Developing Tools for Multimessenger Gravitational Wave Astronomy

We present work in progress to craft open-sourced numerical tools that will enable the calculation of electromagnetic counterparts to gravitational waveforms: the {\tt GiRaFFE} (General Relativistic Force-Free Electrodynamics) code. {\tt GiRaFFE} numerically solves the general relativistic magnetohydrodynamics system of equations in the force-free limit, to model the magnetospheres surrounding compact binaries, in order (1) to characterize the nonlinear interaction between the source and its surrounding magnetosphere, and (2) to evaluate the electromagnetic counterparts of gravitational waves, including the production of collimated jets. We apply this code to various configurations of spinning black holes immersed in external magnetic field, in order to both test our implementation, and to explore the effect of strong gravitational field, high spins and of misalignment between the magnetic field lines an black hole spin, on the electromagnetic output and the collimation of Poynting jets. We will extend our work to collisions of black holes immersed in external magnetic field, which are prime candidates for coincident detection in both gravitational and electromagnetic spectra.Comment: 6 pages, 6 figures, MG15 proceeding

High gravitational waveform accuracy at null infinity

The aim of Cauchy-characteristic extraction is to provide a standardized waveform extraction tool for the numerical relativity community. The new extraction tool contains major improvements and corrections to previous versions and displays convergence. The error introduced by CCE satisfies the time domain criteria required for advanced LIGO data analysis. The importance of accurate waveforms to the gravitational wave astronomy has created an urgency for tools like CCE. The source code has been released to the public and is available as part of the Einstein Toolkit. We welcome applications to a variety of generic Cauchy codes implementing Einstein Equations of General Relativity

Simulating Magnetospheres with Numerical Relativity: The GiRaFFE code

Numerical Relativity is successful in the simulation of black holes and gravitational waves. In recent years, teams have tackled the problem of the interaction of gravitational and electromagnetic waves. We developed a new code for the numerical simulation of neutron and black hole magnetospheres, using the FFE formalism. We tested the performance of the new code named GiRaFFE, in 1D and 3D test suits. We will study magnetospheres, focusing on jets by the Blandford -Znajek mechanism

Gravitational-waveform extraction by the characteristic method

When a pair of black holes spiral into each other and collide, the very fabric of space-time shakes, and gravitational waves are created. Gravitational waves carry information about their source, and will increase our understanding of relativistic systems in astrophysics. Gravitational wave observatories like LIGO and Virgo are tuned to detect the emission of these waves from the inspiral and merger of binary black holes, neutron stars, supernovae, etc… Problem: any small vibration is detected, so templates are essential to discern the real signal. It is hard to compute the waveforms obtained from numerical simulations accurately – gravitational radiation is properly defined only at null infinity, but is estimated at a finite radius. Cauchy-Characteristic Extraction (CCE) is the most precise and refined “extraction” method available. The CCE technique connects the strong-field “Cauchy” evolution of the space-time near the merger to the “characteristic” evolution far from the merger – at null infinity, where the waveform is extracted and detectors measure it. We present a stand-alone “characteristic” waveform extraction tool that has demonstrated accuracy and convergence of the numerical error and is used by the numerical relativity groups for the unambiguous extraction of waveforms. We prove that the numerical error of CCE satisfies the standards of the detection criteria required for Advanced LIGO data analysis. The tool provides a means for accurate calculation of waveforms generated by evolution codes based upon different analytic and numerical formulations of the Einstein equations

Initial value problem for cohomogeneity one gradient Ricci solitons

Consider a smooth manifold $M$. Let $G$ be a compact Lie group which acts on $M$ with cohomogeneity one. Let $Q$ be a singular orbit for this action. We study the gradient Ricci soliton equation \Hess(u)+\Ric(g)+\frac{\epsilon}{2}g=0 around $Q$. We show that there always exists a solution on a tubular neighbourhood of $Q$ for any prescribed $G$-invariant metric $g_Q$ and shape operator $L_Q$, provided that the following technical assumption is satisfied: if $P=G/K$ is the principal orbit for this action, the $K$-representations on the normal and tangent spaces to $Q$ have no common sub-representations. We also show that the initial data are not enough to ensure uniqueness of the solution, providing examples to explain this indeterminacy. This work generalises the papaer "The initial value problem for cohomogeneity one Einstein metrics" of 2000 by J.-H. Eschenburg and McKenzie Y. Wang to the gradient Ricci solitons case

New Numerical Code for Black Hole Initial Data

There are no exact solutions of Einstein Equations that describes a bound system radiating gravitational waves. One needs to resort to numerical simulations, or analytical approximation methods. Current methods to constrained initial data exhibit junk radiation and ambiguities about constrained and free data. It was mathematically proved that given the correct initial data, Einstein equation will yield the expected solution

Learning to Teach and Teaching to Learn

New studies show that students do better in science classes that are taught interactively. We compare two different pedagogical approaches in teaching introductory physics: the lecture-based method, the active learning laboratories. We present the data on student performance on exams, homework, lab activities and tests, from 126 students taking the 200-level introductory physics courses at Marshall University, in Huntington, WV. We discuss the efficiency of each method in fostering the success of students in the introductory physics courses. We find that subtle differentiations can be implicitly detected in students’ exam grades, homework, participation, and choice of major

Adding Light to the Gravitational Waves on the Null Cone

Recent interesting astrophysical observations point towards a multi-messenger, multi-wavelength approach to understanding strong gravitational sources, like compact stars or black hole collisions, supernovae explosions, or even the big bang. Gravitational radiation is properly defined only at future null infinity, but usually is estimated at a finite radius, and then extrapolated. Our group developed a characteristic waveform extraction tool, implemented in an open source code, which computes the gravitational waves infinitely far from their source, in terms of compactified null cones, by numerically solving Einstein equation in Bondi space-time coordinates. The goal is extend the capabilities of the code, by solving Einstein-Maxwell\u27s equations together with the Maxwell\u27s equations, to obtain the energy radiated asymptotically at infinity, both in gravitational and electromagnetic waves. The purpose is to analytically derive and numerically calculate both the gravitational waves and the electromagnetic counterparts at infinity, in this characteristic framework. The method is to treat the source of gravitational and electromagnetic radiation as a black box, and therefore the code will be very flexible, with potentially large applicability

Towards Improved Accuracy of Gravitational Waves Extraction

Results in developing two new methods to improve the accuracy of waveform extraction using characteristic evolution. Numerical method: circular boundaries, with angular dissipation in the characteristic code. Geometric method: computation of Weyl tensor component Y4 at null infinity, in a conformally compactified treatment. Comparison and calibration in tests problems based upon linearized waves