Gnomonic Projection from S⁴ and the Schwarzschild-like Form of the Induced Metric on a Four-Dimensional Subjective Chart (Paper 2)

English: We study the gnomonic (central) projection from a four-dimensional sphere S⁴(R) ⊂ R⁵ onto a four-dimensional tangent hyperplane, derive the induced metric, compute its Christoffel symbols, Riemann tensor, and Einstein tensor, and show that it satisfies the four-dimensional vacuum Einstein equations with a positive cosmological constant Λ = 3/R². Lorentzian continuation gives the de Sitter metric, and a Schwarzschild–de Sitter form arises with a mass parameter. Compared with the four-plus-one-dimensional Schwarzschild–Tangherlini metric. 日本語: 4次元球 S⁴(R) ⊂ R⁵ から4次元接超平面へのグノモン投影を扱う。誘導計量、Christoffel記号、Riemann/Einstein テンソルを計算し、Λ = 3/R² の4次元真空 Einstein 方程式を満たすことを示す。Lorentz連続化で de Sitter 計量、質量パラメータで Schwarzschild–de Sitter 形。4+1 Schwarzschild–Tangherlini 計量と比較。