We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate Γ ∼ exp (Δ S) arises as a consequence of the first law of thermodynamics, T d S = d E + P d V. Therefore, this approach demonstrates how tunneling is intimately connected with the first law of thermodynamics through the principle of conservation of energy. The analysis is also generally applicable to any reasonable theory of gravity so long as the first law of thermodynamics for horizons holds in the form, T d S = d E + P d V. © 2007 Elsevier B.V. All rights reserved.
Sarkar, S., & Kothawala, D. (2008). Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 659(3), 683–687. https://doi.org/10.1016/j.physletb.2007.11.056