Scalar Wave Equation in Schwarzschild Background: For the Schwarzschild metric, the scalar wave equation becomes: (1−2GMc2r)−1∂2Φ∂t2−1r2∂∂r(r2(1−2GMc2r)∂Φ∂r)−1r2sin⁡θ∂∂θ(sin⁡θ∂Φ∂θ)−1r2sin⁡2θ∂2Φ∂ϕ2=0.\left(1 - \frac{2GM}{c^2r}\right)^{-1} \frac{\partial^2 \Phi}{\partial t^2} - \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \left(1 - \frac{2GM}{c^2r}\right)…
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