Macroscopic quantum tunneling: from quantum vortices to black holes and Universe

The paper has been prepared for the JETP issue, dedicated to the 95th anniversary of the birth of E.I. Rashba. E. Rashba stood at the origins of macroscopic quantum tunneling together with his colleagues from the Landau Institute S.V. Iordansky and A.M. Finkelshtein. They pave the way for studying macroscopic quantum tunneling in various systems. In this paper, this approach is extended to cosmological objects such as a black hole and de Sitter Universe. In particular, this allowed to calculate the entropy of Reissner-Nordstr\"om (RN) black hole with two horizons and the corresponding temperature of the thermal Hawking radiation. Several different approaches were used: the method of semiclassical tunneling for calculation of the Hawking temperature; the cotunneling mechanism -- the coherent sequence of tunneling at two horizons, each determined by the corresponding Hawking temperature; the method of singular coordinate transformations for calculations of macroscopic quantum tunneling from the RN black hole to the RN white hole; the method of the adiabatic change of the fine structure constant for the adiabatic transformation from the RN black hole to the Schwarzschild black hole; etc.