Implementation of the dual foliation generalized harmonic gauge formulation with application to spherical black hole excision

Bhattacharyya, Maitraya K.; Hilditch, David; Nayak, K. Rajesh; Renkhoff, Sarah; Rüter, Hannes R.; Bruegmann, Bernd

doi:10.1103/physrevd.103.064072

Cited by 7 publications

(3 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also expect that finer control of constraint violation and coordinates would be of benefit. For the latter we have already implemented the DF-GHG formulation [47][48][49], but the complete generalization of the outer boundary conditions to that setting is ongoing. A further question, already mentioned in passing in [30], is whether or not the curvature spikes we observe have anything to do with BKL behavior.…”

Section: Summary and Discussionmentioning

confidence: 99%

Evolution of Brill waves with an adaptive pseudospectral method

Fernández,

Renkhoff,

Cors

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Section: Summary and Discussionmentioning

confidence: 99%

Evolution of Brill waves with an adaptive pseudospectral method

Fernández,

Renkhoff,

Cors

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

“…where δ is associated to the determinant of the metric in the (t, r) plane. We will be using the Kerr-Schild gauge [35] with r areal radius and C − = −1, and work with the renormalized variable…”

Section: Massless Minimally Coupled Scalar Field Collapsementioning

confidence: 99%

Curvature and dynamical spacetimes: can we peer into the quantum regime?

Cardoso

Hilditch²,

Marouda³

et al. 2023

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

Stationary compact astrophysical objects such as black holes and neutron stars behave as classical systems from the gravitational point of view. Their (observable) curvature is everywhere ``small''. Here we investigate whether mergers of such objects, or other strongly dynamical spacetimes such as collapsing configurations, may probe the strong-curvature regime of General Relativity. Our results indicate that dynamical black hole spacetimes always result in a modest increase $\sim 3$ in the Kretschmann scalar, relative to the stationary state. In contrast, we find that the Kretschmann scalar can dynamically increase by orders of magnitude, during the gravitational collapse of scalar fields, and that the (normalized) peak curvature does {\it not} correspond to that of the critical solution. Nevertheless, without fine tuning of initial data, this increase lies far below that needed to render quantum-gravity corrections important.

show abstract

“…First-order formulations are particularly important when solving the EFE using finite elements or pseudospectral methods [36], see Refs. [34,37,38].…”

Section: Introductionmentioning

confidence: 99%

New first-order formulation of the Einstein equations exploiting analogies with electrodynamics

et al. 2022

View full text Add to dashboard Cite

The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics and magnetohydrodynamics have benefited from a large number of evolution schemes that are able to enforce these constraints and are easily applicable to curvilinear coordinates, unstructured meshes, or N-body simulations, many of these techniques cannot be straightforwardly applied to existing formulations of the Einstein equations. We develop a 3 þ 1 a formulation of the Einstein equations that shows a striking resemblance to the equations of relativistic magnetohydrodynamics and to electrodynamics in material media. The fundamental variables of this formulation are the frame fields, their exterior derivatives, and the Nester-Witten and Sparling forms. These mirror the roles of the electromagnetic four potential, the electromagnetic field strengths, the field excitations and the electric current. The role of the lapse function and shift vector, corresponds exactly to that of the scalar electric potential. The formulation is manifestly first order and fluxconservative, which makes it suitable for high-resolution shock capturing schemes and finite-element methods. Being derived as a system of equations in exterior derivatives, it is directly applicable to any coordinate system and to unstructured meshes, and leads to a natural discretization potentially suitable for the use of machine-precision constraint propagation techniques such as the Yee algorithm and constrained transport. Due to these properties, we expect this new formulation to be beneficial in simulations of many astrophysical systems, such as binary compact objects and core-collapse supernovae as well as cosmological simulations of the early Universe.

show abstract

Implementation of the dual foliation generalized harmonic gauge formulation with application to spherical black hole excision

Cited by 7 publications

References 41 publications

Evolution of Brill waves with an adaptive pseudospectral method

Evolution of Brill waves with an adaptive pseudospectral method

Curvature and dynamical spacetimes: can we peer into the quantum regime?

New first-order formulation of the Einstein equations exploiting analogies with electrodynamics

Contact Info

Product

Resources

About