The Hessian matrix of a scalar field $\phi(x)$ is the matrix of its second partial derivatives, $H_{i j}=\frac{\partial^2 \phi}{\partial x^3 \partial x^3}$. Therefore, the gravitational tidal tensor is simply minus the Hessian matrix of the gravitational potential:

$$ T_{i j}=-H_{i j}(\phi) $$

What is the Hessian matrix of the gravitational potential-L.mp4