On the Nutku—Halil solution for colliding impulsive gravitational waves

1984 ◽  
Vol 396 (1810) ◽  
pp. 55-74 ◽  
Keyword(s):  
Ab Initio ◽  
Gravitational Waves ◽  
Killing Vector ◽  
Single Equation ◽  
Kerr Solution ◽  
Linear Solution ◽  
Killing Vectors ◽  
Ernst Equation ◽  
Set Up ◽  
Explicit Expressions

The equations appropriate for space-times with two space-like Killing-vectors are set up, ab initio , and explicit expressions for the components of the Riemann, the Ricci, and the Einstein tensors in a suitable tetrad-frame are written. The equations for the vacuum are reduced to a single equation of the Ernst type. It is then shown that the simplest linear solution of the Ernst equation leads directly to the Nutku-Halil solution for two colliding impulsive gravitational waves with uncorrelated polarizations. Thus, in some sense, the Nutku-Halil solution occupies the same place in space-times with two space-like Killing-vectors as the Kerr solution does in space—times with one time-like and one space-like Killing-vector. The Nutku-Halil solution is further described in a Newman-Penrose formalism; and the expressions for the Weyl scalars, in particular, make the development of curvature singularities manifest. Finally, a theorem analogous to Robinson’s theorem (but much less strong) is proved for space-times with two space-like Killing-vectors.

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

scholarly journals The geometry of null-like disformal transformations

2019 ◽  
Vol 16 (11) ◽  
pp. 1950180 ◽  
Author(s):  
I. P. Lobo ◽  
G. G. Carvalho
Keyword(s):  
Vector Field ◽  
Conformal Transformation ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Spinor Structure ◽  
Schwarzschild Metric ◽  
Killing Vectors ◽  
Symmetry Properties ◽  
Geometric Objects

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

2021 ◽  
Author(s):  
Ata Donmez ◽  
Ahmet Kahraman
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Behavior ◽  
Severity Index ◽  
System Response ◽  
Gear Pair ◽  
Computationally Efficient ◽  
Linear Solution ◽  
Set Up ◽  
The Impact ◽  
Gear Rattle

Abstract Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

Conformational Structure of Chloromethyldichlorophosphines

2002 ◽  
Vol 57 (6-7) ◽  
pp. 333-336
Author(s):  
Evgenii A. Romanenko ◽  
Alexander M. Nesterenko
Keyword(s):  
Experimental Data ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Electron Correlation ◽  
Basis Set ◽  
Conformational Structure ◽  
Gauche Conformation ◽  
Nuclear Quadrupole ◽  
Set Up ◽  
Good Agreement

IThe 35Cl nuclear quadrupole resonances (77 K) and ab initio calculations of trichloromethyldichlorophosphine () show that it exists in the chess conformation form. The barrier to internal rotation about the P-C bond in I at the RHF/6-31++ G(d,p) level equals to 38.1 kJ mol-1. In chloromethyldichlorophosphine (II) the extension of the basis set up to the RHF/6-311++G(df, pd) level does not improve the description of the most preferable gauche-conformation; only if electron correlation (at the MP2 level) is taken into account the results are in a good agreement with experimental data.

scholarly journals Θεωρία νηματικών δεσμών και η εφαρμογή τους στις συμμετρίες

2019 ◽  
Author(s):  
Λεωνίδας Καρπαθόπουλος
Keyword(s):  
Scalar Field ◽  
Killing Vector ◽  
Dynamical Symmetry ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Conformal Killing Vectors ◽  
Scalar Field Cosmology

Η συμμετρία μίας διαφορικής εξίσωσης αποτελεί ένα σημειακό μετασχηματισμό ο οποίο αφήνει αναλλοίωτες την οικογένεια των λύσεων της διαφορικής εξίσωσης. Υπάρχουν τρεις βασικοί τύποι συμμετριών των διαφορικών εξισώσεων: Οι συμμετρίες Lie, οι Noether και οι Cartan. Εάν ο σημειακός μετασχηματισμός λαμβάνει χώρα στο θεσεογραφικό χώρο τότε η συμμετρία αποτελεί μία σημειακή συμμετρία, διαφορετικά καλείται δυναμική συμμετρία (dynamical symmetry). Εκτός από αυτούς τους τύπους των συμμετριών των διαφορικών εξισώσεων υπάρχει και ένας ακόμα τύπος γεωμετρικών συμμετριών προερχόμενες από τα διανυσματικά πεδία X τα οποία αποτελούν λύση των εξισώσεων της μορφής L_X A= B, όπου το A αποτελεί ένα γεωμετρικό αντικείμενο το οποίο καθορίζεται μέσω της μετρικής και το B είναι ένα τανυστικό πεδίο με τον ίδιο αριθμό και τύπο δεικτών με αυτούς του A. Τέτοιοι τύποι συμμετριών αποτελούν τα διανυσματικά πεδία Killing, (Killing vectors), το ομοθετικό διανυσματικό πεδιο, (Homothetic Killing vector), τα σύμμορφα διανυσματικά πεδία Killing, (Conformal Killing vectors) κ.α.. Σε αυτή τη διδακτορική διατριβή μελετώνται οι συμμετρίες Lie, Noether και Cartan των εξισώσεων κίνησης, διαφορικών εξισώσεων δεύτερης τάξης ενός δυναμικού συστήματος. Επεκτείνουμε προηγούμενα αποτελέσματα κατά τα οποία οι συμμετρίες των διαφορικών εξισώσεων συσχετίζονται με τις γεωμετρικές συμμετρίες της μετρικής όπως αυτή καθορίζεται μέσω της κινητικής ενέργειας (kinetic metric) στην περίπτωση μη αυτόνομων δυναμικών συστημάτων που παρουσιάζουν γραμμική απόσβεση. Εφαρμόζουμε τις συμμετρίες Cartan στην Κοσμολογία βαθμωτού πεδίου (scalar field Cosmology) χρησιμοποιώντας τη δισδιάστατη minisuperspace συνάρτηση Lagrange και προσδιορίζουμε τις συναρτήσεις Δυναμικού για τις οποίες τα επαγόμενα δυναμικά συστήματα είναι ολοκληρώσιμα. Σε κάθε περίπτωση προσδιορίζουμε την αντίστοιχη αναλυτική λύση. Τέλος, αναπτύσσεται μια συστηματική μεθοδολογία μέσω της οποίας προσδιορίζονται όλα τα τετραγωνικά πρώτα ολοκληρώματα διαφορικών εξισώσεων, χωρίς τη χρήση συμμετριών αλλά χρησιμοποιώντας γεωμετρικές μεθόδους. Ακόμα, δείχνουμε πως κάθε τέτοιο πρώτο ολοκλήρωμα μπορεί να προκύψει ως ένα γενικευμένο ολοκλήρωμα Noether μέσω της χρήσης του αντίστροφου Θεωρήματος της Noether. Γι αυτό τον σκοπό εφαρμόζουμε την παραπάνω μεθοδολογία σε συγκεκριμένα παραδείγματα.

SHADE3server: a streamlined approach to estimate H-atom anisotropic displacement parameters using periodicab initiocalculations or experimental information

2014 ◽  
Vol 47 (6) ◽  
pp. 2100-2104 ◽  
Author(s):  
Anders Østergaard Madsen ◽  
Anna A. Hoser
Keyword(s):  
Hydrogen Bonds ◽  
Neutron Diffraction ◽  
Ab Initio ◽  
Experimental Information ◽  
Neutron Diffraction Data ◽  
New Methods ◽  
Anisotropic Displacement Parameters ◽  
Proton Sponges ◽  
Set Up ◽  
Better Than

A major update of theSHADEserver (http://shade.ki.ku.dk) is presented. In addition to all of the previous options for estimating H-atom anisotropic displacement parameters (ADPs) that were offered bySHADE2, the newest version offers two new methods. The first method combines the original translation–libration–screw analysis with input from periodicab initiocalculations. The second method allows the user to input experimental information from spectroscopic measurements or from neutron diffraction experiments on related structures and utilize this information to evaluate ADPs of H atoms. Tools are provided to set up theab initiocalculations and to derive the internal motion from the calculations. The new server was tested on a range of compounds where neutron diffraction data were available. In most cases, the results are significantly better than previous estimates, and for strong hydrogen bonds in proton sponges, theab initiocalculations become crucial.

Experimental Gas Phase 1H NMR Spectra and Basis Set Dependence of ab initio GIAOMO Calculations of 1H and 13C NMR Absolute Shieldings and Chemical Shifts of Small Hydrocarbons

2004 ◽  
Vol 59 (10) ◽  
pp. 1153-1176 ◽  
Author(s):  
Thomas Zuschneid ◽  
Holger Fischer ◽  
Thomas Handel ◽  
Klaus Albert ◽  
Günter Häfelinger
Keyword(s):  
Ab Initio ◽  
Gas Phase ◽  
Nmr Spectra ◽  
Chemical Shifts ◽  
Basis Set ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Phase Measurements ◽  
H Nmr ◽  
Set Up

AbstractHigh-resolution gas phase measurements of 1H NMR spectra at 400 MHz and atmospheric pressure of seven small hydrocarbons are presented. The developed new method and the experimental set-up are described. Ab initio GIAO MO calculations of 1H and 13C NMR absolute shieldings on the HF, MP2 and B3LYP levels using 25 standard gaussian basis sets are reported for these hydrocarbons, based on experimental re distances. The measured gas phase 1H chemical shifts have been converted to an absolute σ0 shielding scale by use of the literature shielding of methane. These and gas phase 13C literature values have been transferred with literature ZPV data to estimated σeexp shieldings which are used to evaluate the basis set dependence of the calculated σe shieldings utilizing linear least squares regressions. Exponential extrapolations of Dunning basis set calculations allow the determination of basis set limits for 1H and 13C shieldings. 1H and 13C chemical shifts have been derived from the HF calculated shieldings with shieldings of TMS which has been geometry optimized and GIAO calculated in each basis. Standard deviations (esd) as low as 0.09 ppm for 1H and 0.76 ppm for 13C calculations have been obtained.The statistically best basis set for simultaneous calculation of 1H and 13C absolute shieldings or relative shifts is 6-311G* within the HF and B3LYP methods. Aiming for highest accuracy and precision, 1H and 13C have to be treated separately. In this case, best results are obtained using MP2/6-311G** or higher for 1H shieldings and MP2/cc-pVTZ for 13C shieldings.

scholarly journals SPACE-TIME DEFORMATIONS AS EXTENDED CONFORMAL TRANSFORMATIONS

2008 ◽  
Vol 05 (02) ◽  
pp. 185-195 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
C. STORNAIOLO
Keyword(s):  
Perturbation Theory ◽  
Gravitational Waves ◽  
Space Time ◽  
Dimensional Manifold ◽  
Conformal Transformations ◽  
Approximate Symmetries ◽  
Killing Vectors ◽  
Definition Of ◽  
Small Deformations

A definition of space-time metric deformations on an n-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation theory giving a natural picture by which gravitational waves are described by small deformations of the metric. As further result, deformations can be related to approximate Killing vectors (approximate symmetries) by which it is possible to parameterize the deformed region of a given manifold. The perspectives and some possible physical applications of such an approach are discussed.

scholarly journals Double Ernst Solution in Einstein–Kalb–Ramond Theory

1997 ◽  
Vol 12 (22) ◽  
pp. 1629-1636 ◽  
Author(s):  
Alfredo Herrera-Aguilar ◽  
Oleg Kechkin
Keyword(s):  
Dimensional Case ◽  
Kerr Solution ◽  
Two Dimensional ◽  
Killing Vectors ◽  
Dipole Configuration

The Kähler formulation of five-dimensional Einstein–Kalb–Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer–Neugebauer-like maps are established for the two-dimensional case. A class of solutions constructed on the basis of the double Ernst one is obtained. It is shown that the double Kerr solution corresponds to a EKR dipole configuration with horizon.

scholarly journals Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Nancy Aggarwal ◽  
Odylio D. Aguiar ◽  
Andreas Bauswein ◽  
Giancarlo Cella ◽  
Sebastian Clesse ◽  
...  
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
High Frequency ◽  
White Paper ◽  
Beyond The Standard Model ◽  
Frequency Range ◽  
Ultra High Frequency ◽  
The Standard Model ◽  
Challenges And Opportunities ◽  
Set Up

AbstractThe first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This white paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band, with a particular focus on Ultra High-Frequency Gravitational Waves (UHF-GWs), covering the MHz to GHz range. The absence of known astrophysical sources in this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising gravitational sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of the workshop “Challenges and opportunities of high-frequency gravitational wave detection” held at ICTP Trieste, Italy in October 2019, that set up the stage for the recently launched Ultra-High-Frequency Gravitational Wave (UHF-GW) initiative.

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