Mainstream claims it is because an energy exchange by the gravitational waves. We do not observe any gravitational wave till now.

An alternative explanation is a relativistic mass which is observed.
Binary stars are rotating around a common centre of gravity. The heavier star (Black Hole) rotates slower in the system because a shorter radius. A lighter star (neutron star) rotates faster because longer radius (distance from the gravity centre). If the distance between stars is short enough the velocity becomes relativistic in the gravitational field. The potential gravitational energy is transformed into a kinetic energy and into a relativistic mass at least.
Faster oscillations of the particles in the stars cause heavier mass. It increases gravitational attractive force, which means shorter radius and faster rotation.

Gravitational attractive force F=GMm/r^2

Kinetic repulsive force F=mv^2/r

Velocity in balance v^2=GM/r

where M = mass of the system under orbit of the less massive star, r= distance between less massive star and gravity centre.

The velocity does not depends on the mass of the less massive star but of the whole mass under orbit. The more massive star also rotates and its rotations are driven by the less massive star. The relativistic motion of the massive central star causes increase of the gravitational attractive force and the strar spirals towards the gravity centre. The process continues till the whole mass will be uniformly distributed on the orbit.

Accretion disc do not disturb a motion of the central star and it is stable very long time. Accretion disc may be even more massive than the central star but it is uniformly distributed on the orbit.

Your analysis is wrong. The force is a frame dependant thing. And it's not called ``kinetic repulsive force'', most of us call it ``centripetal''.

Hi Czeslaw, BenTheMan,
Ben's right but you also have to remember that a BH has a MUCH more powerful gravitational field than a Neutron Star but the strength does decreases inversely proportionally to the distance from it, which would explain why accretion disks can happily revolve around a BH for quite a long time.
Any sharper minds out there please correct any flaws in my reasoning.
Peace,
Ron

And this isn't how binary stars work. See this: http://nobelprize.org/nobel_prizes/physics.../discovery.html

And, from this website:
http://universe.nasa.gov/program/pulsars.html

``The waves carry away orbital energy, causing the two bodies to draw slowly closer together. The perfect match between the observed orbital decay and Einstein's prediction is so exquisite that it has convinced almost all physicists and astronomers that gravitational waves must exist.''

Can you fit the data better?

Mainstream prefers the gravitational waves as an explanation of the binary star collapse.
Why the accretions disc does not collapse by that way ?

They do, just billions of times slower.