> which experiments exactly?

Put a bunch of charge into it to generate a naked singularity. Then look at it.

More usefully: perfect the Penrose process.

There's a few obvious things. What you've got is an almost "vertical" gravity well near the object. A smaller black hole would actually have a steeper gravity well than a large one.

(1) See how gravity behaves at those strengths and scales by firing lasers and particle beams past it, grazing the event horizon, and use that information to test quantum gravity hypotheses and things like string theory. Classical gravity predicts certain results. Quantum and non-classical theories would make different predictions. For example, you might see direct evidence of gravitational quantization very close to the horizon.

(2) Chuck stuff into it: heavy ions, small masses with a coilgun. Measure the results: spectrum, particles emitted, etc.

(3) Chuck stuff into it in a very precise way and use its extreme near-horizon gravitational well as a particle accelerator to achieve collision energies potentially millions of times greater than the LHC. You would not be able to directly observe these collisions, but you could potentially observe stuff kicked out. Orbit it with an array of sensors and magnetic traps.

Bonus: use its gravity well to yeet small probes at interstellar velocities (a few percent 'c' or higher) for flyby missions to photograph exoplanets? I believe you could use the Oberth effect here and do something like fly very close and fire a single Orion-style nuclear pulse at a sacrificial pusher plate. The impulse would accelerate the payload to insane velocities.

No human passengers though, since the acceleration would probably do this: https://www.youtube.com/watch?v=waG8YYTwpAQ

I'm not sure anything after the event horizon right? Since no light == no information.