Name: Chenyue Li (Lyn)

Mentor: Michael Schulz

Department: Physics

**Determine the greybody factor of Hawking radiation from a Schwarzschild black hole**

Black holes release thermal black body radiation, or, Hawking radiation, due to quantum effects. Near the event horizon of a black hole, a particle in a particle-antiparticle pair, which, under normal circumstances, will quickly annihilate the other the moment they are created, can escape the gravitational force of the black hole before the annihilation happens. However, after emission at the event horizon, Hawking radiation is modified by the effective gravitational potential around the black hole. Therefore, some of the particles will travel to infinity while others will be reflected back into the black hole. As a consequence, there will be a correction of the energy spectrum emitted by a black hole, which is called the grey body factor. The goal of this research is to determine the greybody factor of Hawking radiation from a Schwarzschild black hole. We try to achieve this goal by studying the effective radial equation of the Klein-Gordon equation in Schwarzschild spacetime. The methods that we intend to use are direct solution and the WKB approximation. The WKB approximation is used to find approximate solutions of linear differential equations whose highest derivative is multiplied by a small coefficient. In this research, since we view the Hawking radiation as a tunneling process, we will use WKB approximation to approximate solutions of the effective Schrödinger equation.