Effect of the Dilaton Field on the Entropic Force

According to the Eric Verlinde’s arguments on the gravity, we study the entropic force of two spacetimes without and with dilaton field, which are the Schwarzschild black hole and the charged dilaton black hole respectively. Generally, the existence of the dilaton field makes over the spacetime to have unusual asymptotic structure. During the calculations of the entropic force, the key point is to describe the holographic screen of the associated spacetime. In this thesis, we mainly consider three surfaces as being candidates for the holographic screen. These surfaces are called as the static holographic screen, the accelerating surface and the stretched horizon. Thus, by comparing the results of the entropic force of the associated spacetimes, we want to stress the effect of the dilaton field on the entropic force.