Geodesik Ruang Dan Ruang-Waktu Dalam Geometri Reissner-Nordström

Ma'aly, Muhammad Alid Rizky (2025) Geodesik Ruang Dan Ruang-Waktu Dalam Geometri Reissner-Nordström. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Tugas akhir berjudul Geodesik Ruang dan Ruang-Waktu dalam Geometri Reissner Nordström ini bertujuan untuk mendapatkan persamaan orbit gravitasi Newton pada metrik Reissner-Nordström baik dalam ruang-waktu penuh maupun dalam submanifold ruang 3D. Selain itu, penelitian ini juga bertujuan untuk mengetahui pengaruh dari penghilangan kontribusi dimensi waktu melalui penetapan waktu konstan pada submanifold ruang 3D, serta mendapatkan bentuk visualisasi kelengkungan ruang pada metrik Reissner-Nordström melalui embedding diagram. Reissner-Nordström merupakan solusi dari persamaan medan Einstein yang menggambarkan ruang-waktu di sekitar benda bermassa dan bermuatan, dengan simetri sferis dan tak berotasi. Berdasarkan elemen garis dari metrik tersebut, diperoleh persamaan geodesik yang kemudian diturunkan menjadi persamaan orbit gravitasi Newton dalam batas non-relativistik untuk masing-masing kasus. Hasil menunjukkan dengan membandingkan tanda relatif terhadap potensial sentrifugal yang bersifat menolak didapat bahwa dalam ruang-waktu penuh, potensial gravitasinya bersifat menarik dan potensial muatannya bersifat menolak, sementara dalam submanifold ruang 3D, potensial gravitasinya bersifat menolak dan potensial muatannya bersifat menarik, namun keduanya memiliki nilai yang sangat lemah. Embedding diagram juga memberikan gambaran geometris kelengkungan ruang pada bidang ekuatorial dan waktu konstan.
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This undergraduate thesis, titled Space and Space-Time Geodesics in Reissner-Nordström Geometry, aims to obtain Newton's gravitational orbit equations on the Reissner-Nordström metric both in full space-time and in 3D space submanifolds. Additionally, this research seeks to investigate the effect of eliminating the time dimension contribution by setting a constant time on the 3D space submanifold, as well as to visualize the curvature of space in the Reissner-Nordström metric through an embedding diagram. Reissner-Nordström is a solution to Einstein's field equations that describe space-time around massive and charged objects, with spherical symmetry and no rotation. Based on the line elements of the metric, geodesic equations are obtained, which are then derived into Newton's gravitational orbit equations in the non-relativistic limit for each case. The results show that by comparing the signs relative to the repulsive centrifugal potential, it is found that in full space-time, the gravitational potential is attractive and the charge potential is repulsive, while in the 3D space submanifold, the gravitational potential is repulsive and the charge potential is attractive, but both have very weak values. The embedding diagram also provides a geometric illustration of the curvature of space on the equatorial plane and at constant time.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Embedding Diagram, Geodesik, Ruang-Waktu, Submanifold, Embedding Diagram, Geodesics, Space-Time, Submanifold
Subjects:	Q Science Q Science > QB Astronomy Q Science > QB Astronomy > QB336 Gravity anomalies Q Science > QC Physics Q Science > QC Physics > QC665.E38 Electric fields.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Muhammad Alid Rizky Ma'aly
Date Deposited:	06 Aug 2025 01:42
Last Modified:	06 Aug 2025 01:42
URI:	http://repository.its.ac.id/id/eprint/127501

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