A baseball moving sufficiently close to the speed of light could theoretically spend less than a nanosecond inside of the Sun in the balls frame. If a baseball were traveling close enough to the speed of light, could it pass through the Sun?
Edit: Imagine a single proton traveling with 1 TeV of relativistic kinetic energy. It can and does pass right through a human body without fusing, stoping or destroying the person and so on. Now imagine a baseball with enough energy that a single layer of the Sun only one atom in thickness can be easily penetrated without taking away all of the relativistic momentum of the particles constituting the baseball. Then imagine the scenario again with two atom thickness and the required energy to penetrate that layer. Then continue this exercise until a baseball passes through the Sun. If you think that it would "burn up" how would its 4 momentum be conserved? I think it's just a matter of what velocity is required to make it to the other side.