Correspondence between Thermal and Quantum Vacuum Transitions around Horizons

Recently, there are comparable revised interests in bubble nucleation seeded by black holes. However, it is debated in the literature that whether one shall interpret a static bounce solution in the Euclidean Schwarzschild spacetime (with periodic Euclidean Schwarzschild time) as describing a false vacuum decay at zero temperature or at finite temperature. In this paper, we show a correspondence that the static bounce solution describes either a thermal transition of vacuum in the static region outside of a Schwarzschild black hole or a quantum transition in a maximally extended Kruskal-Szekeres spacetime, corresponding to the viewpoint of the external static observers or the freely falling observers, respectively. The Matsubara modes in the thermal interpretation can be mapped to the circular harmonic modes from an $O(2)$ symmetry in the tunneling interpretation. The complementary tunneling interpretation must be given in the Kruskal-Szekeres spacetime because of the so-called thermofield dynamics. This correspondence is general for bubble nucleation around horizons. We propose a new paradox related to black holes as a consequence of this correspondence.Comment: 26 pages; v2: typos corrected; v3: references added, discussion on AdS black holes added, to match the published version; v4(v5): Ref [37] updated, footnote [10] added v6: two typos correcte

Logarithmic divergent friction on ultrarelativistic bubble walls

We calculate the friction experienced by ultrarelativistic bubble walls resulting from the $1 \rightarrow 2$ light-to-heavy transition process, with finite-wall-width effects fully taken into account. In this process, the light particle is excited from the order-parameter scalar field, while the two heavy particles are excitations of a dark matter scalar field. Unlike earlier estimates suggesting a friction scaling as $\gamma_w^0$, where $\gamma_w$ represents the Lorentz factor of the wall velocity, our more precise numerical analysis reveals a logarithmic dependence of the friction on $\gamma_w$. We offer a numerical fit to capture this frictional pressure accurately. Our analysis verifies that the friction stemming from the $1 \rightarrow 2$ light-to-heavy transition is typically much smaller than the friction from the $1 \rightarrow 1$ transmission of the dark matter particles.Comment: 21 pages, 6 figure