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The thermodynamics and the weak cosmic censorship conjecture (WCCC) in a high dimensional RN − AdSd+ 1 black hole with energy-momentum relation are investigated by absorbing a charged particle in the phase space. In the RN − AdSd+ 1 space-time, the cosmological constant Λ is treated as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. We use the energy-momentum relation of the absorbed particle to discuss the thermodynamics of the RN − AdSd+ 1 black hole and to prove the WCCC in the phase space. Based on this assumption, we find that the first law and the second law of thermodynamics are satisfied in normal phase space. On the other hand, in the extend phase space, the first law is satisfied and the second law is violated. Then we study the WCCC in the phase space, we find that the WCCC is satisfied for an extreme black and a near-extreme black hole in the normal phase space. In the extend phase space, the WCCC is satisfied for an extreme black hole and unidentified for a near-extreme black hole.

Based on a higher energy scale, the dispersion relation might be corrected. Correspondingly, the Hamilton–Jacobi equation should also be modified. In this paper, we use the correction to study the fermion tunneling radiation for a Gibbons–Maeda–Garfinkle-Horowitz–Strominger (GMGHS) black hole, a Kerr–NUT black hole, and an Einstein–Maxwell–Dilaton–Axion (EMDA) black hole. The result shows that compared to the charged GMGHS black hole and the rotating Kerr–NUT black hole, the Hawking temperate and the entropy of the rotating charged EMDA black hole not only are related to the correction parameter [Formula: see text] and particle mass [Formula: see text] but also depend on the angle parameter [Formula: see text] of the black hole coordinates.