**2. Entropy Force of Schwarzschild Black Holes**

Let us turn to our example, the Schwarzschild black hole, which we chose for demonstration because of its simplicity and cleanness compared to Kerr or charged Nordstrom black holes. Black holes are known to carry entropy [7–12]. More correctly, since the interior of the black hole is not accessible, it is the black hole horizon that carries an entropy. This came as a surprise, as it implies that the horizon possesses a temperature and therefore must be considered as a macrosystem, which occupies a large number of states. Microscopically, this puzzle has not been resolved until today, even though a large number of attempts have been put forward to elucidate the internal structure of the horizon (see [13–17] and several others). Such considerations were based on the Bekenstein–Hawking entropy and the Hawking radiation of a black hole [11], which is attributed to its finite entropy and thus finite temperature. It implies the existence of a thermodynamic for the black hole horizon with the implication that the horizon physics involves a very large number of states that can be occupied. Jacobson [15] extended this concept to horizons in general in order to develop a thermodynamics of gravitational horizons from which he found that Einstein's gravitational field equations formally play the role of equations of state. This concept was reviewed and extended subsequently by Padmanabhan [16] to speculate about the general importance of horizon physics in general relativity and cosmology, suggesting that all the physics is holographically contained in the physics of horizons.

Schwarzschild black holes are in the first place classical objects. However, their entropy includes the quantum nature of matter at the horizon (cf., e.g., [13]), which is induced by the sharpness of the horizon and indicates that black holes are not purely classical. Let us ask what the entropy force related to the presence of the horizon would be.
