Stationary rotating strings can be viewed as geodesic motions in appropriate metrics on a two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have infinite length with various wiggly shapes. Averaged value of the string energy, the angular momentum and the linear momentum along the string are discussed.
We investigate the wave dynamics of a charged massive scalar field propagating in a maximally rotating (extremal) linear dilaton black hole geometry. We prove the existence of a discrete and infinite family of resonances describing non-decaying stationary scalar configurations (clouds) enclosing these rapidly rotating black holes. The results obtained signal the potential stationary scalar field distributions (dark matter) around the extremal linear dilaton black holes. In particular, we analytically compute the effective heights of those clouds above the center of the black hole.
Hawking's radiation effect of Klein-Gordon scalar field, Dirac particles and Maxwell's electromagnetic field in the non-stationary rotating de Sitter cosmological space-time is investigated by using a method of generalized tortoise co-ordinates transformation. The locations and the temperatures of the cosmological horizons of the non-stationary rotating de Sitter model are derived. It is found that the locations and the temperatures of the rotating cosmological model depend not only on the time but also on the angle. The stress-energy regularization techniques are applied to the two dimensiona…
The shadow of a black hole can be one of the strong observational evidences for stationary black holes. If we see shadows at the center of galaxies, we would say whether the observed compact objects are black holes. In this paper, we consider a formula for the contour of a shadow in an asymptotically-flat, stationary, and axisymmetric black hole spacetime. We show that the formula is useful for obtaining the contour of the shadow of several black holes such as the Kerr-Newman black hole and rotating regular black holes. Using the formula, we can obtain new examples of the contour of the shadow…
A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These solutions are required to satisfy regularity and junction conditions so that they can be possibly used to represent rotating astrophysical objects. Mathematical and physical properties are analyzed. The spacetime two independent parameters are physically interpreted, and they are shown to define two different solution classes together with stating the latters' prop…
The first exact rotating charged black hole solution to the Einstein{nonlinear electrodynamics theory is reported. It is equipped with mass, rotation parameter, electric and magnetic charges, and three parameters due to the electrodynamics: beta is associated to the potential vectors A{mu} and starP{nu}, and two constants, F0 and G0, related to the presence of the invariants F and G in the Lagrangian L(F;G). This Petrov type D solution is characterized by the Weyl tensor eigenvalue Psi2, the Ricci tensor eigenvalue S = 2Phi(11), and the scalar curvature R; it allows for event horizons, exhibit…
It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density, which is cylindrical symmetric in the interior of the dust configuration, is presented. Among other things, this proves the non-existence of homogeneous dust configurations.
In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant $Λ$, and three parameters due to the nonlinear electrodynamics: $β$ is associated to the potential vectors $A_μ$ and ${}^{\star}P_μ$, and two constants, $F_0$ and $G_0$, due to the presence of the invariants $F$ and $G$ in the Lagrangian $L(F(\,x^μ),G(\,x^μ))$. This solution is of Petrov type D, characterized by the Weyl tensor eig…
Motivated by novel results in the theory of wave dynamics in black-hole spacetimes, we analyze the dynamics of a massive scalar field surrounding a rapidly rotating Kerr black hole. In particular, we report on the existence of stationary (infinitely long-lived) regular field configurations in the background of maximally rotating black holes. The effective height of these scalar "clouds" above the central black hole is determined analytically. Our results support the possible existence of stationary scalar field dark matter distributions surrounding rapidly rotating black holes.
Stationary, axisymmetric and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptoti…
The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field in the black-hole spacetime. The analytically derived formula is shown to agree with direct numerical computations of the resonances. Our results provide an upper bound on the instability regime of rapidly-rotating Kerr black holes to massive scalar perturbations.
In previous studies the dynamics of the relativistic particle moving along the rotating pipe was investigated. The simple gedanken experiment was considered. It was shown that at large enough velocities a centrifugal force acting on the bead changes its usual sign and attracts towards the rotation axis. The authors studied motion of the particle along the rotating straight pipe in the frame of the observer located in the center of rotation, also dynamics of centrifugally accelerated relativistic particle was studied in the laboratory frame. In the both cases it was shown that centrifugal force…
We study the interior of distorted stationary rotating black holes on the example of a Kerr black hole distorted by external static and axisymmetric mass distribution. We show that there is a duality transformation between the outer and inner horizons of the black hole, which is different from that of an electrically charged static distorted black hole. The duality transformation is directly related to the discrete symmetry of the space-time. The black hole horizons area, surface gravity, and angular momentum satisfy the Smarr formula constructed for both the horizons. We formulate the zeroth,…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on $\R^5$.
We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.
We consider a general stationary solution and derive the general laws for accretion of rotating perfect fluids. For non-degenerate and degenerate Fermi and Bose fluids we derive new effects that mimic the center-of-mass-energy effect of two colliding particle in the vicinity of horizons. Non-degenerate fluids see their chemical potential grow arbitrarily and ultra-relativistic Fermi fluids see their specific enthalpy and Fermi momentum grow arbitrarily too while the latter vanishes gradually for non-relativistic Fermi fluids. For degenerate Bose fluids two scenarios remain possible as the flui…
Stationary axisymmetric systems that allow for a separability structure
School of Liberal Arts and Sciences, Korea National University of Transportation（韩国交通大学生命科学与艺术学院）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）
In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier-Stocks equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier-Stocks system.
New rotation laws have been recently found for general-relativistic self-gravitating stationary fluids. It was not clear whether they apply to systems rotating with a constant linear velocity. In this paper we fill this gap. The answer is positive. That means, in particular, that these systems should exhibit the recently discovered general-relativistic weak-field effects within rotating tori: the dynamic anti-dragging and the deviation from the Keplerian motion induced by the fluid selfgravity.
