No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity

Understand

Employing the covariant phase space formalism, we discuss black hole thermodynamics in four-dimensional scalar-tensor Einstein-Gauss-Bonnet gravity.

• We argue that logarithmic corrections to Wald entropy previously reported in this theory do not appear, due to the symmetry of the theory under constant shifts of the scalar field.
• Instead, we obtain the standard Bekenstein entropy of general relativity.
• Then, to satisfy the first law of black hole mechanics, the Hawking temperature must be modified.