Naked singularities and quantum gravity

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. We argue that the semiclassical approximation (i.e. quantum field theory on a classical curved background) used in these analyses ceases to be valid about one Planck time before the epoch of naked singularity formation, because by then the curvature in the central region of the star reaches Planck scale. It is shown that during the epoch in which the semiclassical approximation is valid, the total emitted energy is about one Planck unit, and is not divergent. We also argue that back reaction in this model does not become important so long as gravity can be treated classically. It follows that the further evolution of the star will be determined by quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time scale or settles down into a black hole state.Comment: 16 pages, paper rewritten into sections, conclusions unchanged, 4 references added, to appear in Phys. Rev. D (Rapid Communication

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a Rapid Communicatio

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.Comment: 18 pages, 16 figure

Immunohistochemical Examination of a Resected Advanced Hilar Cholangiocarcinoma Arising in a 29-Year-Old Male without Primary Sclerosing Cholangitis

A 29-year-old man with advanced hilar cholangiocarcinoma was successfully treated with an extended right lobectomy. The carbohydrate antigen 19-9 (CA19-9) level was elevated to 939 IU/l, and the pathological findings revealed moderately differentiated tubular adenocarcinoma which involved almost the entire thickness of the hepatic duct and the adjacent liver tissue (T3) and which was associated with lymph node metastasis (N1). It was a stage IIB (T3N1M0) tubular adenocarcinoma according to UICC pathological staging. Immunohistochemical examination revealed that Ki-67, cyclin D1, and MMP-7 were positive, and 14-3-3σ and p27 were negative. The pathological and immunohistochemical findings indicated high malignant potential indicating poor prognosis. We administrated the postoperative adjunct gemcitabine combined with S-1 chemotherapy. The patient is alive without recurrence and doing well two years after surgery. We also review other reports of cholangiocarcinoma patients aged less than 30 years

Topology optimization of nonlinear optical waveguide devices considering output signal phase

A signal output of optical devices with multi-input ports, such as a logic gate, depends on the phase difference between input ports. In order to cascade optical devices, it is essential to design such devices considering not only desired output power but also desired output signal phase. We propose a topology optimization method for optical devices considering the output signal phase. In our approach, the beam propagation method (BPM) is employed as a numerical simulation method and the adjoint variable method (AVM) is used to calculate the sensitivity of output power and signal phase to design parameters. The validity and the effectiveness of our approach are verified through design examples of a three-branching waveguide with linear media and an all-optical logic gate utilizing nonlinear media

Nakedness and curvature strength of shell-focusing singularity in the spherically symmetric space-time with vanishing radial pressure

It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\approx 2y_{0} m^{\beta}$ with $1/3<\beta\le 1$ along the first radial null geodesic from the singularity. The $\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Kr\'olak hold for $\beta=1$ and $y_{0}\ne 1$, not SCC but only LFC holds for $1/2\le \beta <1$, and neither holds for $1/3<\beta <1/2$, for the null geodesic. On the other hand, if GDC is satisfied for the timelike geodesic $r=0$, both SCC and LFC are satisfied for the timelike geodesic, irrespective of the value of $\beta$. Several examples are also discussed.Comment: 11 pages, Accepted for Publication in Classical and Quantum Gravity, References Updated, Grammatical Errors Correcte

In Vivo Microwave Ablation of Normal Swine Lung at High-power, Short-duration Settings

To evaluate the volume and heat-sink effects of microwave ablation (MWA) in the ablation zone of the normal swine lung. MWA at 100 W was performed for 1, 2, and 3 min in 7, 5, and 5 lung zones, respectively. We assessed the histopathology in the ablation zones and other outcome measures: namely, length of the longest long and short axes, sphericity, ellipsoid area, and ellipsoid volume. The mean long- and short-axis diameters were 22.0 and 14.1 mm in the 1-min ablation zone, 27.6 and 20.2 mm in the 2-min ablation zone; and 29.2 and 21.2 mm in the 3-min ablation zone, respectively. All measures, except sphericity, were significantly less with 1-min ablation than with either 2- or 3-min ablation. There were no significant differences between the 2- and 3-min ablation zones, but all measures except sphericity were larger with 3-min ablation. Although there were no blood vessels that resulted in a heat-sink effect within the ablation zones, the presence of bronchi nearby in 5 lung ablation zones resulted in reduced ablation size. In high-power, short-duration MWA, the lung ablation volume was affected by ablation time. Some ablations showed that a heat-sink effect by a neighboring bronchus might occur

Naked singularity formation in the collapse of a spherical cloud of counterrotating particles

We investigate collapse of a spherical cloud of counter-rotating particles. An explicit solution is given using an elliptic integral. If the specific angular momentum $L(r)=O(r^2)$ at $r\to 0$, no central singularity occurs. With $L(r)$ like that, there is a finite region around the center that bounces. On the other hand, if the order of $L(r)$ is higher than that, a central singularity occurs. In marginally bound collapse with $L(r)=4F(r)$, a naked singularity occurs, where $F(r)$ is the Misner-Sharp mass. The solution for this case is expressed by elementary functions. For $4 <L/F<\infty$ at $r\to0$, there is a finite region around the center that bounces and a naked singularity occurs. For $0 \le L/F< 4$ at $r\to0$, there is no such region. The results suggests that rotation may play a crucial role on the final fate of collapse.Comment: 6 pages, Accepted for Publication as a Rapid Communication in Physical Review D, Some Minor Correction

Power, energy, and spectrum of a naked singularity explosion

Naked singularity occurs in the gravitational collapse of an inhomogeneous dust ball from an initial density profile which is physically reasonable. We show that explosive radiation is emitted during the formation process of the naked singularity. The energy flux is proportional to $(t_{\rm CH}-t)^{-3/2}$ for a minimally coupled massless scalar field, while is proportional to $(t_{\rm CH}-t)^{-1}$ for a conformally coupled massless scalar field, where $t_{\rm CH}-t$ is the `remained time' until the distant observer could observe the singularity if the naked singularity was formed. As a consequence, the radiated energy grows unboundedly for both scalar fields. The amount of the power and the energy depends on parameters which characterize the initial density profile but do not depend on the gravitational mass of the cloud. In particular, there is characteristic frequency $\nu_{s}$ of singularity above which the divergent energy is radiated. The energy flux is dominated by particles of which the wave length is about $t_{\rm CH}-t$ at each moment. The observed total spectrum is nonthermal, i.e., $\nu dN/d\nu \sim (\nu/\nu_{s})^{-1}$ for $\nu>\nu_{s}$. If the naked singularity formation could continue until a considerable fraction of the total energy of the dust cloud is radiated, the radiated energy would reach about $10^{54}(M/M_{\odot})$ erg. The calculations are based on the geometrical optics approximation which turns out to be consistent as a rough order estimate. The analysis does not depend on whether or not the naked singularity occurs in its exact meaning. This phenomenon may provide a new candidate for a source of ultra high energy cosmic rays or a central engine of gamma ray bursts.Comment: 34 pages, 13 postscript figures included, to appear in Phys. Rev. D, grammatical errors correcte