling charged AdS black holes in 4D Einstein-Gauss-Bonnet gravity as working substances in a rectangular thermodynamic cycle.
• Deriving thermodynamic quantities such as heat input, work output, and efficiency using the first law of thermodynamics and black hole parameters.
• Introducing the Gauss-Bonnet coupling and electric/magnetic charges as control parameters in the efficiency analysis.
• Computing the efficiency ratio relative to Carnot efficiency to test compliance with the second law of thermodynamics.
• Using analytical expressions for black hole entropy and temperature in the 4D Einstein-Gauss-Bonnet framework.
• Applying standard heat engine formalism to AdS black holes, treating them as systems undergoing cyclic processes.

Experimental results

Research questions

• RQ1 How does the Gauss-Bonnet coupling affect the efficiency of a heat engine based on charged AdS black holes in 4D Einstein-Gauss-Bonnet gravity?
• RQ2 What role does electric charge play in enhancing or diminishing the thermodynamic efficiency of such a heat engine?
• RQ3 How do magnetic charges influence the performance of a heat engine in the Bardeen AdS black hole model within this theory?
• RQ4 Is the efficiency of the 4D Einstein-Gauss-Bonnet black hole heat engine bounded by the Carnot limit, as required by the second law of thermodynamics?

Key findings

• The Gauss-Bonnet coupling and electric charge both contribute to improving the heat engine efficiency in the charged AdS black hole model.
• Magnetic charge and the Gauss-Bonnet parameter similarly enhance the efficiency in the Bardeen AdS black hole heat engine scenario.
• The ratio of the engine efficiency to the Carnot efficiency remains strictly less than one across all parameter regimes.
• This consistent sub-Carnot performance confirms that the second law of thermodynamics is preserved in the 4D Einstein-Gauss-Bonnet black hole heat engine framework.
• The results demonstrate that 4D Einstein-Gauss-Bonnet gravity supports viable thermodynamic cycles with physically consistent efficiency bounds.
• The study establishes a new class of holographic heat engines in a modified gravity theory with tunable efficiency via coupling and charge parameters.