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Three Little Pieces for Computer and Relativity

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General Relativity, Cosmology and Astrophysics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 177))

Abstract

Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore fundamental problems in physics and astrophysics, and I present here three representative examples. These “three little pieces” reflect a personal choice and describe work that I am particularly familiar with. However, many more examples could be made.

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Notes

  1. 1.

    Much of what follows is taken from the discussion presented in Ref. [42].

  2. 2.

    The use of a simplified EOS does not influence particularly the results besides determining the precise time when the HMNS collapses to a black hole.

  3. 3.

    Turbulence in relativistic flows is an extremely challenging problem that is also essentially unexplored. Also in this case, the first relativistic simulations have been performed only recently [63, 64].

  4. 4.

    A similar magnetic-field configuration has been recently reproduced also when simulating the merger of a magnetised neutron star onto a black hole [65].

  5. 5.

    Much of what follows is taken from the discussion presented in Ref. [96].

  6. 6.

    Much of what follows is taken from the discussion presented in Refs. [128–130].

  7. 7.

    I should remark that other explanations have also been suggested. One of them makes use of the Landau-Lifshitz pseudotensor and explains the recoil in terms of the cancellation of large and opposite fluxes of momentum, part of which are “swallowed” by the black hole [131]. Another one is even more essential and explains the antikick is in terms of the spectral features of the signal at large distances, quite independently of the presence of a black-hole horizon [132]. All of these views serve the scope of providing an intuitive description and are in my view equally valid and useful.

  8. 8.

    Another appealing approach that has a similar goal of correlating strong-fields effects with (the visualization of) spacetime curvature has been proposed recently by the group in Caltech [145, 146].

  9. 9.

    Note that the meaningful definition of timeseries cross-correlations requires the introduction of a (gauge-dependent) relation between advanced and retarded time coordinates \(v\) and \(u\). In an initial value problem this is naturally provided by the \(3+1\) spacetime slicing by time \(t\).

  10. 10.

    The latter would properly require either characteristic or a hyperboloidal evolution approach.

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Acknowledgments

The work discussed here has been carried out in collaboration with M. A. Aloy, L. Baiotti, B. Giacomazzo, J. Granot, J. L. Jaramillo, C. Kouveliotou, R. P. Macedo K. Takami, whom I am indebted with. My thanks go also to the numerical-relativity group of the AEI for providing such a stimulating and productive environment. Support comes through the DFG grant SFB/Trans-regio 7 and “CompStar”, a Research Networking Programme of the ESF. The calculations have been performed on the clusters at the AEI.

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  1. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Potsdam, Germany

    Luciano Rezzolla

  2. Institut für Theoretische Physik, Frankfurt, Germany

    Luciano Rezzolla

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Correspondence to Luciano Rezzolla .

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  1. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Jiří Bičák

  2. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Tomáš Ledvinka

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Rezzolla, L. (2014). Three Little Pieces for Computer and Relativity. In: Bičák, J., Ledvinka, T. (eds) General Relativity, Cosmology and Astrophysics. Fundamental Theories of Physics, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-06349-2_19

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