Difference between black hole solutions and wormhole solutions

[extrads]

How do we know which one is a black hole solution(metric) or a wormhole solution(metric)? what is its feature?

 

[WannabeNewton]

Are you talking about Schwarzschild wormholes in particular? In the maximally extended Schwarzschild solution, the region represented by the black hole can easily be differentiated from the region represented by the so called white hole through a Kruskal diagram: http://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

 

[pervect]

I'm not quite sure what the OP wants. Just in case, I should point out that you can't actually traverse the Schwarzschild wormhole, the singularity gets in the way. There are such things as traversable wormholes, but they generally require exotic matter.