Thermodynamics of Schwarzschild-like black holes in modified gravity models

Over the last decades, many methods were developed to prove Hawking radiation. Recently, a semiclassical method known as the tunneling method has been proposed as a more straightforward way of derivating black hole thermodynamical properties. This method has been widely applied to a vast sort of spacetimes with satisfactory results. In this work, we obtain the black hole thermodynamics in the presence of a Lorentz symmetry breaking (LSB). We apply the Hamilton-Jacobi method to Schwarzschild-like black holes, and we investigate whether the LSB affects their thermodynamics. The results found show that the LSB not only changes the black hole thermodynamic quantities but also makes it necessary to modify the standard first law of thermodynamics.