Mode Kuasinormal Dalam Ruang-Waktu Schwarzschild Anti-De Sitter

Machfudi, Ilham Rasyid (2026) Mode Kuasinormal Dalam Ruang-Waktu Schwarzschild Anti-De Sitter. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Mode kuasinormal merupakan osilasi teredam karakteristik yang muncul ketika lubang hitam dikenai perturbasi kecil, dengan frekuensi kompleks ω = ωR − iωI yang bagian realnya menyatakan frekuensi osilasi dan bagian imajinernya menyatakan laju peluruhan. Penelitian ini menentukan dan membandingkan spektrum frekuensi mode kuasinormal perturbasi medan skalar pada dua ruang-waktu, yaitu Schwarzschild yang datar secara asimtotik dan Schwarzschild Anti-de Sitter. Frekuensi eigen diperoleh melalui metode Frobenius yang dikombinasikan dengan metode pecahan berlanjut; khusus pada ruang-waktu Schwarzschild Anti-de Sitter, relasi rekurensi multisuku yang dihasilkan direduksi terlebih dahulu menjadi relasi tiga suku menggunakan eliminasi Gaussian. Perhitungan dilakukan untuk medan skalar tak bermassa (µ = 0) dan bermassa (µ = 1), momentum sudut ℓ = 0, 1, 2, serta mode fundamental dan overtone pertama. Hasil menunjukkan bahwa pada ruang-waktu Schwarzschild peningkatan massa lubang hitam menurunkan bagian real maupun imajiner frekuensi, sedangkan pada Schwarzschild Anti-de Sitter peningkatan jari-jari horizon peristiwa r+ justru menaikkan kedua komponen tersebut. Peningkatan momentum sudut secara konsisten menaikkan bagian real dan menurunkan bagian imajiner frekuensi pada kedua ruang-waktu, sedangkan peningkatan indeks overtone maupun penambahan massa medan skalar menghasilkan kecenderungan yang berbeda antara ruang-waktu Schwarzschild dan Schwarzschild Anti-de Sitter. Seluruh mode yang diperoleh memiliki ωI > 0, sehingga lubang hitam Schwarzschild maupun Schwarzschild Anti-de Sitter bersifat stabil terhadap perturbasi medan skalar, baik untuk medan tak bermassa maupun bermassa.
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Quasinormal modes are the characteristic damped oscillations excited when a black hole is subjected to small perturbations, governed by complex frequencies ω = ωR − iωI whose real part represents the oscillation frequency and whose imaginary part represents the damping rate. This study determines and compares the quasinormal mode frequency spectra of scalar field perturbations in two spacetimes: the asymptotically flat Schwarzschild spacetime and the Schwarzschild Anti-de Sitter spacetime. The eigenfrequencies are obtained using the Frobenius method combined with the continued fraction method; for the Schwarzschild Anti-de Sitter case, the resulting multi-term recurrence relation is first reduced to a three-term relation through Gaussian elimination. The computations are carried out for massless (µ = 0) and massive (µ = 1) scalar fields, angular momenta ℓ = 0, 1, 2, and both the fundamental mode and the first overtone. The results show that in the Schwarzschild spacetime an increase in the black hole mass lowers both the real and imaginary parts of the frequency, whereas in the Schwarzschild Anti-de Sitter spacetime an increase in the event horizon radius r+ instead raises both components. An increase in angular momentum consistently raises the real part while lowering the imaginary part of the frequency in both spacetimes, whereas an increase in the overtone index and the addition of scalar field mass produce differing trends between the Schwarzschild and Schwarzschild Anti-de Sitter spacetimes. All obtained modes have ωI > 0, indicating that both the Schwarzschild and Schwarzschild Anti-de Sitter black holes are stable against scalar field perturbations, for both massless and massive fields.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Medan Skalar, Mode Kuasinormal, SAdS, Schwarzschild, Quasinormal Modes, SAdS, Scalar Field, Schwarzschild
Subjects:	Q Science > Q Science (General) > Q180 Gravitation. Q Science > QB Astronomy > QB336 Gravity anomalies Q Science > QC Physics > QC179 Gravitational waves--Measurement--Statistical methods
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Ilham Rasyid Machfudi
Date Deposited:	30 Jul 2026 06:26
Last Modified:	30 Jul 2026 06:26
URI:	http://repository.its.ac.id/id/eprint/139765

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