Kind of a back to topic question here...


The observed collapse of the binary black hole system radiated a lot of gravitational wave energy,  IIRC that was stated as release of energy equivalent to 3 solar masses.  So the mass of the combined black hole is 3 solar masses less than the combined mass of both black holes before collapse.  I believe that before this direct observation of gravitational waves, there was already evidence of orbital decay of observable high-mass binary systems where the rate of orbital decay correlates with the calculated loss of mass/energy through radiation of gravitational waves.  Though gravity is a weak force, it acts over long distances. A black hole might not be part of a binary pair with something else (another black hole or neutron star or whatever) but it will be causing gravitational effects on other objects - no matter how far away they are, and other objects will cause gravitational effects on the black hole.  Doesn't it follow that a black hole will always radiate some energy (thus always lose mass) as gravitational waves even if not in a collapsing binary system? 





Yes, in a Relativistic system, all rotating objects (not just Black Holes) are always losing energy by radiating gravitational waves.
But, for most objects, the loss of energy is relatively small and the orbital decay is very, very slow.
Given enough time, all orbits decay.
Will the Earth eventually tumble into the Sun?
Probably not.
The Earth will likely be consumed by the expanding Sun long before that.
If the Earth was to survive, in orbit, then given enough time, it would crash into the remnant of the Sun.







Now I found data on the theoretical rate of orbital decay through relativistic loss of mass due to gravitational wave emission in the earth/sun system.  I'm not sure if the calculation was based on an earth/sun binary system or took into account loss of mass from the sun due to orbits of the other planets etc, but anyway the speed of that orbital decay is almost completely insignificant - the orbit would be closer by the width of a hydrogen atom per 300 years.
But the earth orbit around the sun is not decaying as the sun loses mass through fusion and solar wind, about 5.5 million tonnes per second, orbital distance is actually increasing.  Unfortunately in 5 billion years at the present rate of increase in Earth's orbit, we'll only be 80,000km further away than we are now. 





Yes, the relativistic orbital decay is minuscule. But, given enough time (vast Astronomical time >> current age of Universe), all orbits decay.


That is a key difference between Newton and Einstein.


In Newton's theory, any two gravitationally bound objects can orbit their common centre of mass forever.