This thesis explores the connection between the Schwinger effect and Hawking radiation through a heat kernel approach. Through scattering theory, it can be argued that the inverse square potential given by the field equation in the near horizon limit is directly associated with particle production. Through the eigenvalues of this field equation, where solely the inverse square potential is present, the imaginary part of the Lagrangian can be calculated using the poles of the heat kernel. However, this approach involves discarding order terms that are proportional to the eigenvalues. By including these terms, the new non-trivial eigenvalues can be expressed as a sum over the original eigenvalues plus some perturbation, which is assumed to only contribute to the greybody factor. The result is consistent with other approaches and directly shows that the presence of the event horizon is the working mechanism driving particle production analogous to the electric field in sQED.
