# SCHWARZSCHILD SOLUTION OF THE MODIFIED EINSTEIN FIELD EQUATIONS

### Abstract

A reformulation of the Schwarzschild solution of the linearized Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further application of Kruskal-Szekeres coordinates reveals that the interior solution contains maximally extensible geodesics.

### References

[2] D. McMmahon, Relativity Demystified, McGraw-Hill, USA(2006).

[3] F.W. Dyson, A.S. Eddington, C.R. Davidson, A Determination of the De-ection of Light by the Sun's Gravitational Field, from Observations Made at the Total eclipse of May 29, 1919, Philosophical Transactions of The Royal Society of London 220, (1919), 291-333, doi:10.1098/rsta.1920.0009.

[4] K. Schwarzschild, On the Gravitational Field of a Mass Point by Einstein's Theory, Proceedings of The Prussian Academy of Sciences, (1916), 189-196, arXiv:physics/9905030 [physics.hist-ph]

[5] M. P. Hobson , G. P. Efstathiou, A. N. Lasenby, General Relativity: An Intro duction for Physicists, Cambridge University Press, UK(2006), 196-220.

[6] A. Eddington, A Comparison of Whitehead's and Einstein's Formulae, Nature (Letters to The Editor), 113, 2832(1924), 192.

[7] D. Finkelstein, Past-Future Asymmetry of the Gravitational Field of a Point Particle, Physical Review Journal, 110, N0.4(1958), doi:10.1103/PhysRev.110.965.

[8] C.Montgomery, W.Orchiston, I. Whittingham, Michell, Laplace and the Origin of the Black Hole Concept, Journal of Astronomical History and Heritage, 12, 2(2009), 90-96

[9] M. Bartusiak, Blackholes: How an Idea abandoned by Newtonians, hated by Einstein, and gambled on by Hawking, became loved, Yale University Press, USA(2016)

[10] S. Chandrasekhar, The Maximum Mass of Ideal White Dwarfs, Astrophysical Journal, 74, (1931), 81-82

[11] J.R. Oppenheimer, G.M. Volko, On Massive Neutron Cores, Physical Review, 55, 4(1939), 374{381, doi:10.1103/PhysRev.55.374

[12] B.L. Webster,P. Murdin, Cygnus X-1|a Spectroscopic Binary with a Heavy Companion?, it Nature(Letters to Nature), 235, 37-38(1972), 235.

[13] R. Johnston, List of black hole candidates, http://www.johnstonsarchive.net/relativity/bhctable.html, (2016), Accessed on 12th July 2016

[14] L.H. Ford, Quantum Field Theory in Curved Spacetime, arXiv:gr-qc/9707062, (1997).

[15] J.M.M. Senovilla, Singularity Theorems in General Relativity: Achievements and Open Questions, http://arxiv.org/abs/physics/0605007v1, (2006).

[16] R. Gambini, J. Pullin, Loop Quantisation of The Schwarzschild Blackhole,Physical Review Letters, 110, 211301(2013), doi:10.1103/PhysRevLett.110.211301

[17] D. McMmahon, String Theory Demystied, McGraw-Hill, New York(2009), 239-255

[18] Z. Shen, Lectures on Finsler Geometry, Indiana University-Purdue University Indianapolis, USA(2001)

[19] G.S. Asanov, Finsler Geometry, Relativity and Gauge Theories, D Reidei Publishing Company, Holland(1985)

[20] D.S.Wamalwa, J.A. Omolo, Generalised Relativistic Dynamics In A NonInertial Frame of Reference, Indian Journal of Physics, 84, N0.9(2010), 1241-1255

**JOURNAL OF ADVANCES IN PHYSICS**, [S.l.], v. 13, n. 5, p. 4895-4900, june 2017. ISSN 2347-3487. Available at: <https://cirworld.com/index.php/jap/article/view/6132>. Date accessed: 23 aug. 2017. doi: https://doi.org/10.24297/jap.v13i5.6132.

This work is licensed under a Creative Commons Attribution 4.0 International License.