In this letter we compute the correction to the entropy of Schwarzschild black hole due to the vacuum polarization effect of massive scalar field. The Schwarzschild black hole is supposed to be confined in spherical shell. The scalar field obeying mixed boundary condition on the spherical shell.

Considering corrections to all orders in the Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the scalar field on the background of the Schwarzschild black hole without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area. PACS: 04.70.-s, 04.70.Dy, 04.62.+v

Abstract Greybody factors are transmission probabilities of the Hawking radiation, which emitted from black holes and can be obtained gravitational potential holes. The de Rham, Gabadadze, Tolly (dRGT) massive gravity is one theories that modified general relativity. In this paper, we investigate greybody factor scalar field in both asymptotically dS AdS spacetime using WKB rigorous bound metho...

We study the Lorentzian static traversable wormholes coupled to quadratic scalar fields. We also obtain the solutions of the scalar fields and matters in the wormhole background and find that the minimal size of the wormhole should be quantized under the appropriate boundary conditions for the positive nonminimal massive scalar field.