Radiation from Falling Particle

Abstract

It has been said earlier that of all particles with a fixed rest mass and a fixed angular momentum and which are not trapped by the black hole, the orbit which minimizes the energy in the stable circular orbit. In case the falling particle has energy greater than the minimum energy required to settle down to a circular orbit and if it is not first trapped by the black hole, it is possible that a dissipative process such as gravitational radiation will cause the test particle to relax to such a minimum energy. In case, it be not possible for the test particle to relax to such a minimum energy, the particle will spiral down the hole and get accreted to it. In such a type of motion, the capture of the test particle is immediate and the effective potential does not attain a minimum value.  That there is a direct stable circular orbit at r = (3 +√5)m/2 where the energy of the test particle is given by E/     ~– 0.86 and the last direct stable circular orbit is given by r = m where the energy of the test particle is given by E/ ~– 0.58. If in case, the test particle in the orbit r = (3 +√5)m/2, which lies just outside the ergo sphere, begins to loose the energy, it will fall down through the ergo sphere and if it does not get entrapped by the hole, it will settle down in the circular orbit r = m. The particle will follow a spiraling path in falling from the first orbit to the second orbit. Thus, it would be quite interesting to study such an orbit of an accreting particle.

Keywords: Radiation, Energy, Value, Angular Velocity, Fluctuation, Rotating Black Hole.