Hi.
Firstly, we haven't got any hard evidence for parallel universe(s), just some theories that involve them. Therefore, the situation described by Mukul might be correct. All I can do is talk about some of the theories that exist and discuss some of the differences and similarities to Mukul's idea.
What if our whole space is just like sheet having two sides?
If there are parallel universes, then there's very little reason why there would be only two of them. There could be many. If there were many, then there's very little reason why we have some special relationship with just one of these, so that we are one side of a sheet and they are on the other side of the sheet. This may reduce the usefullness of imagining a simple sheet which only has two sides.
Example: The "many worlds" interpretation for Quantum Mechanics.
The many-worlds interpretation implies that there are very many universes, perhaps infinitely many.[11] It is one of many multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realised.
Taken from Wikipedia. https://en.wikipedia.org/wiki/Many-worlds_interpretation
In the many worlds interpreatation the relationship between the different "worlds" (or universes) may only be that we had a common history until the time and point of branching into two separate "worlds" or universes. After the branching there's no requirement or expectation that one world would influence or be influenced by the other world.
If we say that heavy mass objecs bend the space time fabric around it creating a trough then right if we look at the other side of the fabric we can imagine a hill. Similarily in the side of the fabric we live, there can be an uprising that is just a black area where we cant see anything.
This sounds a lot like you are considering General Relativity and considering the common visualisations of spacetime as some sort of fabric.
Firstly, this entire concept of spacetime as some sort of fabric is intended only as a visualisation of what is happening and it's nothing more than that. So we have to start by asking what is it that you think a "hill" or outward curvature of spacetime would do or represent in your model? Presumably the opposite of a trough or inward curvature. For the usual visualisation of spacetime as a fabric, a trough shows a distortion of spacetime so that an ordinary mass would be attracted to the centre of that trough. So a hill would presumably be some area or region that repels ordinary matter or opposes conventional gravity.
We haven't found a region of space where matter is obviously repelled from that point of space. So we haven't found any obvious and isolated "hills" in the fabric of space. However space is big and there would always be problems determining if something was repelled from one region or if it had just been attracted to some other region.
** See late editing below ***
There are some situations where we might assume the existance of something that does work so as to oppose conventional gravity: I'm mainly thinking of dark energy. I suppose this could be explained or considered as something similar to your description of a hill formed by something on the other side of a sheet of fabric. There are some ideas and theories which suggest that dark energy has a particular distribution through space. However, it would tend to be reasonably uniform through space and not form isolated hills like the sort of thing you were describing. So if this dark energy is caused by something "on the other side" of the fabric then the other side would seem to have a much more uniform spread of matter than in our universe (that's ok, it's possible, we can think of the other universe as having diffuse clouds of interstellar gas and very few concentrated lumps of matter like planets, for example).
There are numerous sources of information about dark energy. One recent thread from this forum includes this one: "What do we know about dark energy?", https://www.thenakedscientists.com/forum/index.php?topic=83661.0.
What I am trying to suggest is that there can be a parallel universe on the other side of the fabric and the black hole is just a hole in the fabric joining the two parallel universe on the opposite ends of the Fabric?"
Well that does sound a lot like some existing theories on black holes. The maximally extended Schwarzschild solution for a black hole allows for the existance of multiple regions of spacetime. Note that this does NOT prove the existance of these other regions. It is simply that we can extend the solution in a natural way and then these regions appear. Just because we can extend the mathematics does not guarantee that there is any physical significance to the solution obtained.
Anyway, when represented on a Kruskal diagram, we would be located in one region of spacetime (usually labelled and described as region I, which I know is quite a dull name). What you would normally describe as the interior of the black hole is labelled as region II in the diagram below. However the roman numeral you assign a region starts to show some variation between different sources of information here, there are 4 regions and no universal agreement on how you should label them.
There is also a region IV which is often described as a "white hole" and, more interestingly a region III which appears as a region of spacetime similar to the region I in which we are located.
That region III could be thought of as a parallel universe, a region of spacetime that is similar to our own.
(https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Kruskal_diagram_of_Schwarzschild_chart.svg/390px-Kruskal_diagram_of_Schwarzschild_chart.svg.png)
Kruskal diagram of a maximally extended Schwarzschild solution. Taken from Wikipedia, https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates
In some sense, the black hole would be a point of connection between these two regions, however passing from region I to region III should not be possible. There are no time-like paths connecting the two regions, which just means that passing from one region to the other would require faster-than-light speed movement across the event horizon of the black hole. So there are two things we should consider before we allow our imaginations to run wild and think of all those Sci Fi films and books that feature wormholes connecting two parallel universes:
1. There is no guarantee that there is a region III. It is just an extension of some mathematics with no real world justification.
2. Even if region III exists in some sense, nothing should be able to pass from region I to region III or vice versa. Specifically nothing in one region should be able to interact or influence anything in the other region.
- - - - - - - -
There are many other theories involving multiple universes. This post is already too long, there's no need to try and discuss them all and I'm sure I don't know about all of them anyway.
Let's just go back to Mukul's idea. If it's right then it predicts the existance of "hills" in the fabric of spacetime. So we should be trying to find these "hills". The current research into badly behaved gravity and deviations from current models of gravity would seem to be most easily connected with what a "hill" should do: So that will be theories about dark matter and especially dark energy.
Best Wishes.
**Late editing** Actually there are regions of space that could be considered to repel matter and indeed they are explained equally well as being equivalent to an attraction to other regions. See Halc's post later.