Asymptotic tails of massive scalar fields in a stationary axisymmetric EMDA black hole geometry

The late-time tail behavior of massive scalar fields is studied analytically in a stationary axisymmetric EMDA black hole geometry. It is shown that the asymptotic behavior of massive perturbations is dominated by the oscillatory inverse power-law decaying tail $t^{-(l+3/2)}\sin(\mu t)$ at the intermediate late times, and by the asymptotic tail $t^{-5/6}\sin(\mu t)$ at asymptotically late times. Our result seems to suggest that the intermediate tails $t^{-(l+3/2)}\sin(\mu t)$ and the asymptotically tails $t^{-5/6} \sin(\mu t)$ may be quite general features for evolution of massive scalar fields in any four dimensional asymptotically flat rotating black hole backgrounds.Comment: 6 page

Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole

We investigate the late-time tails of self-interacting (massive) scalar fields in the spacetime of dilaton black hole. Following the no hair theorem we examine the mechanism by which self-interacting scalar hair decay. We revealed that the intermediate asymptotic behavior of the considered field perturbations is dominated by an oscillatory inverse power-law decaying tail. The numerical simulations showed that at the very late-time massive self-interacting scalar hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.

Radiative falloff in the background of rotating black hole

We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D (Rapid Communication

Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations

We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.Comment: 16 page

Hairy Black Holes and Null Circular Geodesics

Einstein-matter theories in which hairy black-hole configurations have been found are studied. We prove that the nontrivial behavior of the hair must extend beyond the null circular orbit (the photonsphere) of the corresponding spacetime. We further conjecture that the region above the photonsphere contains at least 50% of the total hair's mass. We support this conjecture with analytical and numerical results.Comment: 5 page

Mass-Inflation in Dynamical Gravitational Collapse of a Charged Scalar-Field

We study the inner-structure of a charged black-hole which is formed from the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the $r=0$ hypersurface.Comment: Latex, 13 pages including 4 figures, Revtex.st

The fastest way to circle a black hole

Black-hole spacetimes with a "photonsphere", a hypersurface on which massless particles can orbit the black hole on circular null geodesics, are studied. We prove that among all possible trajectories (both geodesic and non-geodesic) which circle the central black hole, the null circular geodesic is characterized by the {\it shortest} possible orbital period as measured by asymptotic observers. Thus, null circular geodesics provide the fastest way to circle black holes. In addition, we conjecture the existence of a universal lower bound for orbital periods around compact objects (as measured by flat-space asymptotic observers): $T_{\infty}\geq 4\pi M$, where $M$ is the mass of the central object. This bound is saturated by the null circular geodesic of the maximally rotating Kerr black hole.Comment: 5 page

Dyonic Kerr-Newman black holes, complex scalar field and Cosmic Censorship

We construct a gedanken experiment, in which a weak wave packet of the complex massive scalar field interacts with a four-parameter (mass, angular momentum, electric and magnetic charges) Kerr-Newman black hole. We show that this interaction cannot convert an extreme the black hole into a naked sigularity for any black hole parameters and any generic wave packet configuration. The analysis therefore provides support for the weak cosmic censorship conjecture.Comment: Refined emphasis on the weak cosmic censorship conjecture, conclusions otherwise unchanged. Also, two sections merged, literature review updated, references added, a few typos correcte

Late-time evolution of the Yang-Mills field in the spherically symmetric gravitational collapse

We investigate the late-time evolution of the Yang-Mills field in the self-gravitating backgrounds: Schwarzschild and Reissner-Nordstr\"om spacetimes. The late-time power-law tails develop in the three asymptotic regions: the future timelike infinity, the future null infinity and the black hole horizon. In these two backgrounds, however, the late-time evolution has quantitative and qualitative differences. In the Schwarzschild black hole background, the late-time tails of the Yang-Mills field are the same as those of the neutral massless scalar field with multipole moment l=1. The late-time evolution is dominated by the spacetime curvature. When the background is the Reissner-Nordstr\"om black hole, the late-time tails have not only a smaller power-law exponent, but also an oscillatory factor. The late-time evolution is dominated by the self-interacting term of the Yang-Mills field. The cause responsible for the differences is revealed.Comment: Revtex, 14 pages, no figure

High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.Comment: 12 pages, 2 figure