(a) Explain in your own words and in a concise way (no more than a short paragraph) what gravitational waves are. (b) Show that the non-vanishing components of the quadrupole moment tensor I" for four particles of masses m₁ located at the points (a,0,0) and (-a, 0, 0), and masses m₂ located at (0, a, 0) and (0, -a, 0) respectively are given by: 1=2m₁ a², 1=2m² a². (c) Compute the components of the quadrupole moment tensor in frame in which the particles are rotating about the z axis on circle of radius a and angular velocity w by considering the following coordinate transformation: x'x cos(wt) - y sin(wt) yx sin(wt) + y cos(wt) (d) Use the quadrupole formula 2=2. to compute the power radiated in gravitational waves by the rotating masses. (Hint: recall that (cos² (wt)) = (sin²(wt)) = ½)

(a) Explain in your own words and in a concise way (no more than a short paragraph) what gravitational waves are. (b) Show that the non-vanishing components of the quadrupole moment tensor I" for four particles of masses m₁ located at the points (a,0,0) and (-a, 0, 0), and masses m₂ located at (0, a, 0) and (0, -a, 0) respectively are given by: 1=2m₁ a², 1=2m² a². (c) Compute the components of the quadrupole moment tensor in frame in which the particles are rotating about the z axis on circle of radius a and angular velocity w by considering the following coordinate transformation: x'x cos(wt) - y sin(wt) yx sin(wt) + y cos(wt) (d) Use the quadrupole formula 2=2. to compute the power radiated in gravitational waves by the rotating masses. (Hint: recall that (cos² (wt)) = (sin²(wt)) = ½)