Is there a core in the moon allowing it to have somewhat stronger gravity than empty Space?

Question: Is there a core in the moon allowing it to have somewhat stronger gravity than empty Space?
- Keywords:
  core,
  gravity,
  moon
Asked by Frozen comet to Anne, Beth, COLFlight, Jon, Tom on 16 Oct 2015.
- Beth Healey answered on 16 Oct 2015:
  
  Hi Frozen Comet!!
  
  The existence of gravity is dependent on the mass and your distance from it.
  
  Consequently empty space has no gravity while the moon does (because the moon has a mass).
  
  Moon gravity is less than that we find on Earth because the moon has less mass.

Question: Is there a core in the moon allowing it to have somewhat stronger gravity than empty Space?