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Showing 1 to 20 of 41 for “"Numerical Relativity"”.
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Numerical relativity in black hole spacetimes
… development of better techniques for the 3 + 1 numerical relativity study of black hole spacetimes. The main result of this thesis is the development of a new technique for avoiding singularities in such spacetimes. In this technique the slices are allowed to penetrate the black hole, but only …
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Gravitational wave extraction in numerical relativity
… of gravitational waves, a prediction of general relativity, is the merger of two black holes. To understand the generation and evolution of gravitational waves in such a case, extensive efforts have been made. One is the construction of highly sensitive detectors, which are likely to find …
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Applications of Numerical Relativity Beyond Astrophysics
Numerical relativity has proven to be a successful and robust tool for non-perturbative studies of gravitational phenomena in the highly dynamical and/or non-linear regime. Perhaps the most prominent achievement in the field is the breakthrough success in simulating the merger of binary black hole …
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Problems in cosmology and numerical relativity
… our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of …
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Numerical relativity in higher-dimensional space-times
The study of general relativity in higher dimensions has proven to be a fruitful avenue of research, revealing new applications of the theory, for instance in understanding strongly coupled quantum field theories through the holographic principle, and proposing an explanation of the hierarchy …
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Numerical relativity from a gauge theory perspective
I present a new method for numerical simulations of general relativistic systems that eliminates constraint violating modes without the need for constraint damping or the introduction of extra dynamical fields. The method is a type of variational integrator. It is based on a discretization of an …
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Axial symmetry and transverse trace-free tensors in numerical relativity
… an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both …
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Horizons, hyperbolic systems, and inner boundary conditions in numerical relativity
… closely connected open questions central to Numerical Relativity. These involve computational, numerical, theoretical, and physical aspects of evolving and understanding dynamical black hole spacetimes. We discuss finding and understanding the event horizon (EH), which is the causal boundary …
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Leveraging numerical relativity formulations for perturbative analysis: applications to quasinormal modes in general relativity
Numerical relativity has become an essential tool for studying highly dynamic and strong-field regimes of general relativity, enabling the simulation of compact object mergers, gravitational col-lapse, and other nonlinear phenomena. At the same time, perturbation theory provides a powerful …
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Bridging the gap between post-Newtonian theory and numerical relativity in gravitational-wave data analysis
… within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches …
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Accurate numerical relativity simulations of non-vacuumspace-times in two dimensions and applications to critical collapse
… stars and its description with methods of numerical relativity. In the first step, a new numerical framework the Whisky2D code will be developed, which solves the relativistic equations of hydrodynamics in axisymmetry. Therefore we consider an improved formulation of the conserved form of …
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Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity
This thesis is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type …
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Computing and analyzing gravitational radiation in black hole simulations using a new multi-block approach to numerical relativity
Numerical simulations of Kerr black holes are presented and the excitation of quasinormal modes is studied in detail. Issues concerning the extraction of gravitational waves from numerical space-times and analyzing them in a systematic way are discussed. A new multi-block infrastructure for solving …
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Oppenheimer-Snyder Collapse in the BSSN Formalism
In general relativity, problems with high degrees of symmetry often serve as illustrative simplifications of complicated scenarios. Oppenheimer-Snyder collapse, an exact solution for the gravitational collapse of a uniform, pressure-less ball of dust into a black hole, provides valuable insight …
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Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences
… waves are a consequence of the general theory of relativity. Direct detection of such waves will provide a wealth of information about physics, astronomy, and cosmology. A worldwide effort is currently underway to make the first direct detection of gravitational waves. The global network of …
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Uncovering gravitational wave signatures of modified theories of gravity and exotic matter
… its history. Using the foundations of general relativity (GR), we are now in the position of being able to model coalescence and merger of binary black holes and neutron stars, and understand how their modelled data fit within the manifold of our GW observations. A key ingredient in source …
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Numerical Modelling of the Dynamics and Gravitational Radiation of Compact Binaries in General Relativity
General relativity (GR), published in 1915 by Albert Einstein, is the modern description of gravity. GR poses that gravitational physics should be described by matter fields existing in a curved space described by differential geometry. The Newtonian gravitational force is viewed as a fictitious …
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Classical, quantum and numerical aspects of modified theories of gravity
… Lastly, we consider the application of numerical relativity techniques to f(R) gravity models. It is well-known that the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) modification of the Arnowitt-Deser-Misner formulation of General Relativity is suitable for the construction of numerical …
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Numerical MHD Simulations in Dynamical Spacetimes
Numerical relativity probes some of the most energetic events in the universe using computer simulations. These simulations must account for the relevant physical processes while, at the same time, evolving the spacetime according to Einstein's equations of general relativity. In particular, …
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