Effect of Dilaton Field on the Entropic Force: in Charged Dilaton Black Hole

Recently there are some arguments, like Verlinde?s theory, which showed that gravity emerges as changing the entropy. It means gravity is not a fundamental force any more. Using information storage in the black holes to get a relation between entropy and gravity is very useful way to make this theory reliable. In this book by looking to the job done by Verlinde 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 candidate of 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.