Black Holes in Quasi-topological Gravity (1003.5357v2)

Abstract: We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and higher-dimensional CFT's. We also investigate the black hole solutions of this new gravity theory. Further we examine the equations of motion of quasi-topological gravity. While the full equations in a general background are fourth-order in derivatives, we show that the linearized equations describing gravitons propagating in the AdS vacua match precisely the second-order equations of Einstein gravity.

• The paper presents a new gravitational action with cubic curvature terms that yield tractable black hole solutions in higher dimensions.
• The paper demonstrates that in an AdS background, graviton propagation simplifies to second-order equations, maintaining consistency with Einstein gravity.
• The paper explores black hole thermodynamics, revealing that while temperature and energy are modified by higher curvature terms, entropy remains unchanged for planar horizons.

Overview of "Black Holes in Quasi-topological Gravity"

The paper "Black Holes in Quasi-topological Gravity" by Robert C. Myers and Brandon Robinson presents an exploration into extending the classical theory of gravity through the inclusion of higher-order curvature terms. This work focuses on analyzing black hole solutions within a framework enriched by curvature-cubed interactions, termed quasi-topological gravity. The analysis is set in the context of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, a prominent duality conjecture in theoretical physics.

Key Contributions

The authors propose a new gravitational action that encompasses cubic curvature terms to probe the dynamics of higher-dimensional CFTs. The paper delineates the construction of this gravitational action incorporating quasi-topological terms that facilitate the paper of new gravitational interactions. Unlike the well-known Gauss-Bonnet gravity, which involves only curvature-squared terms, quasi-topological gravity is designed to provide additional parameters, potentially enriching the landscape of dual CFT characteristics.

Notable Theoretical Insights

The paper demonstrates that black hole solutions in this framework exhibit intriguing stability and thermodynamic behavior:

1. Equation of Motion Simplicity: Despite the intricacy of the full fourth-order equations, the solutions for black holes remain tractable. The black hole solutions are determined by a single integration constant once the horizon's topology is specified, suggesting a form of Birkhoff's theorem in this extended context.
2. Graviton Propagation: The linearized equations describing gravitons exhibit a reduction to second-order equations when propagating in an AdS background. This unexpected simplification maintains the consistency with Einstein gravity predictions and has implications for holographic dual descriptions.
3. Thermodynamic Properties: The paper explores black hole thermodynamics in this new theory, showing how the temperature, entropy, and energy are impacted by quasi-topological terms. The analysis finds that higher curvature terms do not affect the entropy when considering planar horizons.

Implications and Future Directions

The implications of quasi-topological gravity extend beyond theoretical curiosities:

• AdS/CFT Correspondence: By enriching the gravitational side with cubic terms, the corresponding boundary CFTs can explore a broader range of physical behaviors, potentially informing new aspects of strongly coupled gauge theories.
• Stability and Causality: The paper raises questions about the stability and causality constraints inherent in such theories, but also indicates that the simplicity of the AdS gravitons might be key in preserving consistency across broad parameter ranges.
• Dimensional Extension: The framework established paves the way for exploring higher-order interactions, such as quartic or quintic in curvature, aligning with recent interests in extreme quantum gravity regimes potentially accessible in future cosmological or astrophysical observations.

Conclusion

This paper contributes significant extensions to gravitational theory, refining our tools to examine holographically dual quantum field theories under strong coupling. It sets a foundation not only for theoretical advancements in understanding quantum gravity but also for practical examinations of the structure of space-time at a fundamental level. Future research may expand on the robust mathematical frameworks presented here to further align with observational phenomena or explore the theoretical underpinnings of gravitational interactions at higher orders.