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Takahisa Igata

Publications and source records attributed to Takahisa Igata.

52 records · Page 3Linked to original sources
arXiv2017

Energy extraction from Kerr black holes by rigidly rotating strings

In this paper, we show that a rigidly rotating string can extract the rotational energy from a rotating black hole. We consider Nambu-Goto strings stationary with respect to a corotating Killing vector with an uniform angular velocity $ω$ in the Kerr spacetime. We show that a necessary condition of the energy-extraction process is that an effective horizon on the string world sheet, which corresponds to the inner light surface, is inside the ergosphere of the Kerr black hole and the angular velocity $ω$ is less than that of the black hole $Ω_\mathrm{h}$. Furthermore, we discuss global configurations of such strings in both of a slow-rotation limit and the extremal Kerr case.

gr-qc↗
arXiv2016

Self-similar motion of a Nambu-Goto string

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo) Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemaître-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.

gr-qc↗
arXiv2016

Gravitational two solitons in Levi-Civita spacetime

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Civita background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one-solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.

gr-qc↗
arXiv2015

Gravitational solitons in Levi-Civita spacetime

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equation and using the Levi-Civita solution for a seed, we construct a cylindrically symmetric single-soliton solution. Although the Levi-Civita spacetime generally includes singularities on its axis of symmetry, it is shown that for the obtained single-soliton solution, such singularities can be removed by choice of certain special parameters. This single-soliton solution describes propagation of nonlinear cylindrical gravitational shock wave pulses rather than solitonic waves. By analyzing wave amplitudes and time-dependence of polarization angles, we provides physical description of the single-soliton solution.

gr-qc↗
arXiv2014

Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring

The geodesic equation in the five-dimensional singly rotating black ring is non-integrable unlike the case of the Myers-Perry black hole. In the Newtonian limit of the black ring, its geodesic equation agrees with the equation of motion of a particle in the Newtonian potential due to a homogeneous ring gravitational source. In this paper, we show that the Newtonian equation of motion allows the separation of variables in the spheroidal coordinates, providing an non-trivial constant of motion quadratic in momenta. This shows that the Newtonian limit of a black ring recovers the symmetry of its geodesic system, and the geodesic chaos is caused by relativistic effects.

hep-th↗
arXiv2014

Stable Bound Orbits in Six-dimensional Myers-Perry Black Holes

The existence of stable bound orbits of test particles is one of the most characteristic properties in black hole spacetimes. In higher-dimensional black holes, due to the dimensionality of gravity, there is no stable bound orbit balanced by Newtonian gravitational monopole force and centrifugal force as in the same mechanism of the four-dimensional Kerr black hole case. In this paper, however, the existence of stable bound orbits of massive and massless particles is shown in six-dimensional singly spinning Myers-Perry black holes with a value of the spin parameter larger than a critical value. The innermost stable circular orbits and the outermost stable bound orbit are found on the rotational axis.

gr-qc↗
arXiv2013

Stable Bound Orbits of Massless Particles around a Black Ring

We study the geodesic motion of massless particles in singly rotating black ring spacetimes. We find stable stationary orbits of massless particles in toroidal spiral shape in the case that the thickness parameter of a black ring is less than a critical value. Furthermore, there exist nonstationary massless particles bounded in a finite region outside the horizon. This is the first example of stable bound orbits of massless particles around a black object.

hep-th↗
arXiv2012

Stationary Closed Strings in Five-dimensional Flat Spacetime

We investigate stationary rotating closed Nambu-Goto strings in five-dimensional flat spacetime. The stationary string is defined as a worldsheet that is tangent to a timelike Killing vector. Nambu-Goto equation of motion for the stationary string is reduces to the geodesic equation on the orbit space of the isometry group action generated by the Killing vector. We take a linear combination of a time-translation vector and space-rotation vectors as the Killing vector, and explicitly construct general solutions of stationary rotating closed strings in five-dimensional flat spacetime. We show a variety of their configurations and properties.

hep-th↗
arXiv2012

Effect of a Weak Electromagnetic Field on Particle Acceleration by a Rotating Black Hole

We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy can be arbitrarily high if the magnetic field is arbitrarily strong, when a particle collides with a charged particle orbiting the ISCO with finite energy near the horizon of a uniformly magnetized Schwarzschild black hole. We show that the charged particle orbiting the ISCO around a spinning black hole needs arbitrarily high energy in the strong field limit. This suggests that Frolov's process is unstable against the black hole spin. Nevertheless, we see that magnetic fields may substantially promote the capability of rotating black holes as particle accelerators in astrophysical situations.

gr-qc↗
arXiv2010

Chaos in Geodesic Motion around a Black Ring

We study bound orbits of a free particle around a singly rotating black ring. We find there exists chaotic motion of a particle which is gravitationally bound to the black ring by using the Poincare map.

hep-th↗
arXiv2010

Stable Bound Orbits around Black Rings

We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the axis of the ring, and also exist stable circular orbits on the axis as special cases. The stable bound orbits can have arbitrary large size if the thickness of the ring is less than a critical value.

hep-th↗
arXiv2010

Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole

We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electro-magnetic field in black hole spacetimes. We also demonstrate that gravitational and electro-magnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

gr-qc↗
arXiv2010

Toroidal Spiral Strings in Higher-dimensional Spacetime

We report on our progress in research of separability of the Nambu-Goto equation for test strings with a symmetric configuration in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a Hopf loop string which is a special class of the toroidal spirals, we show the complete separation of variables occurs in two cases, Kerr background and Kerr-AdS background with equal angular momenta. We also obtain the dynamical solution for the Hopf loop around a black hole and for the general toroidal spiral in Minkowski background.

hep-th↗
arXiv2009

Dynamics of Toroidal Spiral Strings around Five-dimensional Black Holes

We examine the separability of the Nambu-Goto equation for test strings in a shape of toroidal spiral in a five-dimensional Kerr-AdS black hole. In particular, for a `{\it Hopf loop}\rq string which is a special class of the toroidal spiral strings, we show the complete separation of variables occurs in two cases, Kerr background and Kerr-AdS background with equal angular momenta. We also obtain the dynamical solution for the Hopf loop around a black hole and for the general toroidal spiral in Minkowski background.

hep-th↗
arXiv2009

Toroidal Spiral Nambu-Goto Strings around Higher-Dimensional Black Holes

We present solutions of the Nambu-Goto equation for test strings in a shape of toroidal spiral in five-dimensional spacetimes. In particular, we show that stationary toroidal spirals exist around the five-dimensional Myers-Perry black holes. We also show the existence of innermost stationary toroidal spirals around the five-dimensional black holes like geodesic particles orbiting around four-dimensional black holes.

hep-th↗