Black Hole as a Quantum Field Configuration

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{\mu\nu}=8\pi G \langle \psi|T_{\mu\nu}|\psi \rangle$ and quantum matter fields in a self-consistent manner. As the matter fields we consider $N$ massless free scalar fields ($N$ is large). We find a spherically symmetric self-consistent solution of the metric $g_{\mu\nu}$ and state $|\psi\rangle$. Here, $g_{\mu\nu}$ is locally $AdS_2\times S^2$ geometry, and $|\psi\rangle$ provides $\langle \psi|T_{\mu\nu}|\psi \rangle=\langle0|T_{\mu\nu}|0 \rangle+T_{\mu\nu}^{(\psi)}$, where $|0\rangle$ is the ground state of the matter fields in the metric and $T_{\mu\nu}^{(\psi)}$ consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure $\langle0|T^\theta{}_\theta|0 \rangle$ due to the vacuum fluctuation of the bound modes with large angular momenta. This describes the interior of the black hole when the back reaction of the evaporation is considered. The black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of self-consistent configurations $\{|\psi\rangle\}$, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole. $|\psi\rangle$ also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. As a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter content.Comment: ver4: We added a new paragraph to Sec.2.1. and made Appendix

Interior of Black Holes and Information Recovery

We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole of which the radius $a(t)$ decreases in time. The important point is that the shell can never reach $a(t)$ but it approaches $a(t)-a(t)\frac{d a(t)}{d t}$. This situation holds at any radius because the motion of a shell in a spherically symmetric system is not affected by the outside. In this way, we find that the collapsing matter evaporates without forming a horizon. Nevertheless, a Hawking-like radiation is created in the metric, and the object looks the same as a conventional black hole from the outside. We then discuss how the information of the matter is recovered. We also consider a black hole that is adiabatically grown in the heat bath and obtain the interior metric. We show that it is the self-consistent solution of $G_{\mu\nu}=8\pi G \langle T_{\mu\nu} \rangle$ and that the four-dimensional Weyl anomaly induces the radiation and a strong angular pressure. Finally, we analyze the internal structures of the charged and the slowly rotating black holes.Comment: Appear in Physical Review D. Typos fixed. References, clarifications and new appendixes adde

Phenomenological Description of the Interior of the Schwarzschild Black Hole

We discuss a sufficiently large 4-dimensional Schwarzschild black hole which is in equilibrium with a heat bath. In other words, we consider a black hole which has grown up from a small one in the heat bath adiabatically. We express the metric of the interior of the black hole in terms of two functions: One is the intensity of the Hawking radiation, and the other is the ratio between the radiation energy and the pressure in the radial direction. Especially in the case of conformal matters we check that it is a self-consistent solution of the semi-classical Einstein equation, $G_{\mu\nu}=8\pi G \langle T_{\mu\nu}\rangle$. It is shown that the strength of the Hawking radiation is proportional to the c-coefficient, that is, the coefficient of the square of the Weyl tensor in the 4-dimensional Weyl anomaly.Comment: 10 pages. Detail discussions and references added. Accepted Int. J. Mod. Phys.

Back Reaction of 4D Conformal Fields on Static Geometry

Static, spherically symmetric solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the near-horizon geometry, and that the existence of the horizon requires fine-tuning.Comment: 35 pages, minor modificatio

Fusing enzymes to transcription activator LuxR for the rapid creation of metabolite sensors

Metabolite sensors have been applied for high-throughput screening for improved biosynthetic pathways, as well as for dynamic control of the metabolic networks. Obviously, however, current repertoire of natural sensors covers only a small fraction of the known metabolite. We have been developing the new robust workflow for the rapid creation of metabolite sensors where biosynthetic enzymes can be adopted as the sensory (recognizing) components. Most of the known metabolites act as the direct substrates of some enzymes, and they are recognized and converted by these enzymes in physiologically relevant concentrations. Thus, ever-increasing repertoire of available enzymes is a rich and reliable source of sensory units. We found that the transcription activator LuxR can be fused with various biosynthetic enzymes without losing its function. By adding moderately de-stabilizing mutations, typically by random mutagenesis of the resultant fusion proteins followed by screening a small number (~100) of variants, we could have quickly isolated variants that can activate LuxR-dependent promoter in response to the substrates of the enzymes fused to LuxR. In this presentation, we demonstrate various metabolites can be detected by this manner. Detailed analysis of the thus-obtained fusion proteins indicated that function of LuxR is dependent on the substrate binding-induced stabilization of the enzymes. The biosensors with this mode of action exhibited various unique features. For instance, we found that the sensitivity (EC50) and dynamic range of these sensors to the target metabolites can be flexibly altered by the concentration of homoserine lactones, the cognate ligand of LuxR, in the media. Also, this provides unique opportunity to indirectly visualizing the substrate-binding to the enzyme in high-throughput manner. Indeed, multi-round mutagenesis and screening of the fusion protein of isopentenyl diphosphate isomerase (IDI) with LuxR variant (IDI-LuxR) revealed that many of the mutations that improved sensory performance of IDI-LuxR also elevated the catalytic performance of IDI. Some of such mutations turned out to elevate IDI activity even without fusion partner LuxR. Altogether, by fusing to LuxR, random mutagenesis, and traditional reporter (fluorescence)-based screening, one can not only adopt a variety of biosynthetic enzymes as sensor components but also laboratory evolve their catalytic functions

Ultrasound Stimulation Inhibits Morphological Degeneration of Motor Endplates in the Denervated Skeletal Muscle of Rats

Recovery of motor function after peripheral nerve injury requires treatment of the neuromuscular junction (NMJ), as well as the injured nerve and skeletal muscle. The purpose of this study was to examine the effects of ultrasound (US) stimulation on NMJ degeneration after denervation using a rat model of peroneal nerve transection. Twelve-week-old male Wistar rats were randomly assigned to 3 groups: US stimulation, sham stimulation, and intact. US or sham stimulation was performed on the left tibialis anterior (TA) muscle starting the day after peroneal nerve transection for 5 minutes daily under anesthesia. Four weeks later, the number and morphology of the motor endplates were analyzed to assess NMJ in the TA muscle. The endplates were classified as normal, partially fragmented, or fully fragmented for morphometric analysis. In addition, the number of terminal Schwann cells (tSCs) per endplate and percentage of endplates with tSCs (tSC retention percentage) were calculated to evaluate the effect of tSCs on NMJs. Our results showed that endplates degenerated 4 weeks after transection, with a decrease in the normal type and an increase in the fully fragmented type in both the US and sham groups compared to the intact group. Furthermore, the US group showed significant suppression of the normal type decrease and a fully fragmented type increase compared to the sham group. These results suggest that US stimulation inhibits endplate degeneration in denervated TA muscles. In contrast, the number of endplates and tSC and tSC retention percentages were not significantly different between the US and sham groups. Further investigations are required to determine the molecular mechanisms by which US stimulation suppresses degeneration

4D Weyl Anomaly and Diversity of the Interior Structure of Quantum Black Hole

We study the interior metric of 4D spherically symmetric static black holes by using the semi-classical Einstein equation and find a consistent class of geometries with large curvatures. We approximate the matter fields by conformal fields and consider the contribution of 4D Weyl anomaly, giving a state-independent constraint. Combining this with an equation of state yields an equation that determines the interior geometry completely. We explore the solution space of the equation in a non-perturbative manner for $\hbar$. First, we find three types of asymptotic behaviors and examine the general features of the solutions. Then, by imposing physical conditions, we obtain approximately a general class of interior geometries: various combinations of dilute and dense structures without a horizon or singularity. This represents a diversity of the interior structure. Finally, we show that the number of possible patterns of such interior geometries corresponds to the entropy-area law.Comment: 28 pages, many figure

Unilateral transient high myopization after pediatric strabismus surgery: Observation by anterior segment optical coherence tomography

[Purpose] To describe an unusual case of unilateral transient high myopization after pediatric strabismus surgery. [Observations] A 6-year-old girl with intermittent exotropia had undergone strabismus surgery and experienced a transient decrease in best-corrected visual acuity (BCVA, from 20/20 to 20/33) with high myopization (from +0.25 D to −9.00 D). Slit-lamp microscopy showed anterior chamber inflammation and a narrow angle only in the affected eye. Anterior segment optical coherence tomography (AS-OCT) revealed ciliary body detachment, a narrow angle, a shallow anterior chamber, and an anteroposterior elongation of the crystalline lens in the affected eye. Her symptoms of blurry vision and high myopization improved 8 weeks postoperatively. AS-OCT revealed the resolution of the ciliary body detachment, an open angle, and a deep anterior chamber, with normalization of the anteroposterior length of the crystalline lens. Her BCVA recovered to 20/20 with spherical equivalence of 0 D. [Conclusions and Importance] We reported on an extremely rare case of unilateral transient high myopization following strabismus surgery, which was resolved without additional surgery. This myopization was probably caused due to ciliary body inflammation

Cardiorespiratory fitness and the incidence of type 2 diabetes: a cohort study of Japanese male athletes

BACKGROUND: In Japan, although the incidence of overweight (BMI ≥ 25) is still low compared with that in Europe and the United States, the prevalence of type 2 diabetes has increased over the last 15 years,. In both Japanese and Caucasian populations it has been reported that a high level of cardiorespiratory fitness protects against the development of type 2 diabetes. However, there are no reports focused specifically on athletes that investigate whether high cardiorespiratory fitness at a young age can prevent disease later in life. We examined the relationship between cardiorespiratory fitness at a young age and the development of type 2 diabetes in Japanese athletes using a cohort study. METHODS: The cardiorespiratory fitness of male alumni of the physical education department of Juntendo University, as measured by stored data of a 1,500-m endurance run in college (1971–1991) was compared with their incidence of type 2 diabetes as determined by follow-up questionnaires (2007–2009). This study used Cox’s proportional hazards models and adjusted for age, year of graduation, BMI, smoking, and sports club participation at college age. RESULTS: We collected data on cardiorespiratory fitness at college age and medical history survey data during 2007–2009 from 570 male alumni. The median follow-up period was 26 years (IQR: 23–29 years), and 22 men had developed type 2 diabetes. An inverse relationship was observed between incidence of type 2 diabetes and level of cardiorespiratory fitness at time of college after adjustment for age, year of graduation, BMI, smoking, and sports participation. The adjusted hazards ratio and 95% CI by category (low, medium, and high) were 1.00 (reference), 0.40 (0.14–1.13) and 0.26 (0.07–1.00) (p = 0.03 for trend). CONCLUSIONS: A high level of cardiorespiratory fitness at a young age can help prevent type 2 diabetes later in life