Reinterpretation of Laplacian Operator in Curved Spacetime and Scalar Field around Black Hole

In many papers, the authors show analytical or numerical solutions of Klein-Gordon equation in Schwarzschild spacetime. All these papers use Laplace-Beltrami operator for Klein-Gordon equation in Schwarzschild spacetime. However, some solutions of these papers show the behavior near the event horizon, which may not match the prediction of particle’s behavior with that of General Relativity. In this paper, I present reinterpretation of the second order differential operator instead of Laplace-Beltrami operator. According to this reinterpretation, the behavior of a scalar field matches the prediction of General Relativity and other observations related to the gravitational effect. Further, this reinterpretation may open the door to a unified theory of all four forces in nature.