Naturally, the Law of Conservation of Energy and Law of Conservation of Momentum are also part of relativity theory. These five principles and laws are all you need to construct anything on this web site and any (valid) idea with relativity. You have a choice of what to believe. Successful physicists draw their own conclusions and don't let others (including me) tell them what to think. You will see thought experiments on this web site that don't appear anywhere else. This is because these experiments are not solvable by the more complicated methods currently being taught.
For example, a man is standing on the surface of a planet and reaches up to a higher gravitational potential with a pole. At the higher level, another man has a hold of the other end of the pole. The bottom man pushes the pole (horizontally or vertically). What force does the top man feel? How much energy does he receive from the bottom man?
General Relativity cannot answer these questions. You have been told that General Relativity is the only way to analyse gravitational experiments, but this simply isn't true. Einstein made the Special Theory handle gravitational fields. General Relativity is an overlay of tensor calculus on a Special Relativity framework. General Relativity doesn't invalidate Special Relativity, but incorporates it.
Let's take a look at some serious mistakes in current thinking. If you've been interested in relativity, then you already know what a "wormhole" is. Suppose a mass is at the entrance to a wormhole, moves slowly into the entrance and appears a short time later at the other end, a great distance away. Think about this process as Newton would. Draw a boundary around the volume of space containing the wormhole (both ends and all the space between) and make it an isolated system. What happened to the Law of Conservation of Momentum inside the boundary? Remember, there was no momentum or center of mass change outside the boundary. But a mass has moved a great distance in a short period of time inside the boundary. What would Newton say about that?
Yes, I know that space-time folded back upon itself and the mass didn't really travel that far. You've got to be kidding. You have a choice of believing Newtons Laws, which have been demonstrated to be accurate every time that they have ever been tested, or you can believe that space-time folded back upon itself, which has never been observed. Isn't defective thinking like this the reason that the Scientific Method was conceived in the first place?
Let's take on another subject: black holes. Suppose an object is falling into a black hole. Today's physicists will tell you that the object achieves the speed of light just as it gets to the event horizon. The same physicists will tell you that the mass of the object becomes infinite when that object reaches the speed of light. Infinite? More mass than all the objects in the universe? Doesn't that sound a little bit implausible? I know what you've been told. Time slows down as the object approaches the event horizon, so that it never actually gets there. Time is 'frozen' at the event horizon. So how could a gravity wave from the black hole get past this 'frozen' shell surrounding it? The gravity of a black hole should appear to be zero when the observer is outside the event horizon, not infinite.
There's another problem with black holes. If objects really do become frozen at the event horizon, then all these frozen near infinite masses become black holes themselves. Then they collect more objects in the same way. The acquisition of mass by any black hole would grow exponentially until the entire universe was consumed. This obviously hasn't happened.
The notion that General Relativity somehow replaces the Newtonian model for gravity is a misrepresentation. The surprizing thing about General Relativity is that solutions to it often include the Newtonian gravitational model (or other similar models). You need to inject a gravitational model into General Relativity in order to solve it. It is not a unique model of itself. This is the way the famous Schwarzschild Solution to the General Theory is structured. The current physics establishment doesn't want to say that General Relativity is just the Newtonian gravitational model in fancy dress. The Schwarzschild Solution describes a thought experiment which is simplified to the point that virtually all of General Relativity is stripped away. I shall discuss this further below.
Unfortunately, the General Theory is too complex for the vast majority of physicists who think they understand it. It is impossible for anyone to dispute current solutions to the General Theory, as the discussion quickly degenerates into obtuse discussions of manifold structure and the correct form of this or that tensor. This is very convenient for physicists who are baffled by it all. If nobody really knows what's going on, then anyone can come up with a theory to explain it. Lots of physicists will tell you they understand General Relativity. But black holes and worm holes? Any analysis that breaks the conservation laws is not valid. The General Theory was created with strict adherence to the conservation laws. Tensor Calculus is not the mechanism to create energy, momentum or infinite anything.