  In this work, starting by simple, approximate (quasi-classical) methods
presented in our previous works, we suggest a simple determination of the
(logarithmic) corrections of (Schwarzschild) black hole entropy "without
knowing the details of quantum gravity"(Fursaev). Namely, in our previous works
we demonstrated that all well-known important thermodynamical characteristics
of the black hole (Bekenstein-Hawking entropy, Bekenstein entropy/surface
quantization and Hawking temperature) can be effectively reproduced starting by
simple supposition that black hole horizon circumference holds integer number
of reduced Compton wave lengths corresponding to mass (energy) spectrum of a
small quantum system. (Obviously it is conceptually analogous to Bohr
quantization postulate interpreted by de Broglie relation in Old,
Bohr-Sommerfeld, quantum theory.) Especially, black hole entropy can be
presented as the quotient of the black hole mass and the minimal mass of small
quantum system in ground mass (energy) state. Now, we suppose that black hole
mass correction is simply equivalent to negative classical potential energy of
the gravitational interaction between black hole and small quantum system in
ground mass (energy) state. As it is not hard to see absolute value of the
classical potential energy of gravitational interaction is identical to black
hole temperature. All this, according to first thermodynamical law, implies
that first order entropy correction holds form of the logarithm of the surface
with coefficient -0.5. Our result, obtained practically quasi-classically,
"without knowing the details of quantum gravity", is equivalent to result
obtained by loop quantum gravity and other quantum gravity methods for
macroscopic black holes.
