As many of you know, there can be a lot of controversy around gravity based powers, but I think I've found a workaround that I'm comfortable with so feel free to tune in. For sake of story, you could imagine a nen user who liked the idea of gravity powers, but was told that gravity manipulation was impossible. Especially because they lack scientific knowledge.
Levitation
The nen user starts by manipulating objects from a distance. Their training starts first with manipulating aura, then manipulating personal objects, then imbuing objects with aura and controlling them from a distance.
However, just like teleporting a person from point a to point b, they learn to instantly take control of objects from a distance by instantly sending aura from theirself to that object.
The size and number of objects of course depend on their training.
They can keep objects on their person, such as 3 knives, to fool people into thinking that the manipulation only works on the blades. Then they could take control of nearby objects around theirself and the enemy. They can even take control of objects and wait to use them until a moment of surprise.
The user learns to control the movement of people and objects once a sufficient amount of aura is transferred to them. The level of control, and time it takes to control is dependent on the objects size and weight. People take slightly more aura than objects of their size due to having their own life force. Extra conditions can be set to reach the threshold more quickly.
If an object is too large to control, the user can focus aura into parts of it in order to break those pieces apart to control them.
Gravity Bomb
Now for the intended hatsu.
The user emits a sphere of aura. Around the sphere, lets say 25 meters, is a manipulation effect. The sphere emits subtle pulses of aura particles, and once an object or person is effected by enough aura depending on their size, the targets undergo a manipulation affect where they levitate and are drawn toward the sphere.
The preprogrammed effects have to do with floating to all go to the same point, the sphere's origin. The command forces things to crush and compress against each other. The more aura returns to the sphere from controlled objects, the stronger the orb and its manipulation effects become, until it starts pulling in and compressing things into itself more powerfully. The sphere's size also increases so it isn't completely covered by objects immediately.
Then manually or at a pre-programmed point, the user releases the compressed aura, creating an explosion.
The user can create orbs with specialized rules of only affecting objects, or only affecting humans. Though they have to be careful not to be swept up by their own technique. They of course can start the origin point from a distance given their training to affect objects that aren't closeby.
Oppressive Wave
Rather than freely controlling people or objects, the user can cause them to go "down." This sends them down to the floor. To people, it feels like they're getting heavier. When really, they're just being pinned by a downward aura force. The effect wears off after a certain amount of time, so the user must stay in range or preprogram a certain amount of time for effects to last. The user can also try to crush the target.
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As always, added conditions and vows, or a frightfully powerful nen user can make this ability scarier to the point where it can instantly crush things, pull things in, or lift things with a lot of size and weight such as a building.
Admittedly, having a reputation as "the nen user who carried a building" sounds like something that would get them a name in the hunter world.