Varying Newton constant and black hole to white hole quantum tunneling

Grigory Volovik*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
19 Downloads (Pure)


The thermodynamics of black holes is discussed for the case, when the Newton constant G is not a constant, but it is the thermodynamic variable. This gives for the first law of the Schwarzschild black hole thermodynamics: dSBH = −AdK + TdMBH, where the gravitational coupling K = 1/4G, M is the black hole mass, A is the area of horizon, and TBH is Hawking temperature. From this first law, it follows that the dimensionless quantity M2/K is the adiabatic invariant, which, in principle, can be quantized if to follow the Bekenstein conjecture. From the Euclidean action for the black hole it follows that K and A serve as dynamically conjugate variables. Using the Painleve-Gullstrand metric, which in condensed matter is known as acoustic metric, we calculate the quantum tunneling from the black hole to the white hole. The obtained tunneling exponent suggests that the temperature and entropy of the white hole are negative.

Original languageEnglish
Article number133
Pages (from-to)1-8
Number of pages8
Issue number9
Publication statusPublished - 1 Jan 2020
MoE publication typeA1 Journal article-refereed


  • Black hole
  • Negative entropy
  • Quantum tunneling
  • White hole


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