I Gusti Ngurah Yudi Handayana, Lily Maysari Angraini



Penelitian ini mengkaji singularitas semu pada metrik Reissner-Nordström, yang merupakan solusi persamaan medan Einstein untuk model partikel bermuatan. Kajian dilakukan dengan menganalisis titik-titik singular pada metrik, menghitung tensor kelengkungan Riemann, serta menghitung scalar Kretschmann pada titik-titik tersebut. Perhitungan dilakukan dengan bantuan program Maxima. Hasilnya, singularitas nyata hanya terjadi pada r = 0, sedangkan singularitas semu terjadi pada . Singularitas semu tersebut merupakan representasi dari horizon peristiwa. Terdapat tiga kemungkinan situasi pada horizon peristiwa. Hal menarik terdapat pada situasi r = M, dimana terjadi keseimbangan antara massa dan muatan yang memungkinkan tarikan gravitasi dan tolakan elektromagnetik saling meniadakan. Penelitian ini juga menghasilkan persamaan geodesik pada titik-titik yang tidak menghasilkan nilai infinite pada skalar Kretschmaan.


Kata Kunci : Kelengkungan Riemann, Metrik Reisner-Nordström, Singularitas, Persamaan  Geodesik



This study examines pseudo singularities on the Reissner-Nordström metric which is a solution to Einstein's field equations for charged particle models. The study was carried out by analyzing the singular points on the metric calculating the Riemann curvature tensor, and calculating Kretschmann's scalar at these points. The results show that real singularities only occur at r = 0, whereas pseudo singularity occurs at . There is a point of pseudo singularity that representing the event horizon. There are two possible situations on the event horizon. Interesting things are in the case r = M, where here is a balance between mass and charge which allows gravitational pull and electromagnetic repulsion to cancel each other. This study also yields the geodesic equation point that not yields infinite value of Kretschmaan scalar.


Keywords: Riemann tensor, Reissner-Nordström Metrik, Singularities, Geodesik equation


Riemann tensor; Reissner-Nordström Metric; Singularities; Geodesics equation

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Bernard, C. (2017). Metrik Reissner-Nordström dalam Teori Gravitasi Einstein”, Jurnal Fisika dan Aplikasinya, 13(1), 1-5.

Carroll, S. M. (2004). Spacetime and Geometry, an Introduction to General Relativity. San Francisco: Addison Wesley.

Doeleman, S. S. et. al. (2018). Event Horizon Scale Structure in the Supermassive Black Hole Candidate at the Galactic Centre”, Nature Letter. 455. 78-80.

Graves, J. C. and Brill, D. R. (1960). Oscillatory Character of Reissner-Nordstrom Metrik for an Ideal Charged Wormhole”, Physical Review, 120(4), 1507-1513.

Grön, O and Naess, A. (2011). Einstein's Theory; A Rigorous Introduction for the Mathematically Untrained. London: Springer.

Hod, S. (2014). Kerr-Newman black holes with stationary charged scalar clouds”, Physical Review D. 90. 1-7.

Joshi, P. S. (2007). Gravitational Collapse and Spacetime Singularities. New York: Cambridge University Press.

Narayan, R. and McClintock, J. E. (2008). Advection-dominated accretion and the black hole event horizon”, New Astronomy Reviews. 51. 733-751.

O’neill, B. (1983). Semi-Riemannian Geometry, with applications to Relativity. California : Academic Press

Penrose, R. (1965). Gravitational Collapse and Space- Time Singularities”, Physical Review Letters. 14(3). 57-59.

Wald, R. M. (1979). Construction of Metrik and Vector Potential Perturbations of a Reissner- Nordstrom Black Hole”, Procedeings of the Royal Society A. Lond. 369. 67-81.

Zhou, S. and Liu, W. (2008). Hawking radiation of charged Dirac particles from a Kerr-Newman black hole”, Physical Review D, 77, 1-6.



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