اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExcision and avoiding the use of boundary conditions in numerical relativity
220
0
0.0
(
0
)
تأليف
Justin L. Ripley
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike with respect to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry.
قيم البحث
اقرأ أيضاً
In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einsteins equations. We show that there are a number of physically interesting cases which cannot be treated using distribution theory bu
t require a more general concept. We describe a mathematical theory of nonlinear generalised functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einsteins equations.
We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detectio
n, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infi
nity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to extract the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.
We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries co
ntaining black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star--neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible. Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.
The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to achieving glo
bal simulations of physical usefulness are of an analytic/computational nature. We present here some examples of how analytic insight can lend useful guidance for the improvement of numerical approaches.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
