Thank you so much. I too have ligament tear and I know how annoying it is to no be able to run/jog. Jogging is the ultimate cardio as it burns a lot of calories, but there’s always a chance that you can jerk your knee.
So the sad thing about ligaments is that they never heal 😦 The only thing you can do is strengthen the muscles around them so that you don’t jerk your knee, but you will ALWAYS have to take certain precautions so you don’t injure your ligament. I jerked mine last year in the middle of dancing because it was too strenuous on the knee, so you should be extremely careful about the pressure on your knees.
What you can do for cardio instead of jogging and running is use the elliptical in the gym as it burns a lot of calories. Apart from that, brisk walking on the treadmill with incline helps. You can even cycle, normally or in intervals (fast cycling 1 minute+moderate cycling 30 seconds- repeat).
I also suggest you to do leg extension to strengthen your muscle, avoid lunges if it hurts your knee and squats with support if needed. Basically just stop exercising when your knee pains while working out, its not worth getting injured and being on bed rest a month!
I hope this helped 🙂