On the stability of Kerr’s space-time

1975 ◽  
Vol 344 (1636) ◽  
pp. 65-79 ◽  
Keyword(s):  
Normal Modes ◽  
Space Time ◽  
Kerr Space ◽  
The Stability ◽  
Usual Notation

The stability of Kerr’s space-time with |a| < M , in the usual notation, against infinitesimal perturbations is discussed. No exponentially growing ‘normal modes’ occur. However, since (a) the exponentially decaying modes have not been shown to be complete, (b) there are normal modes with real frequencies, the stability of the Kerr space-time has not been established rigorously.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

scholarly journals Bargmann–Wigner formulation and superradiance problem of bosons and fermions in Kerr space–time

2015 ◽  
Vol 30 (11) ◽  
pp. 1550052 ◽  
Author(s):  
Masakatsu Kenmoku ◽  
Y. M. Cho
Keyword(s):  
Negative Energy ◽  
Space Time ◽  
The Other ◽  
Positive Energy ◽  
Independent Components ◽  
Consistent Description ◽  
Other Hand ◽  
Kerr Space

The superradiance phenomena of massive bosons and fermions in the Kerr space–time are studied in the Bargmann–Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one scalar and three vectors uniquely. The consistent description of the Bargmann–Wigner equations between fermions and bosons shows that the superradiance of the type with positive energy (0 < ω) and negative momentum near horizon (p H < 0) is shown not to occur. On the other hand, the superradiance of the type with negative energy (ω < 0) and positive momentum near horizon (0 < p H ) is still possible for both scalar bosons and spinor fermions.

scholarly journals Spinning cosmic strings in conformal gravity

2020 ◽  
Vol 35 (05) ◽  
pp. 2050024
Author(s):  
Reinoud Jan slagter ◽  
Christopher Levi Duston
Keyword(s):  
Cosmic String ◽  
Energy Condition ◽  
Space Time ◽  
Special Choice ◽  
Mass Relation ◽  
Conformal Gravity ◽  
Field Equations ◽  
Closed Timelike Curves ◽  
The Core ◽  
Kerr Space

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as [Formula: see text], with [Formula: see text] a dilaton field which contains all the scale dependences. The “unphysical” metric [Formula: see text] is related to the [Formula: see text]-dimensional Kerr space–time. The equation for the angular momentum [Formula: see text] decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, [Formula: see text] falls off as [Formula: see text] and [Formula: see text] close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory.

Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

scholarly journals The Stability of Relativistic Systems

1974 ◽  
Vol 64 ◽  
pp. 63-81
Author(s):  
S. Chandrasekhar
Keyword(s):  
Azimuthal Angle ◽  
Normal Modes ◽  
Radiation Reaction ◽  
Axisymmetric Deformation ◽  
Alternative Proof ◽  
Newtonian Theory ◽  
Relativistic Systems ◽  
The Stability

The stability of relativistic systems is reviewed against the background of what is known in the corresponding contexts of the Newtonian theory. In particular, the importance of determining whether Dedekind-like points of bifurcation occur along given stationary axisymmetric sequences is emphasized: the occurrence of such points of bifurcation may signal the onset of secular instability induced by radiation-reaction. (At a Dedekind-like point of bifurcation, the system can be subject, quasistationarily, to a non-axisymmetric deformation with an e2iϕ-dependence on the azimuthal angle ϕ.)A formalism is described in terms of which the normal modes of axisymmetric oscillation of axisymmetric systems can be determined. Specialized to neutral modes of oscillation the formalism provides an alternative proof of Carter's theorem and clarifies the minimal requirements for its validity. A parallel formalism is described for ascertaining whether an axisymmetric system can be subject to a quasi-stationary non-axisymmetric deformation. The possibility of applying this latter formalism to determining whether a Dedekind-like point of bifurcation occurs along the Kerr sequence is considered.

Instability of quasi-geostrophic vortices in a two-layer ocean with a thin upper layer

2003 ◽  
Vol 475 ◽  
pp. 303-331 ◽  
Author(s):  
E. S. BENILOV
Keyword(s):  
Boundary Value Problem ◽  
Lower Layer ◽  
Boundary Value ◽  
Stability Boundary ◽  
Normal Modes ◽  
Layer Depth ◽  
Asymptotic Results ◽  
Gaussian Profile ◽  
Swirl Velocity ◽  
The Stability

We examine the stability of a quasi-geostrophic vortex in a two-layer ocean with a thin upper layer on the f-plane. It is assumed that the vortex has a sign-definite swirl velocity and is localized in the upper layer, whereas the disturbance is present in both layers. The stability boundary-value problem admits three types of normal modes: fast (upper-layer-dominated) modes, responsible for equivalent-barotropic instability, and two slow baroclinic types (mixed- and lower-layer-dominated modes). Fast modes exist only for unrealistically small vortices (with a radius smaller than half of the deformation radius), and this paper is mainly focused on the slow modes. They are examined by expanding the stability boundary-value problem in powers of the ratio of the upper-layer depth to the lower-layer depth. It is demonstrated that the instability of slow modes, if any, is associated with critical levels, which are located at the periphery of the vortex. The complete (sufficient and necessary) stability criterion with respect to slow modes is derived: the vortex is stable if and only if the potential-vorticity gradient at the critical level and swirl velocity are of the same sign. Several vortex profiles are examined, and it is shown that vortices with a slowly decaying periphery are more unstable baroclinically and less barotropically than those with a fast-decaying periphery, with the Gaussian profile being the most stable overall. The asymptotic results are verified by numerical integration of the exact boundary-value problem, and interpreted using oceanic observations.

Sign in / Sign up

Export Citation Format

Share Document