Originally Posted by

**Markus Hanke**
There are a lot of different questions in your post, the answers of which are not necessarily easy to explain.

First of all, General Relativity is a descriptive model of spacetime and gravity - this means it tells us very well *how* gravity behaves, but it has nothing to say as to *why* it does so. Using this model, we can take a given distribution of energy-momentum, and calculate from it how the trajectories of objects in and around it would behave, as well as the evolution of that distribution itself. That's all it does. GR makes no attempt to provide an explanation as to why energy-momentum influences the geometry of spacetime in the particular way it does; part of the reason seem to be fundamental principles of topology, but that's likely not the full story. This is currently an area of ongoing and very active research.

Now to your other questions:

1. The source of gravity is *energy-momentum*, not just mass. The key here is to understand that the mathematical object that describes energy-momentum is not just a single number, but a more complicated object called a tensor; you can envision this as a matrix of 16 real numbers, each of which describes a certain aspect of the energy-momentum distribution.

2. When a mass is in relative motion with respect to an observer, then that observer will say that the object's *relativistic mass* has increased. It is important to understand that 'relativistic mass' can be seen as a measure of an object's resistance to further acceleration - hence, the faster something moves with respect to yourself, the harder it becomes to accelerate that object even more. However, relativistic mass - despite what its rather unfortunate name would imply - is *not* in isolation a source of gravity. That means that the gravity an object in relative motion exerts on itself and its surrounds is not "increased" just by being in relative motion; this would obviously create paradoxes. Mathematically, what happens is that - when you put something in relative motion - some components of the energy-momentum tensor will increase, while others will decrease in magnitude, leaving the overall object unchanged. All of this is not to say that momentum has no effect on gravity - it does -, but only that relativistic mass on its own isn't a source of spacetime distortions.

3. Yes, you can generate gravitational waves by making a chunk of mass spin fast enough, so long as that chunk isn't a perfect sphere ( in which case there will be no gravitational waves ). However, the underlying mechanism is very much more complicated than the simple notion of relativistic mass. A spinning chunk of mass will emit gravitational waves, and it will also distort the background spacetime through which those waves propagate in complicated ways, overall giving quite a complex system.

4. If you spin a long pipe at high velocity, then its two ends no longer share the same notion of simultaneity. Measured from any point on the pipe, the outermost end will start to "lag behind" your own clock, so it will never exceed the speed of light as measured by you. An observer looking on such a spinning setup will see the pipe ceasing to be straight, and instead "bend" backwards with respect to the direction of rotation. There will be a gravitational field associated with such a setup, but again, it will be quite complicated, and not due to 'relativistic mass'. Mathematically, this is quite a difficult scenario to treat.

In general terms, the main message is - when talking about gravity, it is best not to think in terms of 'relativistic mass', since that quantity taken in isolation isn't a source of gravity. It is necessary to consider *all* forms of energy - energy density itself, momentum, pressure, flux etc etc. Gravity cannot be reduced down to a single number; even the concept of "strength of gravity" is problematic, and can't be easily defined.