Hayley Johnson

Professor Michael Schulz

Department of Physics

**Determining the Gray Body Factors of a Schwarzschild Black Hole**

A Schwarzschild black hole is a black hole formed by an electrically neutral, non-rotating, spherical mass. Hawking radiation is a quantum mechanical phenomenon common to all black holes, wherein a black hole should slowly radiate away its mass. We want to determine the gray body factors, which describe the departure of this radiation from a purely thermal black body spectrum, as dictated by the Planck formula.

The gray body factors will depend on the effective potential energy of Schwarzschild spacetime, which will dictate whether particles can tunnel out of the black hole. We will compute this effective potential from the Klein-Gordon equation, which is a relativistic version of the Schrödinger equation. Depending on the effective potential, the effective radial Schrödinger equation may or may not be easily solved explicitly. We will nonetheless solve the equation in two different ways: by finding an analytic expression and by using a WKB approximation. The former will give a more precise transmission coefficient, while the latter will give a more qualitative, conceptual understanding.