How much energy does a star absorb from gravitational waves as it orbits a black hole?

Question

suppose: a star could orbit a black hole in its own solar system. So I wonder how much gravitational wave energy it absorbs from that black hole and does its mass increase as it absorbs gravitational wave energy? Also, if there are other minor planets orbiting that star. What will happen to them?

Answer 1

Gravitational waves are generated by systems whose mass quadrupole moment has a nonzero second derivative. A simplified way to think about this is through acceleration. Acceleration is the second derivative of position.

Accelerating mass is a minimum requirement to produce GWs. There are some special, highly symmetric systems that have non-zero acceleration, but whose mass quadrupole moment doesn't change. These systems won't produce GWs.

A binary star or black hole system does produce GWs. Each mass in the system is constantly accelerating as they orbit around each other. Remember, turning is a change in the direction of velocity, so even a steady speed circular orbit is accelerating.

A spinning sphere does not produce GWs. A point on the surface of the sphere accelerates to turn, but the symmetry of the system means the mass quadrupole moment doesn't change.

All of the this is to explain that the black hole in your system doesn't emit GWs all by itself. The combination black hole plus star system does. The system emits gravitational energy as GWs, causing the orbits of the black hole and star to change. But the star does not absorb any energy from GWs.