What is Frame Draggin, and Gravity Waves where did the idea of them come from in GR?
If you compare gravity to electromagnetism, frame-dragging is somewhat similar to the magnetic field due to moving charges (currents), and gravity waves are somewhat similar to electromagnetic radiation.
Maxwell's equations predict the wavelike solution for electromagnetism which gives rise to radio, light, and the entire electromagnetic spectrum - Einstein's equations of general relativity have similar wavelike solutions, so similar gravity waves should exist. However, AFAIK nobody has detected them directly yet.
Most of the experiments to detect gravitomagnetism / frame dragging involve spinning bodies. While this is not the only way to detect the phenomenon, it's one of the more clear-cut. To use the electromagnetic analogy, a spinning charge has both an electric and a magnetic field, while a non-spinning charge has only an electric field. Thus one way to detect magnetism would be to look for a difference in the behavior of a spinning charge (which would be affected by both electric and magnetic forces) and a non-spinning charge (which would only be affected by electric forces).
Wikipedia "Timeline of Gravitational physics & relativity" lists some dates and people as far as when the effects were first predicted theoretically:
# 1915 - Albert Einstein completes his theory of general relativity. The new theory perfectly matches Mercury's strange motions that baffled Urbain Le Verrier.
# 1916 - Albert Einstein shows that the field equations of general relativity admit wavelike solutions
# 1918 - J. Lense and Hans Thirring find the gravitomagnetic precession of gyroscopes in the equations of general relativity
So both effects were predicted very quickly after Einstein's theory was published.
Frame dragging (aka Lens-Thirring effect) is not very noticeable in a body such Earth, but it must be quite important in a black hole. In concrete, in a Kerr black hole, there exists frame dragging in a zone called ergosphere, situated between the outer event horizon and the stationary limit. The ergosphere is not a fatal zone, you can scape of the black hole if you are in it, but you can't avoid to be dragged by frame dragging while staying in it
so what physical effects might you observe? from both grav waves and dragging, like is the draggin creatine an extra gravity field because say the earth is spinning, thus its gravity field is stronger? or is it some other field?
The Earth's gravitational field induces orbital precession via standard Newtonian gravity. The exception is polar orbits, at which point the Newtonian effects vanish. It's critical to suppress the Newtonian effects because they are huge compared to frame dragging effects.
Separate names with a comma.