String Propagation through a Big Crunch/Big Bang Transition

We consider the propagation of classical and quantum strings on cosmological space-times which interpolate from a collapsing phase to an expanding phase. We begin by considering the classical propagation of strings on space-times with isotropic and anisotropic cosmological singularities. We find that cosmological singularities fall into two classes, in the first class the string evolution is well behaved all the way up to the singularity, whilst in the second class it becomes ill-defined. Then assuming the singularities are regulated by string scale corrections, we consider the implications of the propagation through a `bounce'. It is known that as we evolve through a bounce, quantum strings will become excited giving rise to `particle transmutation'. We reconsider this effect, giving qualitative arguments for the amount of excitation for each class. We find that strings whose physical wavelength at the bounce is less that $\sqrt{\alpha'}$ inevitably emerge in highly excited states, and that in this regime there is an interesting correspondence between strings on anisotropic cosmological space-times and plane waves. We argue that long wavelength modes, such as those describing cosmological perturbations, will also emerge in mildly excited string scale mass states. Finally we discuss the relevance of this to the propagation of cosmological perturbations in models such as the ekpyrotic/cyclic universe.Comment: 15 page

String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $\tau$--coordinate is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$ are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are $r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $\tau$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure

String Instabilities in Black Hole Spacetimes

We study the emergence of string instabilities in $D$ - dimensional black hole spacetimes (Schwarzschild and Reissner - Nordstr\o m), and De Sitter space (in static coordinates to allow a better comparison with the black hole case). We solve the first order string fluctuations around the center of mass motion at spatial infinity, near the horizon and at the spacetime singularity. We find that the time components are always well behaved in the three regions and in the three backgrounds. The radial components are {\it unstable}: imaginary frequencies develop in the oscillatory modes near the horizon, and the evolution is like $(\tau-\tau_0)^{-P}$, $(P>0)$, near the spacetime singularity, $r\to0$, where the world - sheet time $(\tau-\tau_0)\to0$, and the proper string length grows infinitely. In the Schwarzschild black hole, the angular components are always well - behaved, while in the Reissner - Nordstr\o m case they develop instabilities inside the horizon, near $r\to0$ where the repulsive effects of the charge dominate over those of the mass. In general, whenever large enough repulsive effects in the gravitational background are present, string instabilities develop. In De Sitter space, all the spatial components exhibit instability. The infalling of the string to the black hole singularity is like the motion of a particle in a potential $\gamma(\tau-\tau_0)^{-2}$ where $\gamma$ depends on the $D$ spacetime dimensions and string angular momentum, with $\gamma>0$ for Schwarzschild and $\gamma<0$ for Reissner - Nordstr\o m black holes. For $(\tau-\tau_0)\to0$ the string ends trapped by the black hole singularity.Comment: 26pages, Plain Te

Panchromatic models of galaxies: GRASIL

We present here a model for simulating the panchromatic spectral energy distribution of galaxies, which aims to be a complete tool to study the complex multi-wavelength picture of the universe. The model take into account all important components that concur to the SED of galaxies at wavelengths from X-rays to the radio. We review the modeling of each component and provide several applications, interpreting observations of galaxy of different types at all the wavelengths.Comment: 10 pages, 4 figures, invited talk, to appear in the proceedings of: "The Spectral Energy Distribution of Gas-Rich Galaxies: Confronting Models with Data", Heidelberg, 4-8 Oct. 2004, eds. C.C. Popescu and R.J. Tuffs, AIP Conf. Ser., in pres

HAK DAN KEWAJIBAN PERUSAHAAN TERHADAP PEKERJA YANG BEKERJA MELEBIHI BATAS WAKTU

Pemerintah dan perusahaan mempunyai suatu sistem yakni simbiosis mutualisme, yang mana pemerintah Indonesia dan perusahaan sama-sama saling membutuhkan.Adanya perusahan, pengusaha, serta pekerja menciptakan adanya suatu hubungan kerja.Hubungan kerja yang baik akan tercipta jika adanya komunikasi yang baik antara perusahaan dengan pekerja. Komunikasi yang baik akan tercipta bila kontrak-kontrak dalam perjanjian kerja antara perusahaan dengan pekerja jelas,dimana terdapat keseimbangan (equilibrium) antara hak dan kewajiban perusahaan dengan hak dan kewajiban pekerja.  Dalam karya tulis ini penulis menggunakan penelitian hukum normatif dengan mengumpulkan peraturan perundang-undangan, dan literatur-literatur yang diperoleh sebagai bahan penunjang melalui studi kepustakaan. Hasil penelitian menunjukkan tentang apa hak dan kewajiban perusahaan terhadap pekerja yang bekerja melebihi batas waktu serta bagaimana bentuk perlindungan yang dapat dilakukan Pemerintah terhadap pekerja yang bekerja melebihi batas waktu. Pertama, Hak Perusahaan Terhadap Pekerja Yang Bekerja Melebihi Batas Waktu. Pada dasarnya setiap hak dan kewajiban telah diatur dalam suatu peraturan, baik itu umum maupun khususdiatur dalam Undang-Undang No.13 tahun 2003 tentang Ketenagakerjaan, khususnya pasal 77 sampai dengan pasal 85. Kedua, bentuk perlindungan yang dilakukan Pemerintah terhadap pekerja yang bekerja melebihi batas waktu yakni mulai dari tindakan Persiapan, Pengawasan, Penegakan dan juga Eksekusi.Selain keempat hal tersebut, bentuk perlindungan yang dapat dilakukan oleh pemerintah dengan mengadakan sosialisasi-sosialisasi di perusahaan tentang perlindungan pekerja sehingga baik perusahaan maupun pekerja dapat lebih mengerti dan lebih tahu akan adanya perlindungan pemerintah. Dari hasil penelitian dapat ditarik kesimpulan bahwa perusahaan berhak menuntut pekerja untuk melaksanakan pekerjaannya meski sudah melebihi jam kerja yang telah disepakati bersama dalam perjanjian kerja bersama ataupun kesepakatan khusus antara mereka, sedangkan yang menjadi kewajiban pengusaha atau perusahaan yang mempekerjakan pekerja/buruh harus membayar upah/gaji sebagai waktu lembur, kecuali ditentukan lain dalam perjanjian-perjanjian kerja bersama antara perusahaan dan pekerja/buruh. Bentuk Perlindungan yang dapat dilakukan pemerintah untuk melindungi pekerja yang bekerja melebihi batas waktu, adalah dengan melakukan Persiapan, Pengawasan dan Penegakan