First of all, there is no reason to believe that ghosts reside in the fourth dimension. Second, spacetime is governed by the laws of physics. The force of gravity has been proven to have an effect on spacetime. So therefore, if ghosts are hiding in the fourth dimension would have to preside by the laws of physics as we know them.
There is perfectly good reasoning to not even believe, but acknowledge the
possibility extreme likelihood that supernatural beings exist and reside in the fourth (or higher) dimension. It explains so much of what they are capable of doing and how they behave. Here is an analogy presented by a very intelligent author whom I can't recall the name:
The 2nd dimension is a flat plane, say we have Mr. Square and Mr. Sphere of the 3rd dimension. Mr. Square hears a voice saying, "Hey, square!" Mr. Square has no idea where the voice is coming from. Mr. Sphere says, "Up here!" Mr. Square looks left and right and see nothing. Then Mr. Sphere says, "Let me come to you." So Mr. Sphere lowers himself on Mr. Square's plane. When Mr. Square looks to his left, he sees a circle which starts small and then gets larger. Mr. Square is baffled and says, "How did you do that? You are a circle which gets smaller and bigger." Mr. Sphere replies, "In my world I can move up and down, unfortunately, you can only see one slice of me at a time because you live in the second dimension. In my world, I am a round sphere, not a circle."
The point of that story is that we are the squares. We can only see one slice of the 4th dimension at a time as the square could only see one slice of the sphere at a time. In the 4th dimension, time does not exist because we see all of our personal individual existence at once. Notice how ghosts only haunt places they have been to in their life? They are bounded by where they have been, however, they are not bounded by the time in which they visited that place. Thus, they are able to haunt any place they have been to at any given time.
The second point of all that I said is that gravity cannot effect something which does not exist. The limitation of time is non-existent in the fourth dimension. Gravity can effect, and you are absolutely right, time as Einstein discovered upon observing space, but only in the first three dimensions.
--------Separate Thought Process For Fun---------
If you want to get into the fifth dimension, I think the next limitation to get overcome is experiencing only our personal experience. The only way we may perceive the fourth dimension is through death. That would transcend our souls to a higher dimension and eliminate time. Our bodies are a prison keeping our souls in the third dimension. Our souls are of another, higher, dimension. Recall how I brought up ghosts being "bounded by where they have been." This is because we can only recall what we have experienced ourselves. Now, taking it a step further, that sounds like a limitation to me.
If you haven't noticed, there is a pattern. Each dimension exceeds a prior dimension's limitation (refer to my last post for an example.) This is to say that there is another limitation to exceed in the fourth dimension which has been exceeded in the fifth dimension. Probability suggests that this next limitation is only knowing what you have experienced. In the fifth dimension, it is possible that this limitation is exceeded and we are then able to recall things from other being's experiences. That is right, a being or many beings who share a unified collection of experiences would be a candidate for the fifth dimension. This also improves the likelihood of deities and explanation of their powers.