Can I terminate an employee for threatening the management staff and the company through facebook?

In some states employment is "at will."  At will employment means that either party, the employer or the employee may terminate the employment relationship at any time and for, almost, any reason.  If you are in an at wil employment state, termination would likely be ok.  If there is an employment contract in place that states the length of the employment relationship, termination still may be appropriate if it meets the contract's "for cause" language.  Such language typically gives the right to cancel an agreement if the employee takes some level of unfavorable action.  You will want to confirm your state law's on employment duration and review any employment contract language.