Are physical objects necessarily burnt up by the blue sheet inside a black hole?

The electromagnetic radiation that falls into a Reissner-Nordstrom black hole develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We consider classical electromagnetic fields (that were produced during the collapse and then backscattered into the black hole), and investigate the blue-sheet effects of these fields on infalling objects within a simplified model. These effects are found to be finite and even negligible for typical parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters

The Ori-Soen time machine

Ori and Soen have proposed a spacetime which has closed causal curves on the boundary of a region of normal causality, all within a region where the weak energy condition (positive energy density) is satisfied. I analyze the causal structure of this spacetime in some simplified models, show that the Cauchy horizon is compactly generated, and argue that any attempt to build such a spacetime with normal matter might lead to singular behavior where the causality violation would otherwise take place.Comment: 5 pages, RevTeX, 7 figures with epsf, miscellaneous clarifications in v2, minor updates to correspond to version to appear in PR

Penilaian Ekonomi Sampah Kertas Di Kota Medan

Problems were caused by used paper in each area are common problems, especially in urban area, for example Medan city. Types rubbish were generated from household level to the level of industries different, namely organic and inorganic. Example of organic rubbish is a used paper. One of the countermeasures for used paper are not to accumulate by collecting and selling used paper for recycling. The purpose of this study was to identify source used paper, the economic value and the benefits and the flow of marketing of used paper were collected and sold by people in the city of Medan. Based interviews with respondents, the source used paper were from household, market, office, shop and newspaper distributor. The greatest economic value is major collector that Rp. 115.162.500,- of year per respondent. The lowest economic value is collector that Rp. 1.055.000,- of year per respondents. Collected and sold of used paper while were contributing to the collectors that 27,85 % to total income respondents of month; the minor collectors that 38,87 % to total income respondents of month and the major collectors that 68,96 % to total income respondents of month. The flow are marketing of used paper from collectors, minor collectors, major collectors and end at the used paper mill

Approach to equilibrium of diffusion in a logarithmic potential

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x ~ t^(1/2)) and a subdiffusive (x ~ t^{\gamma} with a given {\gamma} < 1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent which characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.Comment: 4 pages, 3 figures; Published versio

The late-time singularity inside non-spherical black holes

It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geometry of black holes indicate a more complicated structure is typical. While it seems likely that an observer falling into a black hole with the collapsing star encounters a crushing spacelike singularity, an observer falling in at late times generally reaches a null singularity which is vastly different in character to the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity. In the spirit of the classic work of BKL we present an asymptotic analysis of the null singularity inside a realistic black hole. Motivated by current understanding of spherical models, we argue that the Einstein equations reduce to a simple form in the neighborhood of the null singularity. The main results arising from this approach are demonstrated using an almost plane symmetric model. The analysis shows that the null singularity results from the blueshift of the late-time gravitational wave tail; the amplitude of these gravitational waves is taken to decay as an inverse power of advanced time as suggested by perturbation theory. The divergence of the Weyl curvature at the null singularity is dominated by the propagating modes of the gravitational field. The null singularity is weak in the sense that tidal distortion remains bounded along timelike geodesics crossing the Cauchy horizon. These results are in agreement with previous analyses of black hole interiors. We briefly discuss some outstanding problems which must be resolved before the picture of the generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi

Self force on particle in orbit around a black hole

We study the self force acting on a scalar charge in uniform circular motion around a Schwarzschild black hole. The analysis is based on a direct calculation of the self force via mode decomposition, and on a regularization procedure based on Ori's mode-sum regularization prescription. We find the four self-force at arbitrary radii and angular velocities (both geodesic and non-geodesic), in particular near the black hole, where general-relativistic effects are strongest, and for fast motion. We find the radial component of the self force to be repulsive or attractive, depending on the orbit.Comment: RevTeX, 4 pages, 4 Encapsulated PostScript figures. Submitted to Phys. Rev. Let

Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime

We present a procedure that allows the construction of the metric perturbations and electromagnetic four-potential, for gravitational and electromagnetic perturbations produced by sources in Kerr spacetime. This may include, for example, the perturbations produced by a point particle or an extended object moving in orbit around a Kerr black hole. The construction is carried out in the frequency domain. Previously, Chrzanowski derived the vacuum metric perturbations and electromagnetic four-potential by applying a differential operator to a certain potential $\Psi$. Here we construct $\Psi$ for inhomogeneous perturbations, thereby allowing the application of Chrzanowski's method. We address this problem in two stages: First, for vacuum perturbations (i.e. pure gravitational or electromagnetic waves), we construct the potential from the modes of the Weyl scalars $\psi_{0}$ or $\phi_{0}$. Second, for perturbations produced by sources, we express $\Psi$ in terms of the mode functions of the source, i.e. the energy-momentum tensor $T_{\alpha \beta}$ or the electromagnetic current vector $J_{\alpha}$.Comment: 20 pages; few typos corrected and minor modifications made; accepted to Phys. Rev.

Comparison of Different Anthropometric Measurements and Inflammatory Biomarkers

Introduction. Different anthropometric variables have been shown to be related to cardiovascular morbidity and mortality. Our aim was to compare the association between different anthropometric measurements and inflammatory status. Methods and results. A cross-sectional study design in which we analyzed the data collected during a five-year period in the Tel Aviv Medical Center Inflammation Survey (TAMCIS). Included in the study were 13,033 apparently healthy individuals at a mean (SD) age of 43. Of these, 8,292 were male and 4,741 female. A significant age-adjusted and multiple-adjusted partial correlation was noted between all anthropometric measurements and all inflammatory biomarkers. There was no significant difference in the correlation coefficients between different biomarkers and anthropometric variables. Conclusion. Most of the common used anthropometric variables are similarly correlated with inflammatory variables. The clinician can choose the variable that he/she finds easiest to use

Computing radiation from Kerr black holes: Generalization of the Sasaki-Nakamura equation

As shown by Teukolsky, the master equation governing the propagation of weak radiation in a black hole spacetime can be separated into four ordinary differential equations, one for each spacetime coordinate. (``Weak'' means the radiation's amplitude is small enough that its own gravitation may be neglected.) Unfortunately, it is difficult to accurately compute solutions to the separated radial equation (the Teukolsky equation), particularly in a numerical implementation. The fundamental reason for this is that the Teukolsky equation's potentials are long ranged. For non-spinning black holes, one can get around this difficulty by applying transformations which relate the Teukolsky solution to solutions of the Regge-Wheeler equation, which has a short-ranged potential. A particularly attractive generalization of this approach to spinning black holes for gravitational radiation (spin weight s = -2) was given by Sasaki and Nakamura. In this paper, I generalize Sasaki and Nakamura's results to encompass radiation fields of arbitrary integer spin weight, and give results directly applicable to scalar (s = 0) and electromagnetic (s = -1) radiation. These results may be of interest for studies of astrophysical radiation processes near black holes, and of programs to compute radiation reaction forces in curved spacetime.Comment: 10 pages, no figures, to appear in Phys. Rev. D. Present version updates the references, fixes some typos, and corrects some of the Introductory tex

QED blue-sheet effects inside black holes

The interaction of the unboundedly blue-shifted photons of the cosmic microwave background radiation with a physical object falling towards the inner horizon of a Reissner-Nordstrom black hole is analyzed. To evaluate this interaction we consider the QED effects up to the second order in the perturbation expansion. We then extrapolate the QED effects up to a cutoff, which we introduce at the Planckian level. (Our results are not sensitive to the cutoff energy.) We find that the energy absorbed by an infalling observer is finite, and for typical parameters would not lead to a catastrophic heating. However, this interaction would almost certainly be fatal for a human being, or other living organism of similar size. On the other hand, we find that smaller objects may survive the interaction. Our results do not provide support to the idea that the Cauchy horizon is to be regarded as the boundary of spacetime.Comment: 6 pages, LaTeX. To appear in Phys. Rev.