Mindfulness and Pushing Away Emotions

If your mind is in a negative mood it takes time to cool thoughts off. You have to acknowledge that you are having these feelings & thoughts, and then try to NOT engage in them further. Simply let them be. If you re-engage in them, the underlying distorted belief system(s) that are the responsible for the thoughts and feelings will otherwise re-activate.

Of course, it needs personal determination to "let be" certain thoughts because we can tell ourselves that we must engage in them, otherwise things in the world get worse.

It isn't easy to let them be; that's why you should focus on the very sensation in your body that is arising. Don't focus on thoughts because they are too rapid and lure you into more thought engaging, resulting in thought, and consequently mood proliferation.

While you are dealing with thoughts and feelings in a cognitive way (curiously observing them and employing patience towards them since they need to cool off, see above), you better also use something behaviourally, that is, seek a better place or distract yourself for a while. Naturally, distraction is not the most elegant solution there is, however sometimes, it is helpful, especially when your mind became completely emotional and distorted and can't think rationally anymore.

That being said, be gentle with yourself. Once the mind is distorted, it needs a little time to cool the mood off, since the emotions are compounded and conditioned. If you don't engage in thoughts, observe the arisen feeling curiously, employ patience with the knowledge: 'Mind is distorted and will take some time to cool off', then you have good chances to overcome (albeit not easily) your mood.

There is nothing unhealthy about annihilating unwholesome emotions.

As I noticed that it leads to my own affliction, it subsided. As I noticed that it leads to the affliction of others... to the affliction of both... it obstructs discernment, promotes vexation & does not lead to Unbinding, it subsided. Whenever thinking imbued with sensuality had arisen, I simply abandoned it, dispelled it, wiped it out of existence.

MN 19

Well you do not say what experience is this ''objectless mindfulness'', which is an odd phrasing, because, beyond the bad word that is mindfulness, there is always an object of concentration or contemplation. And the whole point of contemplation is either to know or track the kaya, the mano and the citta as well as to calm the kaya, the mano and the citta:

• it is easy to track the kaya, mano, citta, for any puthujjana who has sati and is good at tranquilising the kaya, mano and citta

• it is easy to calm the kaya, mano and citta, for any puthujjana who has sati and is good at tracking the kaya, mano, citta, thought, sanna, vedana (in one word, that's call sati samprajanya which is the method to stop the spreading of infatuation and hate towards whatever is loved and hated by puthujjanas)

• in other word, you cannot be good at tranquilizing the kaya, mano and citta without tracking the mano, kaya and citta and you cannot be good at tracking the kaya, mano and citta, without being good at tranquilizing the kaya, mano and citta (which is done by seeing how nice it is to be calm and how awful it is to be agitated).

Fortunately, you claim to calm your mood with the breath, so that's good. Do not forget that after you become tranquil with the breath, you need to contemplate the impermanence of typically the 5 aggregates

SInce you like to contemplate things other than the breath, there are plenty of topics to contemplate here

https://www.accesstoinsight.org/tipitaka/an/an10/an10.060.piya.html

When you want to get the citta into samadhi, you have 4 famous samadhis here. the 2 samadhis with the clearest directions and clear exposition of results are:

And what is the development of concentration that, when developed & pursued, leads to the attainment of knowledge & vision? There is the case where a monk attends to the perception of light and is resolved on the perception of daytime [at any hour of the day]. Day [for him] is the same as night, night is the same as day. By means of an awareness open & unhampered, he develops a brightened mind. This is the development of concentration that, when developed & pursued, leads to the attainment of knowledge & vision.

And what is the development of concentration that, when developed & pursued, leads to mindfulness & alertness? There is the case where feelings are known to the monk as they arise, known as they persist, known as they subside. Perceptions are known to him as they arise, known as they persist, known as they subside. Thoughts are known to him as they arise, known as they persist, known as they subside. This is the development of concentration that, when developed & pursued, leads to mindfulness & alertness.

www.buddha-vacana.org/sutta/anguttara/04/an04-041.html

If the last one is what you call ''objectless mindfulness'', then call it properly by calling it what it is : training for sati samprajanya instead of inventing new words that nobody knows what they mean.

With objectless mindfulness, if I am in a bad mood the mood perseveres. I just observe the bad mood but it doesn't easily stop.

This may be because the attention you're giving to the bad mood is the wrong kind of attention. There may be a clue in you wanting for the bad mood to easily stop. Observe with no anticipation for anything.

However, if I applied concentration on an object such as the breath, the mood immediately dissipates and even sometimes vanishes.

The dissipation of the mood by shifting focus may be a further clue to the mental proliferation that you could be adding to the 'watching' of this bad mood.

Does strong concentration repress emotions, or does it process them in a healthy way? In other words, does focusing on the breath still permit the emotions to be experienced naturally despite an absence of thought or feeling?

It doesn't need to be strong concentration. One just needs to simply switch focus to something else. The something else can become a further problem like an escape though. Notice breath, movement, objects, light gradients... There are many wonderful harmless things to remove us from mental anguish. This is, indeed, healthy and not a repression technique.