Gravitasi Einstein dan Einstein-Maxwell Pada 2+1 Dimensi Dalam Teori Gauge Chern-Simons

Septiawan, Agung Sedayu (2026) Gravitasi Einstein dan Einstein-Maxwell Pada 2+1 Dimensi Dalam Teori Gauge Chern-Simons. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Penelitian ini merumuskan gravitasi Einstein di 2+1 dimensi sebagai teori gauge Chern-Simons dengan grup gauge SO(2, 2) dan menerapkannya pada lubang hitam BTZ serta perluasan Einstein-Maxwell. Melalui ansatz Witten, koneksi spin dan dreibein digabung menjadi koneksi gauge tunggal bernilai pada aljabar Lie so(2, 2) yang dikonstruksi dari prinsip pertama; variasi aksi Chern-Simons mereproduksi secara persis kondisi bebas torsi dan persamaan medan Einstein dengan konstanta kosmologi negatif, membuktikan ekuivalensi kedua formulasi. Solusi lubang hitam BTZ beserta horizon peristiwanya diperoleh secara analitik dalam formalisme dreibein, dengan kasus tanpa rotasi dianalisis sebagai limit yang mereduksi metrik ke bentuk diagonal. Perluasan ke sektor Einstein-Maxwell dilakukan dengan menambahkan aksi Maxwell sebagai sumber materi; persamaan Maxwell diselesaikan secara umum dan tensor energi-momentum elektromagnetik dihitung eksplisit dalam notasi dreibein. Analisis konsistensi menunjukkan bahwa kesa- maan struktural geometris yang dipaksakan oleh ansatz BTZ berbenturan dengan asimetri tensor energi-momentum elektromagnetik, sehingga solusi yang sekaligus bermuatan dan berotasi tidak ada dalam teori Einstein-Maxwell murni di 2+1 dimensi.
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This study formulates Einstein gravity in 2+1 dimensions as a Chern-Simons gauge theory with gauge group SO(2, 2) and applies the formalism to BTZ black holes and the Einstein-Maxwell extension. Through the Witten ansatz, the spin connection and dreibein are unified into a single gauge connection valued in the Lie algebra so(2, 2), which is constructed from first principles; variation of the Chern-Simons action exactly reproduces the torsion-free condition and the Einstein field equations with negative cosmological constant, establishing the equivalence of the two formulations. The BTZ black hole solution and its event horizons are obtained analytically in the dreibein formalism, with the non-rotating limit analyzed as a special case that reduces the metric to diagonal form. The Einstein-Maxwell extension is carried out by adding the Maxwell action as a matter source; the Maxwell equations are solved in full generality and the electromagnetic energy-momentum tensor is computed explicitly in dreibein notation. A consistency analysis reveals that a geometric structural identity imposed by the BTZ ansatz clashes with the asymmetry of the electromagnetic energy-momentum tensor, so that a simultaneously charged and rotating solution does not exist in pure Einstein-Maxwell theory in 2+1 dimensions.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Gravitasi 2+1 dimensi, Chern-Simons, BTZ, Einstein-Maxwell, 2+1 gravity, Chern-Simons, BTZ, Einstein-Maxwell
Subjects:	Q Science Q Science > QB Astronomy > QB336 Gravity anomalies Q Science > QC Physics Q Science > QC Physics > QC111 Density and specific gravity
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Agung Sedayu Septiawan
Date Deposited:	31 Jul 2026 07:27
Last Modified:	31 Jul 2026 07:27
URI:	http://repository.its.ac.id/id/eprint/140594

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