QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Superconductivity was recently observed in the binary iron-based compound, FeSe. It is now shown that under pressure, the transition temperature can rise above 36 K. In addition, no static magnetic ordering is observed for this system, contrary to FeAs superconductors. The discovery of new high-temperature superconductors1 based on FeAs has led to a new ‘gold rush’ in high-TC superconductivity. All of the new superconductors share the same common structural motif of FeAs layers and reach TC values up to 55 K (ref. 2). Recently, superconductivity has been reported in FeSe (ref. 3), which has the same iron pnictide layer structure, but without separating layers. Here, we report the magnetic and electronic phase diagram of β-Fe1.01Se as a function of temperature and pressure. The superconducting transition temperature increases from 8.5 to 36.7 K under an applied pressure of 8.9 GPa. It then decreases at higher pressures. A marked change in volume is observed at the same time as TC rises, owing to a collapse of the separation between the Fe2Se2 layers. No static magnetic ordering is observed for the whole p–T phase diagram. We also report that at higher pressures (starting around 7 GPa and completed at 38 GPa), Fe1.01Se transforms to a hexagonal NiAs-type structure and exhibits non-magnetic behaviour.

Electronic and magnetic phase diagram of β-Fe1.01Se with superconductivity at 36.7 K under pressure

The recent discovery of possible high-temperature superconductivity in single-layer FeSe films has generated significant experimental and theoretical interest. In both the cuprate and the iron-based high-temperature superconductors, superconductivity is induced by doping charge carriers into the parent compound to suppress the antiferromagnetic state. It is therefore important to establish whether the superconductivity observed in the single-layer sheets of FeSe--the essential building blocks of the Fe-based superconductors--is realized by undergoing a similar transition. Here we report the phase diagram for an FeSe monolayer grown on a SrTiO3 substrate, by tuning the charge carrier concentration over a wide range through an extensive annealing procedure. We identify two distinct phases that compete during the annealing process: the electronic structure of the phase at low doping (N phase) bears a clear resemblance to the antiferromagnetic parent compound of the Fe-based superconductors, whereas the superconducting phase (S phase) emerges with the increase in doping and the suppression of the N phase. By optimizing the carrier concentration, we observe strong indications of superconductivity with a transition temperature of 65±5 K. The wide tunability of the system across different phases makes the FeSe monolayer ideal for investigating not only the physics of superconductivity, but also for studying novel quantum phenomena more generally.

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Phase diagram and electronic indication of high-temperature superconductivity at 65 K in single-layer FeSe films

The exact mechanism for superconductivity in iron-based superconductors remains elusive, but is thought to involve complex interactions between many orbitals. Using angle-resolved photoelectron spectroscopy, Liu et al. report the electronic structure of the single-layer parent compound FeSe.

http://surface.iphy.ac.cn/SF4/publications/papers/2012/12%20Electronic%20origin%20of%20high-temperature%20superconductivity%20in%20single-layer%20FeSe%20superconductor,%20Nat.%20Commun.%203,%20931%20(2012).pdf

Electronic origin of high-temperature superconductivity in single-layer FeSe superconductor

The superconducting state is characterized by a pairing of electrons with a superconducting gap 
on the Fermi surface. In iron-based superconductors, an unconventional pairing state has been argued for theoretically. We used scanning tunneling microscopy on Fe(Se,Te) single crystals to image the quasi-particle scattering interference patterns in the superconducting state. By applying a magnetic field to break the time-reversal symmetry, the relative sign of the superconducting gap can be determined from the magnetic-field dependence of quasi-particle scattering amplitudes. Our results indicate that the sign is reversed between the hole and the electron Fermi-surface pockets ( s ± -wave), favoring the unconventional pairing mechanism associated with spin fluctuations.

https://science.sciencemag.org/content/sci/328/5977/474.full.pdf

Unconventional s-wave superconductivity in Fe(Se,Te).

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein–Hawking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.

https://iopscience.iop.org/article/10.1088/0256-307X/25/7/015/pdf

Canonical Entropy and Phase Transition of Rotating Black Hole

Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution from the vicinity of the horizon.

Spherically symmetric black-hole entropy without brick walls

We extend the classical Damour–Ruffini method and discuss Hawking radiation spectrum of high-dimensional rotating black hole using Tortoise coordinate transformation defined by taking the reaction of the radiation to the spacetime into consideration. Under the condition that the energy and angular momentum are conservative, taking self-gravitation action into account, we derive Hawking radiation spectrums which satisfy unitary principle in quantum mechanics. It is shown that the process that the black hole radiates particles with energy ω is a continuous tunneling process. We provide a theoretical basis for further studying the physical mechanism of black-hole radiation.

Hawking radiation of a high-dimensional rotating black hole

We extend the classical Damour-Ruffini method and discuss Hawking radiation in Kerr-Newman-de Sitter(KNdS) black hole. Under the condition that the total energy, angular momentum and charge of spacetime are conserved, taking the reaction of the radiation of the particle to the spacetime and the relation between the black hole event horizon and the cosmological horizon into consideration, we derive the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal one. It is related to the change of the Bekenstein-Hawking entropy corresponding the black hole event horizon and the cosmological horizon. It is consistent with an underlying unitary theory.

Hawking radiation of Kerr-Newman-de Sitter black hole

We extend the classical Damour–Ruffini method and discuss Hawking radiation in Kerr–Newman–de Sitter (KNdS) black hole. Under the condition that the total energy, angular momentum and charge of spacetime are conserved, taking the reaction of the radiation of the particle to the spacetime and the relation between the black hole event horizon and the cosmological horizon into consideration, we derive the black hole radiation spectrum. The radiation spectrum is no longer a pure thermal one. It is related to the change of the Bekenstein–Hawking entropy corresponding the black hole event horizon and the cosmological horizon. It is consistent with the underlying unitary theory.

Wu Yue-Qin

Papers

Canonical Entropy and Phase Transition of Rotating Black Hole

Spherically symmetric black-hole entropy without brick walls

Hawking radiation of a high-dimensional rotating black hole

Hawking radiation of Kerr-Newman-de Sitter black hole

Hawking radiation of Kerr–Newman–de Sitter black hole