Narrow Results

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

In this paper, we employ a new form of the extended uncertainty principle to investigate the thermal properties of the Schwarzschild and Reissner–Nordström. After we construct the formalism, we obtain the mass-temperature function for the Schwarzschild black hole. We follow a heuristic method to derive the entropy function after we obtained the heat capacity function. Then, we derive the mass-temperature and mass-charge-temperature functions of the Reissner–Nordström black hole in the new formalism. After we obtain the heat capacity and entropy functions, we present a comprehensive and comparative analysis of all these functions. We find that the deformation parameter changes drastically some of the thermodynamic function characteristics.

In this invited review, we discuss the evaporation of a black hole, with emphasis on the resulting macroscopically distinct patterns of Hawking radiation. The density matrix of this radiation can approach a pure final state in the form of a highly entangled macroscopic superposition state. We note that this exact property is exhibited in replica wormhole calculations, and also in quantum hair effects on Hawking radiation amplitudes. Finally, we revisit the information paradox (Mathur’s theorem and firewalls), showing that it can be resolved by macroscopic entanglement.