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Register a new userRemarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium
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The general analysis of the relations between masses and angular momenta in the configurations composed of two balancing extremal Kerr particles is made on the basis of two exact solutions arising as extreme limits of the well-known double-Kerr spacetime. We show that the inequality M^2 >= |J| characteristic of an isolated Kerr black hole is verified by all the extremal components of the Tomimatsu and Dietz-Hoenselaers solutions. At the same time, the inequality can be violated by the total masses and total angular momenta of these binary systems, and we identify all the cases when such violation occurs.
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We revisit monochromatic and isotropic photon emissions from the zero-angularlinebreak-momentum sources (ZAMSs) near a Kerr black hole. We investigate the escape probability of the photons that can reach to infinity and study the energy shifts of these escaping photons, which could be expressed as the functions of the source radius and the black hole spin. We study the cases for generic source radius and black hole spin, but we pay special attention to the near-horizon (near-)extremal Kerr ((near-)NHEK) cases. We reproduce the relevant numerical results using a more efficient method and get new analytical results for (near-)extremal cases. The main non-trivial results are: in the NHEK region of a (near-)extremal Kerr black hole, the escape probability for a ZAMS tends to $frac{7}{24}approx 29.17%$, independent of the NHEK radius; at the innermost of the photon shell (IPS) in the near-NHEK region, the escape probability for a ZAMS tends to begin{equation} frac{5}{12} -frac{1}{sqrt{7}} + frac{2}{sqrt{7}pi}arctanfrac{1}{sqrt{7}}approx12.57% . onumber end{equation} The results show that the photon escape probability remains a relatively large nonzero value even though the ZAMS is in the deepest region of a near-horizon throat of a high spin Kerr black hole, as long as the ZAMS is outside the IPS. The energies of the escaping photons at infinity, however, are all redshifted but still visible in principle.
The full metric describing a stationary axisymmetric system of two arbitrary Kerr sources, black holes or hyperextreme objects, located on the symmetry axis and kept apart in equilibrium by a massless strut is presented in a concise explicit form involving five physical parameters. The binary system composed of a Schwarzschild black hole and a Kerr source is a special case not covered by the general formulas, and we elaborate the metric for this physically interesting configuration too.
Inspirals of stellar mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. Detection of these sources and extracting information from the signal relies on accurate theoretical models of the binary dynamics. We cast the equations describing binary inspiral in the extreme mass ratio limit in terms of action angle variables, and derive properties of general solutions using a two-timescale expansion. This provides a rigorous derivation of the prescription for computing the leading order orbital motion. As shown by Mino, this leading order or adiabatic motion requires only knowledge of the orbit-averaged, dissipative piece of the self force. The two timescale method also gives a framework for calculating the post-adiabatic corrections. For circular and for equatorial orbits, the leading order corrections are suppressed by one power of the mass ratio, and give rise to phase errors of order unity over a complete inspiral through the relativistic regime. These post-1-adiabatic corrections are generated by the fluctuating piece of the dissipative, first order self force, by the conservative piece of the first order self force, and by the orbit-averaged, dissipative piece of the second order self force. We also sketch a two-timescale expansion of the Einstein equation, and deduce an analytic formula for the leading order, adiabatic gravitational waveforms generated by an inspiral.
We extend the validity of Dains angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are invariant under a U(1) action and which admit a twist potential.
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