We discuss the macroscopic quantum tunneling from the black hole to the white hole of the same mass. Previous calculations in [G. E. Volovik, Universe 6, 133 (2020)] demonstrated that the probability of the tunneling is p ∝exp(−2SBH), where SBH is the entropy of the Schwarzschild black hole. This in particular suggests that the entropy of the white hole is with minus sign the entropy of the black hole, SWH(M) = −SBH(M) = −A/(4G). Here, we use a different way of calculations. We consider three different types of the hole objects: black hole, white hole and the fully static intermediate state. The probability of tunneling transitions between these three states is found using singularities in the coordinate transformations between these objects. The black and white holes are described by the Painleve–Gullstrand coordinates with opposite shift vectors, while the intermediate state is described by the static Schwarzschild coordinates. The singularities in the coordinate transformations lead to the imaginary part in the action, which determines the tunneling exponent. For the white hole the same negative entropy is obtained, while the intermediate state — the fully static hole — has zero entropy. This procedure is extended to the Reissner–Nordström black hole and to its white and static partners, and also to the entropy and temperature of the de Sitter Universe.

中文翻译：

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通过中间静态从黑洞到白洞

我们讨论了从黑洞到相同质量的白洞的宏观量子隧穿。[GE Volovik,宇宙 6, 133 (2020)] 证明了隧道的概率是p ∝经验(-2小号BH)， 在哪里小号BH是史瓦西黑洞的熵。这特别表明，白洞的熵与黑洞的熵为负号，小号WH(米) = -小号BH(米) = -一种/(4G). 在这里，我们使用不同的计算方式。我们考虑三种不同类型的空洞对象：黑洞、白洞和完全静止的中间状态。使用这些对象之间的坐标变换中的奇点可以找到这三个状态之间的隧道转换的概率。黑洞和白洞由具有相反位移向量的 Painleve-Gullstrand 坐标描述，而中间状态由静态 Schwarzschild 坐标描述。坐标变换中的奇点导致作用中的虚部，这决定了隧道指数。对于白洞，获得了相同的负熵，而中间状态——完全静态的洞——的熵为零。