Don't objects steadily evaporate over time by emitting gravity waves?

No, because this process is so inefficient.

Although the mass of every body includes the energy stored in its gravitational field, the only way to get a body to loose energy by gravity is by way of gravitational radiation.

General Relativity theory says that gravity waves and radiation are produced by accelerating the body. However, in order for a body to lose mass this way, you need to accelerate the body enormously because gravity waves are so weak.

The acceleration felt by two dense neutron stars orbiting around each other every minute at a distance of a few hundred kilometers is the most extreme acceleration known. It is not very effective in causing the bodies to loose much mass compared to the feeble mass lost by the electromagnetic radiation leaving their surfaces.

Copyright 1997 Dr. Sten Odenwald