Bayangan Lubang Hitam Statis Simetris Sferis pada Metrik Schwarzschild, Schwarzschild-Kottler, dan Reissner-Nordström

Anggraini, Silvia Dwi (2025) Bayangan Lubang Hitam Statis Simetris Sferis pada Metrik Schwarzschild, Schwarzschild-Kottler, dan Reissner-Nordström. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penelitian ini bertujuan untuk menganalisis struktur bayangan lubang hitam dari tiga solusi ruang-waktu statis dan simetris sferis, yaitu metrik Schwarzschild, Schwarzschild–Kottler, dan Reissner–Nordström. Dengan menggunakan pendekatan teoritis dalam kerangka relativitas umum dan bantuan simulasi numerik, dilakukan formulasi persamaan gerak foton berdasarkan prinsip konservasi energi dan momentum sudut. Radius orbit foton ditentukan dari titik ekstremum potensial efektif radial, sedangkan parameter dampak kritis digunakan untuk menghitung ukuran bayangan yang diamati oleh pengamat jauh. Visualisasi dilakukan melalui perangkat lunak MATLAB, mencakup grafik potensial efektif, trayektori foton, dan radius bayangan. Hasil penelitian menunjukkan bahwa radius bayangan berbanding lurus dengan massa lubang hitam pada ketiga metrik. Kehadiran konstanta kosmologi positif dalam metrik Schwarzschild-Kottler menyebabkan peningkatan radius bayangan secara teoritis, sedangkan muatan listrik dalam metrik Reissner–Nordström menyebabkan penyusutan radius bayangan. Perbandingan antar metrik menujukkan bahwa parameter fisis seperti Λ dan Q secara signifikan memengaruhi karakteristik optik lubang hitam, meskipun dengan dampak yang berbeda.
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This research aims to analyze the shadow structure of black holes described by three static and spherically symmetric spacetime solutions: the Schwarzschild, Schwarzschild–Kottler, and Reissner–Nordström metrics. Using a theoretical approach within the framework of general relativity and aided by numerical simulations, the equations of motion for photons are formulated based on the principles of energy and angular momentum conservation. The photon orbit radius is determined from the extremum of the radial effective potential, while the critical impact parameter is used to calculate the shadow radius observed by a distant observer. Visualization is performed using MATLAB, including plots of the effective potential, photon trajectories, and shadow radius. The results show that the shadow radius is directly proportional to the black hole mass for all three metrics. The presence of a positive cosmological constant in the Schwarzschild–Kottler metric leads to a theoretical increase in the shadow radius, whereas electric charge in the Reissner–Nordström metric causes a reduction in the shadow size. The comparison between metrics highlights that physical parameters such as Λ and Q significantly affect the optical properties of black holes, though with different impacts.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Black hole shadow, Critical impact parameter, Photon geodesics. Bayangan lubang hitam, Geodesik foton, Parameter dampak kritis
Subjects:	Q Science Q Science > QB Astronomy Q Science > QB Astronomy > QB336 Gravity anomalies Q Science > QC Physics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Silvia Dwi Anggraini
Date Deposited:	05 Aug 2025 07:19
Last Modified:	05 Aug 2025 07:19
URI:	http://repository.its.ac.id/id/eprint/127500

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