The generalized uncertainty relation and the quantum entropy of static spherical black hole surrounded by quintessence due to spin fields

By using the brick-wall model, the quantum entropies of static spherical black hole surrounded by quintessence due to the Weyl neutrino, electromagnetic, massless Rarita–Schwinger, and gravitational fields for the source-free case are investigated from a generalized uncertainty relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic, and logarithmic divergences at ultraviolet σ → 0, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. After the smallest length scale is taken into account, we find that the contribution of the gravitational interactions to the entropy is larger than the usual dominant term and becomes a part of the whole dominant term, so it is very important and cannot be neglected.

THE ENTROPY OF A DIELECTRIC BLACK HOLE

In a dielectric black hole background, photons will be radiated via Hawking evaporation mechanism. In this paper, we calculate the entanglement entropy associated with a static dielectric black hole by employing 't Hooft's brick-wall model. It is found that the lowest energy of radiated particles is coordinate dependent. The resulted entanglement entropy is composed of three parts: a parameter independent leading constant term [Formula: see text], a logarithmic correction term and some series terms. The convergency of the series terms is also discussed.

Entropy of charged dilaton-axion black hole with minimal length revisited

Using the generalized uncertainty principle, we calculate the entropy of the charged dilaton-axion black hole for both asymptotically flat and non-flat cases by counting degrees of freedom near the horizon. The divergence of density of states and free energy appearing in the thin film brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.

COMPUTING THE ENTROPY OF KERR–NEWMAN BLACK HOLE WITHOUT BRICK WALLS METHOD

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein–Hawking entropy of Kerr–Newman black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in Kerr–Newman black hole and are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space–time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the calculation, the constant λ introduced in the generalized uncertainty principle is related to polar angle θ in an axisymmetric space–time.

ENTANGLEMENT ENTROPY OF THE SIX-DIMENSIONAL HOROWITZ–STROMINGER BLACK HOLE

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein–Hawking entropy of six-dimensional Horowitz–Strominger black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in six-dimensional Horowitz–Strominger black hole and the fields are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space–time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. Using the quantum statistical method, we directly calculate the partition function of the Bose and Fermi fields under the background of the six-dimensional black hole. The difficulty in solving the wave equations of various particles is overcome.