Quantum Entropy of the Schwarzschild Black Hole due to Gravitational Perturbations

The quantum entropies of the Schwarzschild black hole arising from the axial and polar gravitational perturbations are investigated by using the‘brick-wall’model. It is shown that, although the axial and polar perturbational potentials have quite different forms, the black hole entropies due to both the gravitational perturbations are equivalent. We also find that the logarithmic correction, which can be expressed in the form ln(A_H/ε⁴), is 30 times larger than that of the scalar field.