Introduction to 3+1 Numerical Relativity

By M. Alcubierre. 2008

688 citations recorded by the source corpus.

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In Astronomy and Astrophysics

Citations in the corpus

GRChombo: Numerical relativity with adaptive mesh refinement (2015, methodology): “e of the eld, ˚, and . Our evolution is carried out using the full 3+1 BSSN equations, without assuming or adapting coordinates to spherical symmetry. We are able to replicate the results obtained in [69], subject to some minor dierences due to the fact that we evolve with the puncture gauge rather ”
The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics (2011, methodology): “ of numerical relativity and GR hydrodynamics, including the underlying dierential geometry and tensor analysis. Detailed introductions to numerical relativity have recently been given by Alcubierre [120], Baumgarte & Shapiro [121], and Centrella et al. [122]. GR hydrodynamics has been reviewed ”
Recent developments in gravitational collapse and spacetime singularities (2011, result): “ng E2 be less divergent as R→ 0 as compared to the term involving ℓ2. This then gives the following results for R<Rb: Stable circular orbits : M0 ≤ 2/3, (80) Unstable circular orbits : M0 >2/3. (81) Depending on the value of M0, either all circular orbits in the interior of this object are sta”
Numerical Relativity: Solving Einstein's Equations on the Computer (2011, background): “Theﬁrsttextbookdevoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]).”
Black-hole binaries, gravitational waves, and numerical relativity (2010, methodology): “alfoundations underlying currentblack-holemerger simulations, highlighting the key issues involved in achieving successful evolutions. For more detailed treatments, we direct the interested reader to Alcubierre (2008) or (Gourgoulhon, 2007). A. Einstein’sEquations The central task of numerical relat”
Numerical methods for finding stationary gravitational solutions (2015, background): “As it stands, without matter, the issue of finding initial data is well understood [4, 7, 72].”
Superradiant instabilities in astrophysical systems (2012, background): “[63]) and consider the background spacetime in generic 3þ 1 form”
The black hole accretion code (2016, background): “This leads to the timelike unit vector normal to the slices Σt [40, 85]”
Gravitational waves from neutron star mergers and their relation to the nuclear equation of state (2019, background): “sical information, gauges play an important role in numerical stability, for example in countering grid stretching. For explanations on all these issues, well-written textbooks are nowadays available [98, 99, 100, 101, 102]. Despite such diculties, nowadays the number of research groups with their o”