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Singularitas ruang-waktu pada teori relativitas umum telah ditinjau. Definisi singularitas telah diperjelas menggunakan kriteria singularitas berdasarkan skalar Kretschmann. Letak Daerah singularitas pada tiga jenis ruang-waktu pun telah diketahui berdasarkan perhitungan skalar Kretschmann menggunakan software gratis Maxima yang sangat mempermudah perhitungannya. Tiga jenis ruang-waktu itu adalah ruang-waktu bermetrik Schwarzschild, ruang-waktu bermetrik Reissner-Nordstorm, serta ruang-waktu bermetrik Robertson-Walker dengan model alam semesta Einstein-de Sitter.

The Rashba splitting are found in the buckled square lattice. Here, by applying fully relativistic density-functional theory (DFT) calculation, we confirm the existence of the Rashba splitting in the conduction band minimum of various two-dimensional MX monochalcogenides (M = Ge, Sn and X = S, Se, Te) exhibiting a pair inplane Rashba rotation of the spin textures. A strong correlation has also been found between the size of the Rashba parameter and the atomic number of chalcogen atom for Γ and M point in the first Brillouin zone. Our investigation clarifies that the buckled square lattice are promising for inducing the substantial Rashba splitting suggesting that the present system is promising for spintronics device.

Linear response theory in quantum theory with its linear response function and its quantization process has been formulated. The relation between the linear response function with its generalized susceptibility, its symmetry properties, and its analyticity has been studied. These properties produce the dispersion relation or Kramers-Kronig relation. The explicit form of the quantum response function and generalized susceptibility also been reviewed. Applications of linear response functions have been described for three elementary processes. The process discussed is the magnetic field disturbance in the magnetic system that generates magnetic susceptibility, and the electric field disturbance in the electrical system that generates electrical conductivity tensor and the ferromagnet Heisenberg that generates its generalized susceptibility.