Local Solar Time is essentially the Local Hour Angle of the Sun, but offset so that midnight is 0h and noon is 12h. The hour angle is computed by $$ \begin{align*} H &= \theta_0 + \lambda - \alpha \\ or \\ H &= \theta - \alpha \\ \\ SolarTime &= H - 12 \end{align*} $$ Where \(H\) is the Local Hour Angle, \(\theta_0\) is Greenwich Sidereal Time, \(\theta\) is Local Sidereal Time, \(\lambda\) is the Longitude, and \(\alpha\) is the Right Ascension.

Local Solar Time: