[Paper Review] Clouds of string in $4D$ novel Einstein-Gauss-Bonnet black holes

Dharm Veer Singh, Sushant G. Ghosh+1 more|arXiv (Cornell University)|Mar 31, 2020

Black Holes and Theoretical Physics3 citations

TL;DR

This paper presents an exact charged black hole solution in novel 4D Einstein-Gauss-Bonnet gravity coupled to clouds of string, deriving corrected thermodynamic quantities. Unlike entropy, mass, temperature, and free energy are modified by the string cloud, while the Bekenstein-Hawking area law acquires a logarithmic correction; the black hole exhibits thermodynamic stability below a critical radius due to positive heat capacity and negative free energy.

ABSTRACT

Recently it has been shown that the Einstein-Gauss-Bonnet (EGB) gravity, by rescaling the coupling constant as $\alpha/(D-4)$ and taking the limit $D ightarrow 4$ at the level of the equations of motion, becomes nontrivially ghost-free in $4D$ - namely the novel $4D$ EGB gravity. We present an exact charged black hole solution to the theory surrounded by clouds of string (CS) and also analyze their thermodynamic properties to calculate exact expressions for the black hole mass, temperature, and entropy. Owing to the corrected black hole due to the background CS, the thermodynamic quantities have also been corrected except for the entropy, which remains unaffected by a CS background. However, as a result of the novel $4D$ EGB theory, the Bekenstein-Hawking area law turns out to be corrected by a logarithmic area term. The heat capacity $C_+$ diverges at a critical radius $r=r_C$, where incidentally the temperature has a maximum, and the Hawking-Page transitions even in absence of the cosmological term and $C_+ > 0$ for $r_+ < r_C$ allowing the black hole to become thermodynamically stable. In addition, the smaller black holes are globally preferred with negative free energy $F_+<0$. Our solution can also be identified as a $4D$ monopole-charged EGB black hole. We regain results of spherically symmetric black hole solutions of general relativity and that of novel $4D$ EGB, respectively, in the limits $\alpha o 0$ and $a=0$.

Motivation & Objective

• To extend novel 4D Einstein-Gauss-Bonnet gravity to include charged black hole solutions coupled to clouds of string.
• To investigate how the presence of string clouds modifies black hole thermodynamics in the absence of a cosmological constant.
• To analyze thermodynamic stability through heat capacity and free energy, identifying critical behavior at a specific radius.
• To recover general relativity and standard 4D EGB results in appropriate limits (α→0 and α=0).

Proposed method

• Rescale the Gauss-Bonnet coupling constant as α/(D−4) and take the D→4 limit at the level of equations of motion to define the novel 4D EGB theory.
• Construct an exact solution for a charged black hole in this 4D EGB framework with a cloud of string background.
• Derive expressions for black hole mass, temperature, entropy, and free energy using the modified metric and field equations.
• Analyze thermodynamic stability by computing heat capacity C₊ and free energy F₊, identifying a critical radius r_C where C₊ diverges.
• Apply the first law of thermodynamics and calculate corrections to the Bekenstein-Hawking area law, finding a logarithmic term.
• Verify consistency by recovering general relativity and standard 4D EGB solutions in the limits α→0 and α=0.

Experimental results

Research questions

• RQ1 How does the presence of a cloud of string background affect the thermodynamic quantities of a charged black hole in novel 4D Einstein-Gauss-Bonnet gravity?
• RQ2 Does the Bekenstein-Hawking area law remain valid, or is it corrected by quantum effects encoded in the 4D EGB framework?
• RQ3 At what critical radius does the heat capacity diverge, and what does this imply for thermodynamic stability?
• RQ4 Can Hawking-Page-like transitions occur in the absence of a cosmological constant in this 4D EGB model?
• RQ5 How do the free energy and heat capacity determine the global thermodynamic preference of small black holes?

Key findings

• The black hole mass, temperature, and free energy are corrected by the string cloud background, while entropy remains unaltered by this background.
• The Bekenstein-Hawking area law is corrected by a logarithmic term due to the novel 4D EGB gravity, indicating quantum corrections to black hole entropy.
• The heat capacity C₊ diverges at a critical radius r_C, where the temperature reaches a maximum, signaling a phase transition point.
• For r₊ < r_C, C₊ > 0, indicating thermodynamic stability of small black holes in this model.
• The free energy F₊ is negative for small black holes, indicating global thermodynamic preference for these configurations.
• The solution reduces to general relativity and standard 4D EGB black holes in the limits α→0 and α=0, respectively, confirming consistency with known theories.