There are more things
in heaven and earth...
than are dreamt of in your philosophy.
Hamlet (I, v, 166–167)
Certainly the most intriguing prospect behind observing gravitational waves (Gravitational Wave: A gravitational disturbance that travels through space like a wave. This type of wave is analogous to an Electromagnetic Wave. Gravitational waves are given off by most movements of anything with mass. Usually, however, they are quite difficult to detect. Physicists are currently working hard to directly detect gravitational waves. Experiments like LIGO and LISA are designed for this purpose. ) is the great unknown. While the possibility of finding strange new things that scientists have only dreamt of is tantalizing, even more so is the chance to find objects that physicists have not yet begun to imagine. Gravitational waves give us a powerful way to look into places astronomers have never before been able to see — hidden behind walls of luminous matter that interfere with light, or hidden in the deepest recesses of time.
Each time scientists have used new instruments to peer into the heavens, they have discovered novel phenomena. When Galileo used one of his first telescopes, he found moons orbiting Jupiter — providing firm evidence that the Earth was not the center of the Universe. Radio telescopes discovered Quasars, and the Neutron (Neutron: One of the particles in an atomic nucleus. These particles have no electric charge, but they hold together the protons (positive particles in a nucleus), and account for roughly half of the particles in the nucleus. Neutrons are fermions, and are believed to form the majority of the matter in a neutron star.) Stars (Neutron Star: A type of star which is very old, having cooled off and stopped nuclear fusion reactions. When gravity pulls the star down on itself, the electrons and protons are squeezed together, leaving just neutrons. The star is then supported against gravity by "neutron degeneracy pressure" (no two neutrons can be in the same place at the same time). These are produced when a star is too heavy to be a white dwarf (White Dwarf: A type of star which is very old, having cooled off and stopped nuclear fusion reactions. A white dwarf is supported by "electron degeneracy pressure" (no two electrons can be in the same place at the same time). These are produced when a star is not heavy enough to turn into a Neutron Star or a Black Hole. )})|white dwarves}), but not heavy enough to turn into a Black Hole. ) responsible for them. The first microwave telescope found the Cosmic Microwave Background, which conclusively showed that our Universe began in a much smaller and hotter state: the Big Bang (Big Bang: An astrophysical theory of the beginning of the Universe. It suggests that the Universe began in a very tiny region of space, and exploded outward. Astrophysicists believe that this occurred roughly 14 billion years ago. Other astrophysical theories for the beginning of the Universe — like the Braneworld theory — exist, though none is as thoroughly studied and supported by the data as the Big Bang model. Scientists have no idea what came before the Big Bang.).
While we can speculate on all sorts of weird events in the Universe, nature is endlessly surprising. As Richard Feynman put it, “I think Nature's imagination is so much greater than Man's. It is never gonna let us relax.” The most enticing reason to search with gravitational-wave detectors is not to find those things we think must exist, but to find those that lie waiting to be discovered.
Read about Numerical Relativity (Numerical Relativity: The branch of Relativity research which deals with simulating the development of Spacetime (Spacetime: A concept in physics which merges our usual notion of space with our usual notion of time.), using computers. This is believed to be the only possible way to understand things like the merger of two Black Holes.)