[DISPROVED] My thougts on gavitational waves and ETI

One of the greatest breakthrough of applied science in my lifetime happened relatively recently: we detected gravitational waves. In essence, we have detected a grativational "ripple" of gravity; much like you would feel your boat rock in a still pond if someone were to throw a heavy rock into it. But regardless of how amazing this is, it is also extremely sad.

Consider the following. If you had a space ship, and accelerated it close to the speed of light, tons of things would happen. The most important one is that you would need unconceivable amounts of energy to sustain acceleration. In fact, because the mass of your space-ship is non-zero, you would need an infite amount of energy to reach c. But for the sake of argument, lets assume you are some alien race with the means to accomplish this, such as anything along the lines of a Bussard ramjet to get really close to c without violating any law of physics.

Then, for an external observer, and much like Poul Anderson describes it in Tau Zero; as your speed approaches c, the mass of your ship m must approach infinity. Meaning that you would be the most extreme and odd thing travelling through space: a junk with the tremendous mass of a whole sun, buzzing at a speed reserved for photons (and gravitational waves).

Now, if going back to our previous analogy, we felt our boat rock because someone stirred the water with a rock, how come we don't detect any transatlantic cruiser our pond? Why don't we detect any extraterrestrial intelligence (ETI) using this most extreme of technology to travel from one star to another? After all, reaching extreme speeds should be doable for an advanced Type I civilization, and more so for a Type II.

Is it that these civilization have found a more energy-efficient means of travel? Or because our sensors were not pointed in the right direction? Or is it... because we are completely alone?

Important update

After discussing the matter on reddit, I realized I had comitted a major mistake in my above reasoning. As it happens to be, I had a major misconception regarding relativity and how gravitational work.

First, the formula for relativity is not E=mc², but E²=(mc²)²+(pc)², where p stands for the momentum of the object. In simple terms, E=mc² is only valid for static objects (or relatively low speeds) such as the way we usually treat solar systems and the such. But at relativistic speeds, the momentum becomes very important, as it's not the mass that increases when a ship/projectile flies at near light speed, but this term. Consequently, a 1 ton space ship traveling at c, still weights 1 ton.

On the other hand, gravitational waves are not caused by objects fling in a straight line, but by objects that are under acceleration. And in this regard, a LOT of acceleration; such as two neutron stars orbiting at close proximity around each other. Accordingly, no alien craft or weapon would have probably undergone the necessary accelerations for us to detect with today's technology.

In any case, I want to thank everyone who got involved in this topic and had the patience to introduce me to this fascinating topic. I stand corrected :)