Download or read book Black Hole Evaporation in Semi-classical Approach written by Shintaro Sawayama and published by Shintaro Sawayama. This book was released on with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider how the mass of the black hole decreases by the Hawking radiation in the Vaidya spacetime, using the concept of dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that the final state is the Minkowski spacetime in our particular model. We finally solved the equation which describes how black hole mass decreases. The back-reaction problem of the Hawking radiation has not been solved by the conventional method by solving the Einstein equation. While we can solve this problem using the following three ideas. First idea is to use the dynamical horizon equation which only needs information of the horizon surface. Then we calculate usual field equation as the integration equation. Second we taken negative energy into account near the black hole horizon. Using the negative energy we can enlarge the dynamical horizon to the timelike case. Third, we use the Vaidya metric. Usually the Einstein equation and the dynamical horizon equation are not compatible. However, using the Vaidya metric as a background we can use the dynamical horizon equation in place of the Einstein equation.