Abstract
We investigate a vacuum decay around a spinning seed black hole by using the Israel junction condition and conclude that the spin of black hole would suppress a vacuum decay rate compared to that for a non-spinning case, provided that the surface of vacuum bubble has its ellipsoidal shape characterized by the Kerr geometry. We also find out that in the existence of a near-extremal black hole, a false vacuum state can be more stabilized than the case of the Coleman-de Luccia solution. A few necessary assumptions to carry the calculations are discussed.
Highlights
We assume that the typical shape of the nucleated vacuum bubble would be determined by the angular components of metric, which is a natural extension of the case of vacuum decays around Schwarzschild black hole (BH) [33]
We briefly review the vacuum decay around a non-rotating BH, pioneered by Hiscock [32]. He calculated the Euclidean action of a vacuum bubble surrounding a static BH at the origin by imposing the thin-wall approximation, and obtained two primary results that the Euclidean action of a vacuum bubble in the existence of the seed BH is always less than the corresponding Coleman-de Luccia (CDL) bubble action [4], and that there is the maximum mass of the seed BH, below which the classical Euclidean solution exists
The primary assumption is that a nucleated vacuum bubble has its thin wall, and so we used the Israel junction condition to investigate the Euclidean dynamics of the bubble
Summary
We briefly review the vacuum decay around a non-rotating BH, pioneered by Hiscock [32] He calculated the Euclidean action of a vacuum bubble surrounding a static BH at the origin by imposing the thin-wall approximation, and obtained two primary results that the Euclidean action of a vacuum bubble in the existence of the seed BH is always less than the corresponding Coleman-de Luccia (CDL) bubble action [4], and that there is the maximum mass of the seed BH, below which the classical Euclidean solution. Gregory et al [33], improved the calculation of the Euclidean action in the existence of the BH by properly taking the conical singularities into account, and it was shown that the resulting action can be larger than the CDL action only when the background spacetime is close to the Nariai limit [35, 36]. A brief review of the Euclidean solution around a BH, based on [32, 33], is presented
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