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MALBEC: a new CUDA-C ray-tracer in general relativity

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Abstract

A new CUDA-C code for tracing orbits around non-charged black holes is presented. This code, named MALBEC, take advantage of the graphic processing units and the CUDA platform for tracking null and timelike test particles in Schwarzschild and Kerr. Also, a new general set of equations that describe the closed circular orbits of any timelike test particle in the equatorial plane is derived. These equations are extremely important in order to compare the analytical behavior of the orbits with the numerical results and verify the correct implementation of the Runge–Kutta algorithm in MALBEC. Finally, other numerical tests are performed, demonstrating that MALBEC is able to reproduce some well-known results in these metrics in a faster and more efficient way than a conventional CPU implementation.

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References

  1. The LSC: Advanced ligo. Class. Quantum Grav. 32(7), 074001 (2015)

    Article  ADS  Google Scholar 

  2. Sundararajan, P.A., Khanna, G., Hughes, S.: Binary black hole merger gravitational waves and recoil in the large mass ratio limit. Phys. Rev. D 81(10), 104009 (2010)

    Article  ADS  Google Scholar 

  3. Chandrasekhar, S.: The Mathematical Theory of Black Holes, vol. 69. Oxford University Press, Oxford (1998)

    MATH  Google Scholar 

  4. Jefremov, P.I., Yu Tsupko, O., Bisnovatyi-Kogan, G.S.: Innermost stable circular orbits of spinning test particles in schwarzschild and kerr space-times. Phys. Rev. D 91(12), 124030 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  5. Pugliese, D., Quevedo, H., Ruffini, R.: Motion of charged test particles in Reissner–Nordström spacetime. Phys. Rev. D 83(10), 104052 (2011)

    Article  ADS  Google Scholar 

  6. Levin, J., Perez-Giz, G.: A periodic table for black hole orbits. Phys. Rev. D 77(10), 103005 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  7. Fujita, R., Hikida, W.: Analytical solutions of bound timelike geodesic orbits in kerr spacetime. Class. Quantum Grav. 26(13), 135002 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Mino, Y.: Perturbative approach to an orbital evolution around a supermassive black hole. Phys. Rev. D 67(8), 084027 (2003)

    Article  ADS  Google Scholar 

  9. Warburton, N., Barack, L., Sago, N.: Isofrequency pairing of geodesic orbits in kerr geometry. Phys. Rev. D 87(8), 084012 (2013)

    Article  ADS  Google Scholar 

  10. Vincent, F.H., Paumard, T., Gourgoulhon, E., Perrin, G.: Gyoto: a new general relativistic ray-tracing code. Class. Quantum Grav 28(22), 225011 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Kuchelmeister, D., Müller, T., Ament, M., Wunner, G., Weiskopf, D.: Gpu-based four-dimensional general-relativistic ray tracing. Comput. Phys. Commun. 183(10), 2282–2290 (2012)

    Article  ADS  Google Scholar 

  12. The Compute Unified Device Architecture CUDA. NVIDIA Corporation 2018. http://developer.nvidia.com

  13. Gourgoulhon, E.: 3 + 1 Formalism in General Relativity: Bases of Numerical Relativity, vol. 846. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  14. York Jr., J.W.: Kinematics and dynamics of general relativity. In: Smarr, L.L. (ed.) Sources of Gravitational Radiation, pp. 83–126. Cambridge University Press, Cambridge (1979)

    Google Scholar 

  15. van Holten, J.W.: Gravitational waves and black holes. Fortschr. Phys. 45, 439–516 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Poisson, E.: A Relativist’s Toolkit: The Mathematics of Black-hole Mechanics. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  17. Bardeen, J.M., Press, W.H., Teukolsky, S.A.: Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972)

    Article  ADS  Google Scholar 

  18. Nvidia, C.U.D.A.: Nvidia cuda c programming guide. Nvidia Corp. 120(18), 8 (2011)

    Google Scholar 

  19. Butcher, J.C.: Numerical Methods for Ordinary Differential Equations, 2nd edn. Wiley, Chichester (2008)

    Book  MATH  Google Scholar 

  20. CUDA-C Best practice guide. NVIDIA Corporation 2018. http://docs.nvidia.com/cuda/cuda-c-best-practices-guide/index.html

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Acknowledgements

The author would like to thank to Dr. Omar Ortiz for his suggestions concerning the convergence test.

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  1. Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A. A. 678, Bucaramanga, Colombia

    G. D. Quiroga

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  1. G. D. Quiroga
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Correspondence to G. D. Quiroga.

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Quiroga, G.D. MALBEC: a new CUDA-C ray-tracer in general relativity. Gen Relativ Gravit 50, 75 (2018). https://doi.org/10.1007/s10714-018-2387-z

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