Self-force with (3+1) codes: a primer for numerical relativists

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $< 1$. We also demonstrate consistency between $t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.Comment: 23 pages, 13 figure

Accurate evolutions of inspiralling and magnetized neutron-stars: equal-mass binaries

By performing new, long and numerically accurate general-relativistic simulations of magnetized, equal-mass neutron-star binaries, we investigate the role that realistic magnetic fields may have in the evolution of these systems. In particular, we study the evolution of the magnetic fields and show that they can influence the survival of the hypermassive-neutron star produced at the merger by accelerating its collapse to a black hole. We also provide evidence that even if purely poloidal initially, the magnetic fields produced in the tori surrounding the black hole have toroidal and poloidal components of equivalent strength. When estimating the possibility that magnetic fields could have an impact on the gravitational-wave signals emitted by these systems either during the inspiral or after the merger we conclude that for realistic magnetic-field strengths B<~1e12 G such effects could be detected, but only marginally, by detectors such as advanced LIGO or advanced Virgo. However, magnetically induced modifications could become detectable in the case of small-mass binaries and with the development of gravitational-wave detectors, such as the Einstein Telescope, with much higher sensitivities at frequencies larger than ~2 kHz.Comment: 18 pages, 10 figures. Added two new figures (figures 1 and 7). Small modifications to the text to match the version published on Phys. Rev.

Chemical kinetics modelling study on fuel autoignition in internal combustion engines

Chemical kinetics has been widely acknowledged as a fundamental theory in analysis of chemical processes and the corresponding reaction outputs and rates. The study and application of chemical kinetics thus provide a simulation tool to predict many characteristics a chemical process. Oxidation of hydrocarbon fuels applied in internal combustion engines is a complex chemical process involving a great number of a series of chained reaction steps and intermediate and simultaneous species. Symbolic and Numerical description of such a chemical process leads to the development and application of chemical kinetics models. The up-to-date application of chemical kinetics models is to the simulation of autoignition process in internal combustion engines. Multi-zone thermodynamic combustion modelling has been regarded as a functional simulation approach to studying combustion process in IC engines as a decent compromise between computation accuracy and efficiency. Integration of chemical kinetics models into multi-zone models is therefore a potential modelling method to investigate the chemical and physical processes of autoignition in engine combustion. This research work has been therefore concerned with the development, validation and application of multi-zone chemical kinetic engine models in the simulation of autoignition driven combustion in SI and HCCI engines. The contribution of this work is primarily made to establish a mathematical model based on the underlying physical and chemical principles of autoignition of the fuel-air mixture in SI and HCCI engines. Then, a computer code package has been developed to numerically solve the model. The derived model aims at improving the understanding of autoignition behaviour under engine-like conditions and providing an investigative tool to autoignition characteristics. Furthermore, as part of the ongoing program in the research of free piston engines, the results of this work will significantly aid in the investigation and simulation of the constant volume autoignition applied in free piston engines

Chemical kinetics modelling study on fuel autoignition in internal combustion engines

Chemical kinetics has been widely acknowledged as a fundamental theory in analysis of chemical processes and the corresponding reaction outputs and rates. The study and application of chemical kinetics thus provide a simulation tool to predict many characteristics a chemical process. Oxidation of hydrocarbon fuels applied in internal combustion engines is a complex chemical process involving a great number of a series of chained reaction steps and intermediate and simultaneous species. Symbolic and Numerical description of such a chemical process leads to the development and application of chemical kinetics models. The up-to-date application of chemical kinetics models is to the simulation of autoignition process in internal combustion engines. Multi-zone thermodynamic combustion modelling has been regarded as a functional simulation approach to studying combustion process in IC engines as a decent compromise between computation accuracy and efficiency. Integration of chemical kinetics models into multi-zone models is therefore a potential modelling method to investigate the chemical and physical processes of autoignition in engine combustion. This research work has been therefore concerned with the development, validation and application of multi-zone chemical kinetic engine models in the simulation of autoignition driven combustion in SI and HCCI engines. The contribution of this work is primarily made to establish a mathematical model based on the underlying physical and chemical principles of autoignition of the fuel-air mixture in SI and HCCI engines. Then, a computer code package has been developed to numerically solve the model. The derived model aims at improving the understanding of autoignition behaviour under engine-like conditions and providing an investigative tool to autoignition characteristics. Furthermore, as part of the ongoing program in the research of free piston engines, the results of this work will significantly aid in the investigation and simulation of the constant volume autoignition applied in free piston engines

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review article originally published in 2002; available on-line at http://www.livingreviews.org

Compact binary evolutions with the Z4c formulation

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to truncation errors are between one and three orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of four smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the ADM mass from surface integrals. For equal-mass non-spinning binary puncture black hole evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of two smaller. In the same evolutions we find that away from the punctures the Hamiltonian constraint violation is reduced by between one and two orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirm earlier results in spherical symmetry. The boundary conditions avoid spurious and non-convergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge

From Equal-mass to Extreme-mass-ratio Binary Inspirals: Simulation Tools for Next Generation Gravitational Wave Detectors

Current numerical codes can successfully evolve similar-mass binary black holes systems, and these numerical waveforms contributed to the success of the LIGO Collaboration\u27s detection of gravitational waves. LIGO requires high resolution numerical waveforms for detection and parameter estimation of the source. Great effort was expended over several decades to produce the numerical methods used today. However, future detectors will require further improvements to numerical techniques to take full advantage of their detection capabilities. For example, the Laser Interferometer Space Antenna (LISA) will require higher resolution simulations of similar-mass-ratio systems than LIGO. LISA will also be able to detect extreme-mass-ratio inspiral (EMRI) systems. The EMRIs require a perturbative approach, and these techniques lags far behind numerical relativity. Improvements to current similar-mass codes and development of EMRI codes are necessary for future gravitational wave studies. My first project improved the underlying framework of the Einstein Toolkit (ETK). I improved the ETK by implementing a new method for scheduling ghost zone synchronization and application of boundary conditions. The new approach reduces inter-processor communication overhead and improves the user experience. These improvements to the ETK improve its computational efficiency and enable users to more easily contribute to the collaboration. I also implemented the first-order perturbative evolution equations for the EMRI system. This work builds on code for simulating the toy model of a particle with a scalar charge. This code differs from other time domain codes by evolving self-consistently by using the full self-force to provide a highly accurate waveform. I extended this code to be capable of evolving gravitational fields. I implemented even and odd master functions for the Regge-Wheeler-Zerilli gauge and verified convergence of the energy and angular momentum fluxes to frequency domain results. I derived and implemented evolution equations in the Lorenz gauge. The evolution equations in the Lorenz gauge are considerably more complicated than the Regge-Wheeler-Zerilli gauge, and my code currently does not match the expected results. Still, my code is stable at long times and has effective constraint damping. These two codes represent significant progress towards the self-consistent evolution of the EMRI system at first order