Temperatur Hawking dari Lubang Hitam Kerr-Vaidya

Rahmani, Muhammad Hanif (2024) Temperatur Hawking dari Lubang Hitam Kerr-Vaidya. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Radiasi Hawking adalah konsep penting dalam fisika teoritis dan merupakan upaya pertama yang berhasil menggabungkan mekanika kuantum dan relativitas umum dalam satu kerangka kerja. Temperatur lubang hitam Schwarzschild dan Kerr cukup sederhana untuk diperoleh. Namun, solusi ini hanya berlaku untuk ruang-waktu vakum, sementara lubang hitam yang berevaporasi membutuhkan tensor energi-momentum radiasi null yang tidak sama dengan nol. Metrik Vaidya bermanfaat sebagai alat matematis yang dapat menangkap banyak fitur penting dari ruang-waktu lubang hitam bermassa dinamis atau berevaporasi. Dalam kasus evaporasi lambat, metrik simetri bola umum dapat direpresentasikan oleh metrik Vaidya linear masuk di wilayah dekat-cakrawala. Metrik Vaidya kemudian ditransformasi menjadi bentuk konformal Rindler, memungkinkan penentuan temperatur Hawking untuk daerah dekat dengan cakrawala. Transformasi konformal juga diterapkan pada solusi Kerr-Vaidya, di mana solusi tersebut menghadirkan model yang lebih baik untuk lubang hitam berotasi dan bermassa dinamis. Dari metrik yang telah ditransformasi, didapatkan formulasi temperatur Hawking lubang hitam dalam ruang-waktu tersebut. Formula tersebut kemudian digunakan untuk menentukan nilai teoritis temperatur Hawking dari beberapa lubang hitam supermassif di pusat galaksi.
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Hawking radiation is a major concept in theoretical physics and represents the first successful attempt to combine quantum mechanics and general relativity within a unified framework. It is straightforward to derive the temperature of Schwarzschild and Kerr black holes. However, these solutions only apply to vacuum spacetime, while evaporating black holes require a non-zero null radiation energy-momentum tensor. The Vaidya metric serves as a mathematical tool capable of capturing many essential features of dynamic mass or evaporating black hole spacetimes. In the limit of slow evaporation, the general spherically symmetric metric can be represented by the linear ingoing Vaidya metric in the near-horizon region. The Vaidya metric was then transformed to a conformally Rindler form, enabling the determination of the Hawking temperature for the region near the horizon. The conformal transformation was also applied to the Kerr-Vaidya solution, where the solution presents a better model for rotating and dynamic mass black holes. From the transformed metrics, the Hawking temperature formulation for the black holes in those spacetimes were obtained. The formula was then used to determine the theoretical Hawking temperature values for some supermassive black holes at the center of galaxies.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Lubang Hitam, Radiasi Hawking, Relativitas Umum, Black Hole, General Relativity, Hawking Radiation
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Muhammad Hanif Rahmani
Date Deposited:	16 Feb 2024 07:03
Last Modified:	16 Feb 2024 07:03
URI:	http://repository.its.ac.id/id/eprint/106734

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