  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.
