Is samatha concentration meditation's object always an idea, concept or something else?
Why meditate on a concept and what else besides concepts are there to meditate on?
Samarha means tranquillity state of the mind. Keeping this state for the considerable time is the result of the meditation.
There are many ways you can do it, there are many meditation techniques to do this which are not advised in buddhism.
Meditation can be done concentrating on something like air, fire, soil etc.
But in buddhism you may concentrate on
insatiable state of the world.
When mind is thinking about something it goes to neutral/calm state, where it won't react to inputs but just read them as it is.
There are 40 meditation objects are prescribed in Visuudhimagga.
At its best, samatha meditation almost never involves an idea, concept, etc. Apart from the brahmaviharas, meditations on the foulness of the body, and a handful of other techniques, samatha almost by definition can't involved any kind of discursive thinking. It would simply be impossible to enter into higher states of concentration with this kind of mental content in place. In fact, the Visuddhimagga and other texts make a point of saying that while the 1st jhana can be reached by any number of techniques, in order for it to be exceeded discursive content has to be abdonded (and frankly, I'd argue that the 1st jhana can only be approached by conceptual techniques; there's just no "room" for conceptual thought when one attains absorption). Even in Rinzai Zen, where we work with koans, you aren't brooding or ruminating on the huatou (i.e. the part of the koan that you say over and over again in seated meditation). Rather, the word becomes an object of focus - no different than the tip of your nose, the breath, a kasina, the dan tien, etc. What you are really aiming for is a mental energy that is applied and sustained. The less discursive that mental energy is, the easier it will be for your concentration to stabilize and mature. It's why it's often better to stick with objects like the breath. You can direct your mental energy there in a way that doesn't give rise to extraneous mental content.
So much of samatha involves letting go (vossagga). As your concentration deepens, it will become exceedingly apparent just how riling and disruptive even the slightest thought object actually is. If what you are after is pure concentration, it seems counterproductive to enter into any practice relies on the production of mental content no matter how refined or virtuous that content might seem.