Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$ . In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$ , the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(\mu \ln (M/r))$ , where $\mu \equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.     

Gravitational radiation from an extreme Kerr black hole

We analytically investigate gravitational radiation induced by a test particle falling into an extreme Kerr black hole. Assuming the radiation is dominated by the infinite sequence of quasi-normal modes which has the limiting frequencym/(2M), wherem is an azimuthal eigenvalue andM is the mass of the black hole. we find the radiated energy diverges logarithmically in time. Then we evaluate the back reaction to the black hole by appealing to the energy and angular momentum conservation laws. We find the radiation has a tendency to increase the ratio of the angular momentum to mass of the black hole, which is completely different from the non-extreme case, while the contribution of the test particle is to decrease it.     

Gravitational radiation from a particle with zero orbital angular momentum plunging into a Kerr black hole

We have computed the energy ΔE, the momentum ΔP and the angular momentum ΔJ of gravitational radiation induced by a particle of mass μ and of zero orbital angular momentum plunging in the θ = π/2 plane into a Kerr black hole of mass M(?μ) and angular momentum Ma. It is found that ΔE for a = 0.99M is 4.45 × 10^-2 (μ²/M)c², which is 4.27 times larger than that for the a = 0 case.     

Massive particle radiation from Gibbons-Maeda black hole

This paper investigated the massive particle radiation from Gibbons-Maeda black hole by using a semi-classical method.The calculations showed that,if the self-gravitation of the radiated particle is taken into account,the radiation spectrum deviates from exact black body spectrum and the rate of tunneling equals precisely the exponent of the difference of the black hole entropies before and after emission.The conclusion supports the viewpoint of information conservation.     

Gravitational self-force on a particle orbiting a Kerr black hole

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self-forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) mode-sum regularization method. We also address the gauge-regularization problem, as well as a few other issues involved in the calculation of gravitational radiation reaction in Kerr spacetime.     

Gravitational radiation induced by a particle falling along the Z-axis into a Kerr black hole

We have computed the spectrum and the energy of gravitational radiation induced by a test particle of mass μ falling along the z-axis into a Kerr black hole of mass M(? μ) and angular momentum Ma(a < M). It is found that the total energy radiated is 0.0170 0.0170 μc²μM when α = 0.99M, which is 1.65 times larger than that when α = 0, i.e., the Schwarzschild black hole case.     

Gravitational radiation by a particle with nonzero orbital angular momentum falling into a Kerr black hole

We have computed the energy of the gravitational waves induced by a particle with nonzero orbital angular momentum μL_z plunging into a Kerr black hole in an equatorial plane. It is found that for the same |L_z| a corotating particle emits more energy than a counter-rotating one, which is due to the change of the frequency of the quasi-normal mode with the increase of the angular momentum of the black hole.