Does the Aurora Explode?

After the Aurora's Drive Core explodes, the ship's wreckage is surrounded by Radiation and is unapproachable without a Radiation Suit. While quite dangerous and far out, the player can visit the Aurora early in-game before it explodes, although multiple tools are needed to properly explore the ship.

Can you stop the aurora from exploding Subnautica?

The aurora explosion allows you into the ship to fix the engine leak. You can't prevent it.

How do you get into the Aurora after explosion?

The Aurora is not initially accessible at the beginning of the game, even with the Radiation Suit equipped. Before you can get into the Aurora you have to wait for it to explode, blasting away the entire front end of the ship in the process. That explosion will create the opening where we can enter the Aurora.