Breakdown of self-similar evolution in homogeneous perfect fluid collapse

The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the equation of state $P=\alpha\rho$, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation $\alpha \ll 1$, we analytically derive an infinite set of the normal modes and their growth (or decay) rate. The existence of one unstable normal mode is found to conclude that the self-similar behavior in homogeneous collapse of a sufficiently low pressure perfect fluid must terminate and a certain inhomogeneous density profile can develop with the lapse of time.Comment: 9 pages, 1 figure, references added, published in Physical Review

Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state $P=\alpha\rho$. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by $\exp{(i\omega\log|t|)}$, and present some sufficient conditions for the absence of non-oscillatory unstable normal modes with purely imaginary $\omega$.Comment: 17 pages, 3 figures, matched to the published versio

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from "quasi-normal" modes of the self-similar system as well as "high-frequency" waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation, and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.Comment: 20 pages, 7 figures, references added to match the published versio

Asymptotic behavior of dynamical variables and naked singularity formation in spherically symmetric gravitational collapse

Considering gravitational collapse of matter, it is important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla \textit{et al.} to spherically symmetric gravitational collapse of perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.Comment: Version published in PR

Evidence for Large Electric Polarization From Collinear Magnetism in TmMnO\u3csub\u3e3\u3c/sub\u3e

There has been tremendous research activity in the field of magneto-electric (ME) multiferroics after Kimura et al (2003 Nature 426 55) showed that antiferromagnetic and ferroelectric orders coexist in orthorhombically distorted perovskite TbMnO3 and are strongly coupled. It is now generally accepted that ferroelectricity in TbMnO3 is induced by magnetic long-range order that breaks the symmetry of the crystal and creates a polar axis (Kenzelmann et al 2005 Phys. Rev. Lett. 95 087206). One remaining key question is whether magnetic order can induce ferroelectric polarization that is as large as that of technologically useful materials. We show that ferroelectricity in orthorhombic (o) TmMnO3 is induced by collinear magnetic order, and that the lower limit for its electric polarization is larger than in previously investigated orthorhombic heavy rare-earth manganites. The temperature dependence of the lattice constants provides further evidence of large spin–lattice coupling effects. Our experiments suggest that the ferroelectric polarization in the orthorhombic perovskites with commensurate magnetic ground states could pass the 1 μC cm-2 threshold, as predicted by theory (Sergienko et al 2006 Phys. Rev. Lett. 97 227204; Picozzi et al 2007 Phys. Rev. Lett. 99 227201)

Hitomi X-Ray Studies of Giant Radio Pulses from the Crab Pulsar

To search for giant X-ray pulses correlated with the giant radio pulses (GRPs) from the Crab pulsar, we performed a simultaneous observation of the Crab pulsar with the X-ray satellite Hitomi in the 2300 keV band and the Kashima NICT radio telescope in the 1.41.7 GHz band with a net exposure of about 2 ks on 2016 March 25, just before the loss of the Hitomi mission. The timing performance of the Hitomi instruments was confirmed to meet the timing requirement and about 1000 and 100 GRPs were simultaneously observed at the main pulse and inter-pulse phases, respectively, and we found no apparent correlation between the giant radio pulses and the X-ray emission in either the main pulse or inter-pulse phase. All variations are within the 2 fluctuations of the X-ray fluxes at the pulse peaks, and the 3 upper limits of variations of main pulse or inter-pulse GRPs are 22% or 80% of the peak flux in a 0.20 phase width, respectively, in the 2300 keV band. The values for main pulse or inter-pulse GRPs become 25% or 110%, respectively, when the phase width is restricted to the 0.03 phase. Among the upper limits from the Hitomi satellite, those in the 4.510 keV and 70300 keV bands are obtained for the first time, and those in other bands are consistent with previous reports. Numerically, the upper limits of the main pulse and inter-pulse GRPs in the 0.20 phase width are about (2.4 and 9.3) 10(exp 11) erg cm(exp 2), respectively. No significant variability in pulse profiles implies that the GRPs originated from a local place within the magnetosphere. Although the number of photon-emitting particles should temporarily increase to account for the brightening of the radio emission, the results do not statistically rule out variations correlated with the GRPs, because the possible X-ray enhancement may appear due to a >0.02% brightening of the pulse-peak flux under such conditions

Rerouting of the lignin biosynthetic pathway by inhibition of cytosolic shikimate recycling in transgenic hybrid aspen

Lignin is a phenolic polymer deposited in the plant cell wall and is mainly polymerized from three canonical monomers (monolignols), i.e., p-coumaryl, coniferyl, and sinapyl alcohols. After polymerization, these alcohols form different lignin substructures. In dicotyledons, monolignols are biosynthesized from phenylalanine, an aromatic amino acid. Shikimate acts at two positions in the route to the lignin building blocks. It is part of the shikimate pathway which provides the precursor for the biosynthesis of phenylalanine, and is involved in the transesterification of p-coumaroyl-CoA to p-coumaroyl shikimate, one of key steps in the biosynthesis of coniferyl and sinapyl alcohols. The shikimate residue in p-coumaroyl shikimate is released in later steps, and the resulting shikimate becomes available again for the biosynthesis of new p-coumaroyl shikimate molecules. In this study, we inhibited cytosolic shikimate recycling in transgenic hybrid aspen by accelerated phosphorylation of shikimate in the cytosol through expression of a bacterial shikimate kinase. This expression elicited an increase in p-hydroxyphenyl units of lignin and, by contrast, a decrease in guaiacyl and syringyl units. Transgenic plants with high shikimate kinase activity produced a lignin content comparable to that in wild-type plants and had an increased processability via enzymatic saccharification. Although expression of many genes was altered in the transgenic plants, elevated shikimate kinase activity did not exert a significant effect on the expression of the majority of genes responsible for lignin biosynthesis. The present results indicate that cytosolic shikimate recycling is crucial to the monomeric composition of lignin rather than for lignin content