Wormhole - In the game, it would basically be just an aesthetic object, appearing as a strange light distortion like in the movie Interstellar.
Black Dwarf - The cooled remnant of a white dwarf. A massive, smooth chunk of carbon or other metals floating in space.
White Hole - An object with negative mass, and thus negative gravity.
Energy Vortex - Another aesthetic object. The name pretty much says it all; it's a vortex of energy. The player could consider them portals, interdimensional rifts, etc.. Mass and radius are entirely customizable (not bound to each other). The color would be customizable.
Ion Cloud - Basically just a very small nebula. Like the energy vortex, this object's mass, radius, and color would be customizable. The players could also customize its shape.