Theoretical Physics

Application of the Euler Lagrange Formalism for Determining the Equation of Motion in the Case of Radial Fall into a Non-Rotating, Charged Black Hole

Download PDF (259.8 KB) PP. 93 - 96 Pub. Date: April 27, 2017

DOI: 10.22606/tp.2017.22006

Author(s)

A. Sfarti^*
CS Dept., 387 Soda Hall, UC Berkeley, USA

Abstract

In this paper we set to accomplish two things: determine the equation of motion for an uncharged test probe falling radially into a charged, non-rotating black hole and determine the relationship between coordinate acceleration and coordinate speed. The paper is concerned only what happens outside the event horizon, since we are using only the external Reissner-Nordstrom equations in the derivations. What happens inside the event horizon (the presence of a wormhole connecting the black hole to a white hole) is outside the scope of this paper.

Keywords

General relativity, Reissner-Nordstrom metric, Euler-Lagrange formalism.

References

[1] A. Sfarti, “Application of the Euler-Lagrange method in determination of the coordinate acceleration”, EJP, 37, 3, 2016

[2] A. Sfarti, “Euler-Lagrange Solution for Calculating Particle Orbits in Gravitational Fields”, Fizika A, 19, 4, 2010

[3] Rindler,W. “Relativity-Special,General and Cosmological”, 2006, Oxford Press, pp205

[4] R.A.Mould, “Basic Relativity”, Springer-Verlag, 2002, p329.

[5] A Sfarti, “The Two Test Probe Chase”. JAPSI, 6, 4, 2016

[6] D. Raine, E. Thomas, “Black Holes”, Imperial College Press, 2005

[7] J.B. Hartle, “Gravity: An Introduction to Einstein’s General Relativity”, 2003, Addison-Wesley

[8] S Chandrashekhar, The Mathematical Theory of Black Holes, Oxford University Press Inc., 2000