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arXiv 2203.06155hep-thgr-qc
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关于de Sitter黑洞和约束瞬子的欧几里德Action

On the Euclidean Action of de Sitter Black Holes and Constrained Instantons

Edward K. Morvan, Jan Pieter van der Schaar, Manus R. Visser

摘要:

我们计算了Schwarzschild-de Sitter黑洞在壳层上的欧几里德作用量,并利用约束瞬子的形式考虑了它们在引力路径积分中的贡献.虽然欧几里得德西特黑洞几何具有一般质量的圆锥奇点,但它们的壳作用是有限的,并且与欧几里得时间周期无关,等于黑洞和宇宙视界熵之和的负。我们应用这个结果来计算一个非旋转的,中性的任意质量的黑洞在空的de Sitter空间中自发成核的概率,它分为一个常数和一个“非微扰”的贡献,后者对应于适当的鞍点瞬子在Nariai极限。我们还推测我们的结果的一些进一步的应用,最显着的潜在的非微扰修正德西特真空中的双折射。

英文摘要:

We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontaneously in empty de Sitter space, which separates into a constant and a "non-perturbative" contribution, the latter corresponding to the proper saddle-point instanton in the Nariai limit. We also speculate on some further applications of our results, most notably as potential non-perturbative corrections to correlators in the de Sitter vacuum.

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