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Applying Parikh–Wilczek's semiclassical quantum tunneling method, we investigate the tunneling radiation characteristics of a torus-like black hole and Kerr–Newman–Kausya de Sitter black hole. Both black holes have the cosmological constant Λ, but a torus-like black hole is in anti-de Sitter spacetime and the other black hole is in de Sitter spacetime. The derived results show that the tunneling rate is related to the change of Bekenstein–Hawking entropy, and the factual radiated spectrum is not precisely thermal, but is consistent with an underlying unitary theory, which gives a might explanation to the paradox of black hole information lost.

Adopting the Hamilton–Jacobi method, we investigated the tunneling radiation of a deform Hořava–Lifshitz black hole, and the original tunneling rate and Hawking temperature are obtained. Based on the generalized uncertainty principle, recent researches imply that the quantum gravity corrected the Dirac equation exactly. Hence, the corrected Dirac equation can express the tunneling behavior of fermions may be more suitable, and meanwhile, the corrected Hawking temperature of the Hořava–Lifshitz black hole is obtained. Comparing with previous results, we find that the Hawking temperature is not only related to the mass of black hole, but also related to the mass and energy of outgoing fermions. Finally, we inferred that the Hawking radiation would stop by the reason of the quantum gravity, and the remnant of the black hole exists naturally, also the singularity of the black hole is avoided.

Parikh–Wilczek's recent work, which treats the Hawking radiation as semiclassical tunneling process from the event horizon of the static Schwarzschild and Reissner–Nordström black holes, indicates that the factually radiant spectrum deviates from the precisely thermal spectrum after taking the self-gravitation interaction into account. In this paper, we extend Parikh–Wilczek's work to study the Hawking radiation via tunneling from new form of rotating Kerr–Newman–Kasuya solution and obtain a corrected radiation spectrum, which is related to the change of Bekenstein–Hawking entropy, and is not pure thermal, but is consistent with the underlying unitary theory and then satisfies the first law of the black hole thermodynamics. Meanwhile, in this framework, we point out that the information conservation is only suitable for the reversible process.

Taking the self-gravitational interaction and unfixed background space–time into account, we discuss the tunneling radiation of the Dilaton–Maxwell black hole by the Hamilton–Jacobi method. The result shows that the tunneling rate is related not only to the change of Bekenstein–Hawking entropy, but also to a subtle integral about the black hole mass, which does not satisfy the unitary theory and is different from Parikh and Wilczek's result. This implies that information loss in black hole evaporation is possible.