Lorentz violation and Hawking--Page metastability in Bumblebee--AdS gravity
arXiv:2411.06188
Abstract
The standard Hawking--Page description of AdS black holes, based on an on-shell Gibbs free-energy crossing, does not resolve the metastable black-hole branch or the barrier-mediated conversion between competing phases. We address this issue for neutral AdS black holes in Bumblebee gravity by constructing the generalized off-shell Gibbs free-energy landscape in the canonical ensemble at fixed effective pressure. We find analytically that the minimum temperature \(T_{\min}\) is independent of the Lorentz-violating parameter \(α\), whereas the Hawking--Page temperature \(T_{\mathrm{HP}}\) increases monotonically with \(α\). Consequently, the locally stable but globally disfavored large-black-hole window \(T_{\min}<T<T_{\mathrm{HP}}\) broadens with increasing \(α\). Within the off-shell framework, we derive closed-form expressions for the global-preference gap \(ΔG_{\mathrm{glob}}\), which measures the free-energy difference between the large-black-hole minimum and thermal AdS, and the barrier height \(ΔG_{\mathrm{bar}}\), which measures the separation between the small-black-hole saddle and the large-black-hole minimum. We recover the Schwarzschild--AdS limit as \(α\to0\). These results establish the off-shell free-energy landscape as a precise thermodynamic framework for diagnosing Lorentz-violating effects in AdS black-hole phase structure.
arXiv comment12 pages, 7 figures