Wave-type equations of low regularity

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.Comment: 16 pages, 1 figur

Piecewise Conserved Quantities

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017 (http://www.springer.com/in/book/9783319516998

Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not existComment: 18 pages, accepted for publication in Brazilian J Physic

General Minimal Flavor Violation

A model independent study of the minimal flavor violation (MFV) framework is presented, where the only sources of flavor breaking at low energy are the up and down Yukawa matrices. Two limits are identified for the Yukawa coupling expansion: linear MFV, where it is truncated at the leading terms, and nonlinear MFV, where such a truncation is not possible due to large third generation Yukawa couplings. These are then resummed to all orders using non-linear sigma-model techniques familiar from models of collective breaking. Generically, flavor diagonal CP violating (CPV) sources in the UV can induce O(1) CPV in processes involving third generation quarks. Due to a residual U(2) symmetry, the extra CPV in B_d-\bar B_d mixing is bounded by CPV in B_s-\bar B_s mixing. If operators with right-handed light quarks are subdominant, the extra CPV is equal in the two systems, and is negligible in processes involving only the first two generations. We find large enhancements in the up type sector, both in CPV in D-\bar D mixing and in top flavor violation.Comment: 5 pages and no figure

Gravitational collapse with tachyon field and barotropic fluid

A particular class of space-time, with a tachyon field, \phi, and a barotropic fluid constituting the matter content, is considered herein as a model for gravitational collapse. For simplicity, the tachyon potential is assumed to be of inverse square form i.e., V(\phi) \sim \phi^{-2}. Our purpose, by making use of the specific kinematical features of the tachyon, which are rather different from a standard scalar field, is to establish the several types of asymptotic behavior that our matter content induces. Employing a dynamical system analysis, complemented by a thorough numerical study, we find classical solutions corresponding to a naked singularity or a black hole formation. In particular, there is a subset where the fluid and tachyon participate in an interesting tracking behaviour, depending sensitively on the initial conditions for the energy densities of the tachyon field and barotropic fluid. Two other classes of solutions are present, corresponding respectively, to either a tachyon or a barotropic fluid regime. Which of these emerges as dominant, will depend on the choice of the barotropic parameter, \gamma. Furthermore, these collapsing scenarios both have as final state the formation of a black hole.Comment: 18 pages, 7 figures. v3: minor changes. Final version to appear in GR

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit

Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms, additions, missing references welcome; v2: minor changes, added reference

Rotation-Measures across Parsec-scale Jets of FRI radio galaxies

We present the results of a parsec-scale polarization study of three FRI radio galaxies - 3C66B, 3C78 and 3C264 - obtained with the Very Long Baseline Array at 5, 8 and 15 GHz. Parsec-scale polarization has been detected in a large number of beamed radio-loud active galactic nuclei, but in only a handful of the relatively unbeamed radio galaxies. We report here the detection of parsec-scale polarization at one or more frequencies in all three FRI galaxies studied. We detect Faraday rotation measures of the order of a few hundred rad/m^2 in the nuclear jet regions of 3C78 and 3C264. In 3C66B polarization was detected at 8 GHz only. A transverse rotation measure gradient is observed across the jet of 3C78. The inner-jet magnetic field, corrected for Faraday rotation, is found to be aligned along the jet in both 3C78 and 3C264, although the field becomes orthogonal further from the core in 3C78. The RM values in 3C78 and 3C264 are similar to those previously observed in nearby radio galaxies. The transverse RM gradient in 3C78, the increase in the degree of polarization at the jet edge, the large rotation in the polarization angles due to Faraday rotation and the low depolarization between frequencies, suggests that a layer surrounding the jet with a sufficient number of thermal electrons and threaded by a toroidal or helical magnetic field is a good candidate for the Faraday rotating medium. This suggestion is tentatively supported by Hubble Space Telescope optical polarimetry but needs to be examined in a greater number of sources.Comment: Accepted for publication in The Astrophysical Journal, March 2009 - 20 v694 issu

Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at √s = 7 TeV with the ATLAS detector

This paper presents a measurement of the cross-section for high transverse momentum W and Z bosons produced in pp collisions and decaying to all-hadronic final states. The data used in the analysis were recorded by the ATLAS detector at the CERN Large Hadron Collider at a centre-of-mass energy of √s = 7 TeV;{\rm Te}{\rm V}$and correspond to an integrated luminosity of$4.6\;{\rm f}{{{\rm b}}^{-1}}$. The measurement is performed by reconstructing the boosted W or Z bosons in single jets. The reconstructed jet mass is used to identify the W and Z bosons, and a jet substructure method based on energy cluster information in the jet centre-of-mass frame is used to suppress the large multi-jet background. The cross-section for events with a hadronically decaying W or Z boson, with transverse momentum${{p}_{{\rm T}}}\gt 320\;{\rm Ge}{\rm V}$and pseudorapidity$|\eta |\lt 1.9$, is measured to be${{\sigma }_{W+Z}}=8.5\pm 1.7$ pb and is compared to next-to-leading-order calculations. The selected events are further used to study jet grooming techniques