Consideration is given to the evolution of stationary axisymmetric
rotating Kerr naked singularities due to the accretion of matter from
thin corotating disks. Within the framework of the Page-Thorne model of
accretion disks, it is shown that the naked singularity must evolve
towards an extreme black hole state provided sufficient mass is
accreted. Analytical expressions for the time evolution of the Kerr
naked singularity as a function of initial mass and angular momentum are
then obtained for the cases of a constant accretion rate, an accretion
rate proportional to black hole mass, and an accretion rate
self-regulated at the critical rate. It is pointed out that for
accretion in binary systems, singularities of mass less than 10 solar
masses may be converted into black holes only for angular momentum very
close to unity. Effects of the capture of the radiation emitted by the
disk by the singularity or the disk itself and of changes in disk
geometry at the later stages of black hole conversion are also
considered
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The photon trajectories in the Kerr-Newman metric are described in both
the black hole and naked singularity cases. The radial motions of
photons are discussed, and by finding the turning points of the radial
motion, the regions allowed for this motion are determined. The region
of negative radii is considered, and it is found that the qualitative
differences between the Kerr-Newman metric and the Kerr metric occur
only below the inner horizon and around naked singularities. In some
cases stable circular orbits exist in the equatorial plane, and in other
cases there are no spherical orbits on positive radii at all.
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Consideration is given to the evolution of stationary axisymmetric rotating Kerr naked singularities due to the accretion of matter from thin corotating disks. Within the framework of the Page-Thorne model of accretion disks, it is shown that the naked singularity must evolve towards an extreme black hole state provided sufficient mass is accreted. Analytical expressions for the time evolution of the Kerr naked singularity as a function of initial mass and angular momentum are then obtained for the cases of a constant accretion rate, an accretion rate proportional to black hole mass, and an accretion rate self-regulated at the critical rate. It is pointed out that for accretion in binary systems, singularities of mass less than 10 solar masses may be converted into black holes only for angular momentum very close to unity. Effects of the capture of the radiation emitted by the disk by the singularity or the disk itself and of changes in disk geometry at the later stages of black hole conversion are also considered
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The photon trajectories in the Kerr-Newman metric are described in both the black hole and naked singularity cases. The radial motions of photons are discussed, and by finding the turning points of the radial motion, the regions allowed for this motion are determined. The region of negative radii is considered, and it is found that the qualitative differences between the Kerr-Newman metric and the Kerr metric occur only below the inner horizon and around naked singularities. In some cases stable circular orbits exist in the equatorial plane, and in other cases there are no spherical orbits on positive radii at all.
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The astrophysical and observational consequences of the (possible)
existence of Kerr naked singularities (NSs) are examined, and the
circular geodesic orbits in the equatorial plane of a rotating NS are
studied. It is shown that, owing to the existence of negative-energy
orbits, the extraction of rotational energy from these NSs is
astrophysically plausible for both the dissipative processes (by
gravitational radiation or by viscous heating of accretion disks) and
the Penrose process. In addition, the motion of the shell of incoherent
matter in the field of a rotating NS is investigated; the shell,
initially spherical, is found to become prolate along the symmetry axis
during the fall, and to be oblate when the shell returns to infinity.
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The astrophysical and observational consequences of the (possible) existence of Kerr naked singularities (NSs) are examined, and the circular geodesic orbits in the equatorial plane of a rotating NS are studied. It is shown that, owing to the existence of negative-energy orbits, the extraction of rotational energy from these NSs is astrophysically plausible for both the dissipative processes (by gravitational radiation or by viscous heating of accretion disks) and the Penrose process. In addition, the motion of the shell of incoherent matter in the field of a rotating NS is investigated; the shell, initially spherical, is found to become prolate along the symmetry axis during the fall, and to be oblate when the shell returns to infinity.
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The scalar wave equation is separated in the field of a charged,
rotating Kerr-Newman black hole; properties of the effective potential
barriers are assessed. Exact stationary solutions for massless scalar
fields in the Kerr-Newman geometry are developed, and the no-hair
hypothesis is confirmed. In addition, the proof of Detweiler and Ipser
(1973) concerning the stability of Kerr black holes with respect to
axisymmetric scalar perturbations is found to be applicable to the
Kerr-Newman case as well.
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The scalar wave equation is separated in the field of a charged, rotating Kerr-Newman black hole; properties of the effective potential barriers are assessed. Exact stationary solutions for massless scalar fields in the Kerr-Newman geometry are developed, and the no-hair hypothesis is confirmed. In addition, the proof of Detweiler and Ipser (1973) concerning the stability of Kerr black holes with respect to axisymmetric scalar perturbations is found to be applicable to the Kerr-Newman case as well.
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The authors investigate the motion of a test particle in the Kerr metric
using Boyer-Lindquist coordinates, extending the results of de Felice
and Calvani (FC) (1972) to cases not covered by them, and also
considering further details concerning, in particular, photons moving
along the principal null congruences. Whereas FC considered only
nonnegative values of L = q + l-squared, here negative values are
treated. Curves are drawn showing l-aquared as a function of Theta for a
fixed positive Gamma and typical values of L, demonstrating the
oscillatory nature of the latitudinal motion. Four families of photon
world lines with constant latitudes are found. A graph of L/a-squared
versus x for a fixed l/a is drawn from calculations, which is used to
analyze the r-motions of photons.
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