arXiv:2508.13221v1 Announce Type: new
Abstract: We present the most general class of charged black hole solutions in third-order Lovelock gravity within even-dimensional spacetimes in the presence of an electromagnetic field. These solutions feature nonconstant-curvature horizons that affect geometry when n>=8. The near-origin behavior of the metric reveals a timelike singularity for electrically charged cases, in contrast to the spacelike singularity found in the uncharged case. We investigate thermodynamic stability in both the grand canonical and canonical ensembles. In the grand canonical ensemble, stability is determined by the positivity of both the Hessian determinant and the temperature. In the canonical ensemble, the sign of the heat capacity governs stability. We identify both first- and second-order phase transitions, including a van der Waals-like behavior characterized by instability at intermediate black hole sizes. Our results reveal a rich phase structure influenced by Lovelock corrections and electromagnetic fields, and demonstrate how conserved charges affect black hole evaporation and stabilization.
Conclusions
The study of charged black hole solutions in third-order Lovelock gravity within even-dimensional spacetimes has revealed a rich phase structure influenced by Lovelock corrections and electromagnetic fields. These solutions feature nonconstant-curvature horizons that impact geometry in significant ways, particularly when n>=8. The near-origin behavior of the metric shows a timelike singularity for electrically charged cases, unlike the spacelike singularity seen in uncharged scenarios. Thermodynamic stability in both the grand canonical and canonical ensembles depends on various factors, including the Hessian determinant, temperature, and heat capacity. First- and second-order phase transitions, as well as van der Waals-like behavior, have been identified, highlighting the complexity of black hole systems under these conditions.
Future Roadmap
- Explore further the implications of Lovelock corrections on black hole thermodynamics
- Investigate the interplay between electromagnetic fields and black hole stabilization mechanisms
- Study the effects of conserved charges on black hole evaporation processes
- Develop numerical simulations to analyze the behavior of black hole solutions in third-order Lovelock gravity
- Consider applications of these findings to other areas of theoretical physics, such as string theory and holography
Potential Challenges
- Complexity of mathematical frameworks in higher-order gravity theories
- Computational limitations for analyzing black hole solutions in multidimensional spacetimes
- Difficulty in extrapolating results to real-world observational data
Opportunities on the Horizon
- Enhanced understanding of the thermodynamic properties of charged black holes in exotic gravity theories
- Potential insights into fundamental aspects of black hole physics and gravitational interactions
- Implications for the development of novel theoretical approaches to studying complex spacetime geometries