Vacuum states near black holes
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Quantum Vacuum States Near Black Holes: Hartle-Hawking, Boulware, and Unruh Vacua
The study of quantum vacuum states near black holes reveals that different vacua are relevant depending on the region and the physical scenario. Near the event horizon of non-rotating black holes, the quantum vacuum closely resembles the Hartle-Hawking vacuum, which describes a thermal equilibrium state with Hawking radiation. Far from the horizon, the vacuum state transitions to the Boulware vacuum, which is empty at infinity but becomes singular at the horizon, highlighting the importance of the observer's location and the black hole's properties in defining the vacuum state 19. In the context of black holes formed by gravitational collapse, the Unruh vacuum is often used, as it matches the physical "in-vacuum" state near the horizon and captures the process of black hole evaporation .
Vacuum Decay and Metastability Around Black Holes
Black holes can influence the stability of vacuum states in quantum field theory. Both non-rotating and spinning black holes can act as catalysts for vacuum decay, potentially shortening the lifetime of metastable vacua such as the electroweak vacuum. The presence of a black hole can enhance the probability of vacuum bubble nucleation, especially for evaporating black holes, which may have significant implications for cosmology 368. However, the spin of a black hole tends to suppress the vacuum decay rate compared to non-spinning cases, and near-extremal black holes can further stabilize false vacuum states .
Thermal Effects and False Vacuum Decay in Black Hole Environments
When black holes are in thermal equilibrium with their surroundings (the Hartle-Hawking state), the decay of false vacuum states is dominated by static, time-independent solutions rather than the time-dependent tunneling processes seen in flat spacetime at low temperatures. This behavior is observed across various types of black holes, including Schwarzschild, Reissner-Nordström, and higher-dimensional cases, and is consistent with the periodicity set by the black hole's Hawking temperature 456.
Quantum Effects and Vacuum Polarization Near Black Hole Horizons
Quantum fields near black hole horizons exhibit unique polarization effects. For charged black holes, the vacuum polarization can induce currents near the inner horizon, with the direction and magnitude of these currents depending on the black hole's parameters and the quantum state of the field. Notably, close to extremality, the inner horizon tends to discharge, and quantum effects dominate over classical predictions, leading to strong, state-independent current blow-ups . Additionally, quantum fermion fields on charged black holes can exhibit superradiant-like effects, resulting in nonthermal particle fluxes and energy loss, with the interpretation of these phenomena depending on the choice of vacuum state .
Special Cases: AdS2 Black Holes and Vacuum Ambiguities
In the context of AdS2 black holes, several distinct vacuum states can be constructed, including the Boulware, Hartle-Hawking, and SL(2) invariant vacua. These vacua differ in their Green functions, stress tensors, and entanglement entropy, with quantum corrections leading to nonzero entanglement entropy and violations of finite-temperature decoupling. The choice of vacuum state also affects the boundary quantum mechanics and the physical interpretation of correlation functions .
Conclusion
The nature of quantum vacuum states near black holes is highly sensitive to the black hole's properties, the observer's location, and the physical context. Different vacua—such as the Hartle-Hawking, Boulware, and Unruh states—play crucial roles in describing the quantum field behavior near and far from the horizon. Black holes can catalyze or suppress vacuum decay, and quantum effects near horizons can lead to novel phenomena like vacuum polarization and superradiance. The study of these vacua is essential for understanding both fundamental quantum field theory in curved spacetime and the stability of our universe.
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On thermal false vacuum decay around black holes
The Euclidean solution for the decay of the Hartle-Hawking vacuum around black holes is always static, unlike in flat spacetime, where time-dependent solutions are possible.
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