[Paper Review] Instability of small AdS black holes in sixth-order gravity

Yun Soo Myung, De-Cheng Zou|arXiv (Cornell University)|Apr 6, 2018

Black Holes and Theoretical Physics20 references3 citations

TL;DR

This paper investigates the instability of small anti-de Sitter (AdS) black holes in sixth-order gravity, which combines Ricci cubic gravity and Lee-Wick terms. By solving a Lichnerowicz-type linearized equation, it identifies unstable Ricci tensor perturbations in small AdS black holes within Ricci cubic gravity, confirms the correlated stability conjecture via thermodynamic analysis, and discovers a new non-AdS black hole solution using a static eigenfunction of the Lichnerowicz operator.

ABSTRACT

We investigate the stability analysis of AdS black holes in the higher dimensional sixth-order gravity. This gravity is composed of Ricci cubic gravity and Lee-Wick term. It indicates that the Ricci tensor perturbations exhibit unstable modes for small AdS black holes in Ricci cubic gravity by solving the Lichnerowicz-type linearized equation. We show that the correlated stability conjecture holds for the AdS black hole by computing all thermodynamic quantities in Ricci cubic gravity. Furthermore, we find a newly non-AdS black hole in Ricci cubic gravity by making use of a static eigenfunction of the Lichnerowicz operator.

Motivation & Objective

• To analyze the stability of small anti-de Sitter (AdS) black holes in higher-derivative gravity theories.
• To investigate whether the correlated stability conjecture holds in Ricci cubic gravity by computing thermodynamic quantities.
• To explore the existence of new black hole solutions beyond AdS by leveraging the Lichnerowicz operator's eigenfunctions.
• To determine the role of Ricci tensor perturbations in triggering instability in small AdS black holes.

Proposed method

• Solving a Lichnerowicz-type linearized equation to analyze Ricci tensor perturbations in small AdS black holes.
• Applying the Lichnerowicz operator to identify unstable modes in the gravitational sector of Ricci cubic gravity.
• Computing thermodynamic quantities such as mass, entropy, and specific heat to test the correlated stability conjecture.
• Using a static eigenfunction of the Lichnerowicz operator to construct a new non-AdS black hole solution.
• Combining Ricci cubic gravity with the Lee-Wick term to model sixth-order gravity and assess its implications on black hole stability.

Experimental results

Research questions

• RQ1 Do small AdS black holes in Ricci cubic gravity exhibit unstable Ricci tensor perturbations?
• RQ2 Is the correlated stability conjecture valid for AdS black holes in Ricci cubic gravity based on thermodynamic analysis?
• RQ3 Can a new non-AdS black hole solution be derived from the static eigenfunctions of the Lichnerowicz operator in Ricci cubic gravity?
• RQ4 How does the inclusion of the Lee-Wick term in sixth-order gravity affect the stability of small AdS black holes?

Key findings

• Unstable Ricci tensor perturbations are found in small AdS black holes within Ricci cubic gravity through solution of the Lichnerowicz-type linearized equation.
• The correlated stability conjecture is confirmed for AdS black holes in Ricci cubic gravity via computation of thermodynamic quantities.
• A new non-AdS black hole solution is discovered by utilizing a static eigenfunction of the Lichnerowicz operator in Ricci cubic gravity.
• The instability of small AdS black holes is primarily driven by Ricci tensor modes, indicating a breakdown of classical stability in this regime.