# Supermassive Black Holes....

Consider a SBH Binary System free from the influence of the stars....This system can be treated as $$2$$ Massive Black holes each of Mass $$M$$ moving under the influence of the other in a circle of radius $$a$$....Consequently Energy is lost due to emission of gravitational waves.The rate of Energy lost is given by $dE/dt=-(1024/5)(G/c^5)(\omega ^3 I)^2$.where $$I$$ represents the Quadruple Moment $$I=2Ma^2$$ of the system.Calculate the time taken by the SBH binary to shrink to a radius $$r(Schwarszchild radius<)<a$$.(initial radius). If $$t$$ can be expressed as $$t=\alpha a^\gamma c^\beta /\psi G^\phi M^\zeta$$.Where $$(\alpha ,\psi )=1$$.Compute the sum of $$\alpha +\beta +\gamma +\psi +\phi +\zeta$$...We this say the Binary SBH merged.

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