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Register a new userStable circular orbits in higher-dimensional multi-black hole spacetimes
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We consider the dynamics of particles, particularly focusing on circular orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two equal mass black holes. It is widely known that in the 5D Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable circular orbits. In contrast, we show that in the 5D MP background, stable circular orbits can always exist when the separation of two black holes is large enough. More precisely, for a large separation, stable circular orbits exist from the vicinity of horizons to infinity; for a medium one, they appear only in a certain finite region bounded by the innermost stable circular orbit and the outermost stable circular orbit outside the horizons; for a small one, they do not appear at all. Moreover, we show that in MP spacetimes in more than 5D, they do not exist for any separations.
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We consider the motion of massive and massless particles in a five-dimensional spacetime with a compactified extra-dimensional space where a black hole is localized, i.e., a caged black hole spacetime. We show the existence of circular orbits and reveal their sequences and stability. In the asymptotic region, stable circular orbits always exist, which implies that four-dimensional gravity is more dominant because of the small extra-dimensional space. In the vicinity of a black hole, they do not exist because the effect of compactification is no longer effective. We also clarify the dependence of the sequences of circular orbits on the size of the extra-dimensional space by determining the appearance of the innermost stable circular orbit and the last circular orbit (i.e., the unstable photon circular orbit).
We investigate the geodetic precession effect of a parallely transported spin-vector along a circular geodesic in the five-dimensional squashed Kaluza-Klein black hole spacetime. Then we derive the higher-dimensional correction of the precession angle to the general relativity. We find that the correction is proportional to the square of (size of extra dimension)/(gravitational radius of central object).
We present results from the evolution of spacetimes that describe the merger of asymptotically global AdS black holes in 5D with an SO(3) symmetry. Prompt scalar field collapse provides us with a mechanism for producing distinct trapped regions on the initial slice, associated with black holes initially at rest. We evolve these black holes towards a merger, and follow the subsequent ring-down. The boundary stress tensor of the dual CFT is conformally related to a stress tensor in Minkowski space which inherits an axial symmetry from the bulk SO(3). We compare this boundary stress tensor to its hydrodynamic counterpart with viscous corrections of up to second order, and compare the conformally related stress tensor to ideal hydrodynamic simulations in Minkowski space, initialized at various time slices of the boundary data. Our findings reveal far-from-hydrodynamic behavior at early times, with a transition to ideal hydrodynamics at late times.
We report on the end state of nonaxisymmetric instabilities of singly spinning asymptotically flat Myers-Perry black holes. Starting from a singly spinning black hole in D=5,6,7 dimensions, we introduce perturbations with angular dependence described by m=2, m=3, or m=4 azimuthal mode numbers about the axis of rotation. In D=5, we find that all singly spinning Myers-Perry black holes are stable, in agreement with the results from perturbation theory. In D=6 and 7, we find that these black holes are nonlinearly stable only for sufficiently low spins. For intermediate spins, although the m=2 bar mode becomes unstable and leads to large deformations, the black hole settles back down to another member of the Myers-Perry family via gravitational wave emission; surprisingly, we find that all such unstable black holes settle to the same member of the Myers-Perry family. The amount of energy radiated into gravitational waves can be very large, in some cases more than 30% of the initial total mass of the system. For high enough spins, the m=4 mode becomes the dominant unstable mode, leading to deformed black holes that develop local Gregory-Laflamme instabilities, thus forming a naked singularity in finite time, which is further evidence for the violation of the weak cosmic censorship conjecture in asymptotically flat higher-dimensional spacetimes.
We study linear nonradial perturbations and stability of a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a test particle in stationary axisymmetric spacetimes which possess a reflection symmetry with respect to the equatorial plane. The proposed approach is applied to Kerr solution and Majumdar-Papapetrou solution to Einstein equation. Finally, we reexamine MSCOs for a modified metric of a rapidly spinning black hole that has been recently proposed by Johannsen and Psaltis [PRD, 83, 124015 (2011)]. We show that, for the Johannsen and Psaltiss model, circular orbits that are stable against radial perturbations for some parameter region become unstable against vertical perturbations. This suggests that the last circular orbit for this model may be larger than the ISCO.
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