On Black Holes’ Statistical Entropy And F(R) Gravity Effect

Since Einstein built General Relativity, black hole,as a prediction of General Relativity theory, has been studied by many scholars. People attempted to reveal the nature of black hole and statistical origin of its entropy. Along with the advancement of society,nature has proposed new puzzle to human and f(R) theory come into human sight as a possible interpretation. In this paper, we mainly use state density modified to all orders in Planck length from a generalized uncertainty principle to calculate statistical entropy of black hole and the gravity effect of f(R) theory in mercury procession.In chapter1, first of all, we introduce the basic concept and theory of black hole,then we discuss the statistical origin of black hole entropy which includes:holographic principle, theory of entanglement entropy, Euclidean method, thermal gas method, induce quantum gravity method, Xhern-Simons theory,"brick wall" and "thin-layer"computing method. Lastly,we introduce the relation of General Relativity and f(R) gravity theory.In chapter2, we firstly introduce the generalized position-momentum uncertainty relation and modified density equation base on quantum gravity and perturbation of string theory. Then we use state density modified to all orders in Planck length,equation of Klein-Gordon and general tortoise-coordinate transformation to acquire the statistical entropy of Reissner-Nordstrom-de Sitter black hole and general spherically symmetric non-stationary black hole. We come to the conclusion that the entropy of black hole is proportional to its event area without artifical cut-off which agrees with the results of other methods.In chapter3, we use specific f(R) gravity model to get the value of mercury procession per century. We firstly use the condiction of four dimention velocity normalization to acquire specified f(R) gravity motion equation and estimate the magnitude of all terms of the equation,then simplify the second order differential equation. At last,we get the numerical value by computer program which agrees with the observation values within the experiment error.