TY - JOUR

T1 - From black hole to white hole via the intermediate static state

AU - Volovik, G. E.

N1 - Funding Information:
I thank M. Zubkov and A. Zelnikov for discussions, T. Jacobson for criticism and S. Odintsov for attracting my attention to his papers on negative entropy and on the thermodynamically nonequivalent frames. This work has been supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694248).
Publisher Copyright:
© 2021 World Scientific Publishing Co. Pte Ltd. All rights reserved.

PY - 2021/6/7

Y1 - 2021/6/7

N2 - 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.

AB - 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.

KW - Black hole

KW - de Sitter.

KW - macroscopic quantum tunneling

KW - white hole

UR - http://www.scopus.com/inward/record.url?scp=85107659619&partnerID=8YFLogxK

U2 - 10.1142/S0217732321501170

DO - 10.1142/S0217732321501170

M3 - Article

AN - SCOPUS:85107659619

SN - 0217-7323

VL - 36

JO - MODERN PHYSICS LETTERS A

JF - MODERN PHYSICS LETTERS A

IS - 17

M1 - 2150117

ER -