PENROSE INEQUALITY FOR HIGHER DIMENSIONAL CHARGED BLACK HOLES - AGRI FATURAHMAN (NIM : 10214091),
In this final project we discuss the motivations, interpretation, and proof of Penrose's inequality for higher dimensional charged black holes performed by de Lima-Girao-Lozorio-Silva on his paper. The discussion begins with explanation about the background of Penrose's inequality, which is the formulation for validated cosmic censorships conjecture, proposed by Roger Penrose. The Penrose inequality is still an open problem in Mathematical Physics until now. For Further discussion, we begin with several concepts about General Relativity related to Penrose inequality, including ADM mass formulation, introduction to hypersurface geometry, and initial value problem in General Relativity. Then, we discuss on the proof of Penrose's inequality, wich is performed by de Lima-Girao-Lozorio-Silva on his paper. The discussion includes an explanation about the technical proof of Penrose inequality, the qualitative explanation about theorems in his paper, and detailed calculations that the authors did for completed some sections of his paper. At the end, the authors carried out a preliminary study of the formulation another Penrose inequality for charged black holes, applicable to 𝑛≥3 dimensions, to complete the specific Penrose inequality in certain cases present in the paper de Lima-Girao-Lozorio-Silva.