Solar System vs. black hole

 so if our sun were captured by a black hole?

In principle, yes, a rogue black hole could pass close enough to the Solar System to become gravitationally bound to it, but the odds are extraordinarily tiny. And if it did happen, the outcome would probably be more complicated than "the black hole immediately eats the Solar System." 

A few points: 

• Black holes do not vacuum up everything around them. If the Sun were magically replaced by a black hole of exactly the same mass, Earth's orbit would remain essentially unchanged. Gravity depends on mass, not on whether that mass is a star or a black hole.
  

• The real danger would be gravitational disruption. A passing or captured black hole would perturb planetary orbits. Depending on its mass and trajectory, planets could be thrown into new orbits, ejected from the Solar System, sent into the Sun, or collide with one another.
  

• If the Solar System somehow became a binary system consisting of the Sun and a black hole orbiting each other, stable planetary orbits might still exist in some configurations. We know binary star systems can host planets. However, the process of forming such a binary through a close encounter would likely be violent enough to destabilize many existing planetary orbits.
  

• Being "eaten" by the black hole is actually less likely than being gravitationally scattered away. Black holes are physically very small compared to the vast distances between planets. Even a black hole with several times the Sun's mass would have an event horizon only a few tens of kilometers across. Direct impacts would be rare.
  

• A more massive black hole, such as one hundreds or thousands of times the Sun's mass, would be much more destructive gravitationally. It could strip planets from the Sun's control and potentially capture or eject them.
  

So the most probable sequence would be: 

1. Rogue black hole approaches.
   

1. Planetary orbits become disturbed.
   

1. Some planets are ejected, others move inward or outward.
   

1. The Sun and black hole might form a temporary or long-lived binary if conditions are just right.
   

1. Over millions of years, the Solar System could become chaotic and eventually lose many or all of its planets.
   

Ironically, the Solar System being torn apart gravitationally is much more likely than the planets literally being swallowed by the black hole. The black hole's gravity is the real threat, not its event horizon.