Numerical relativity in spherical coordinates with the Einstein Toolkit

Vassilios Mewes, Yosef Zlochower, Manuela Campanelli, Ian Ruchlin, Zachariah B. Etienne, Thomas W. Baumgarte

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

Original languageEnglish
Article number084059
JournalPhysical Review D
Volume97
Issue number8
DOIs
StatePublished - Apr 30 2018
Externally publishedYes

Funding

The authors would like to thank Emanuele Berti for useful discussions and Dennis B. Bowen for a careful reading of the manuscript. We gratefully acknowledge the National Science Foundation (NSF) for financial support from Grants No. OAC-1550436, No. AST-1516150, No. PHY-1607520, No. PHY-1305730, No. PHY-1707946, No. PHY-1726215, to RIT, as well as Grants No. PHYS-1402780 and No. PHYS-1707526 to Bowdoin College. V. M. also acknowledges partial support from AYA2015-66899-C2-1-P, and RIT for the FGWA SIRA initiative. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) [allocation TG-PHY060027N], which is supported by NSF Grant No. ACI-1548562, and by the BlueSky Cluster at RIT, which is supported by NSF Grants No. AST-1028087, No. PHY-0722703, and No. PHY-1229173. Funding for computer equipment to support the development of SENR/NRPy+ was provided in part by NSF EPSCoR Grant No. OIA-1458952 to West Virginia University. Computational resources were also provided by the Blue Waters sustained-petascale computing NSF Project No. OAC-1516125.

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