Preprint / Version 1

Passage of Time for an Astronaut Rotating around a Rotating (Kerr) Black Hole Using Python- An Application of General Theory of Relativity

##article.authors##

  • Aadit Sengupta American School in London, London, England

DOI:

https://doi.org/10.58445/rars.936

Keywords:

General Theory of Relativity, Schwarzschild Black Hole, Kerr Black Hole, Time Dilation, Astronaut

Abstract

The General Theory of Relativity (GTR) is a cornerstone of modern physics, revolutionizing our understanding of gravity, depicting it as a curvature of spacetime. Among its solutions, the Kerr equation stands out, describing the spacetime around a rotating mass. This paper delves into exact solutions like the Schwarzschild solution for non-rotating masses and extends to the Kerr solution for rotating black holes. It specifically explores time dilation of an astronaut in the Kerr metric, which is influenced by parameters such as radial distance, angular momentum, and polar angle. The study employs Python for computational analysis, visualizing time dilation through plots that reflect varying black hole rotations and observer positions, offering a nuanced understanding of relativistic effects in extreme gravitational fields.

 

References

Norton, John. "How Einstein found his field equations: 1912-1915." Historical studies in the physical sciences 14.2 (1984): 253-316.

Jorge Pinochet. “General Relativity in a Nutshell I.” Physica Scripta, vol. 98, no. 12, Nov. 2023, p. 126103.

Temple, Blake, and Craig A. Tracy. "From Newton to Einstein." The American mathematical monthly 99.6 (1992): 507-521.

Roeder, R. C. "Einstein and Cosmology." Journal of the Royal Astronomical Society of Canada, Vol. 73, P. 349, 1979 73 (1979): 349

Cataldo, Carmine. "On the Schwarzschild Solution: a Review." International Journal of Advanced Engineering Research and Science 4.9 (2017): 237254.

Teukolsky, Saul A. "The kerr metric." Classical and Quantum Gravity 32.12 (2015): 124006.

Szekeres, S. P. "An explanation of the Newman-Janis algorithm." arXiv preprint gr-qc/9807001 (1998).

Gürlebeck, Norman. "No-hair theorem for black holes in astrophysical environments." Physical Review Letters 114.15 (2015): 151102.

Isi, Maximiliano, et al. "Testing the no-hair theorem with GW150914." Physical Review Letters 123.11 (2019): 111102.

Google Colaboratory, Google Colab, [Online]. Available: https://colab.google/

“Welcome to Python.org.” Python.org, 18 Jan. 2024, www.python.org.

Aadit Sengupta, "Passage of Time for an Astronaut Rotating Around a Schwarzschild Black Hole - An Application of General Theory of Relativity," SSRG International Journal of Applied Physics, vol. 10, no. 3, pp. 22-26, 2023.

Harte, Abraham I. "Taming the nonlinearity of the Einstein equation." Physical Review Letters 113.26 (2014): 261103.

Bambi, Cosimo, and Leonardo Modesto. "Rotating regular black holes." Physics Letters B 721.4-5 (2013): 329-334.

Zhang, Jingyi, and Zheng Zhao. "New coordinates for Kerr–Newman black hole radiation." Physics Letters B 618.1-4 (2005): 14-22.

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Posted

2024-02-03

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