Angular momentum and separation constant in the Kerr metric

1980 ◽  
Vol 13 (5) ◽  
pp. 1701-1708 ◽  
Author(s):  
F de Felice
Keyword(s):  
Angular Momentum ◽  
Kerr Metric

scholarly journals ORBITS IN A NON-KERR DYNAMICAL SYSTEM

2011 ◽  
Vol 21 (08) ◽  
pp. 2261-2277 ◽  
Author(s):  
G. CONTOPOULOS ◽  
G. LUKES-GERAKOPOULOS ◽  
T. A. APOSTOLATOS
Keyword(s):  
Angular Momentum ◽  
Outer Region ◽  
Kerr Black Hole ◽  
Compact Object ◽  
Kerr Metric ◽  
Integrable Case ◽  
Closed Curves ◽  
Surface Of Section ◽  
Fundamental Frequencies ◽  
Chaotic Orbits

We study the orbits in a Manko–Novikov type metric (MN) which is a perturbed Kerr metric. There are periodic, quasi-periodic, and chaotic orbits, which are found in configuration space and on a surface of section for various values of the energy E and the z-component of the angular momentum Lz. For relatively large Lz there are two permissible regions of nonplunging motion bounded by two closed curves of zero velocity (CZV), while in the Kerr metric there is only one closed CZV of nonplunging motion. The inner permissible region of the MN metric contains mainly chaotic orbits, but it contains also a large island of stability. When Lz decreases, the two permissible regions join and chaos increases. Below a certain value of Lz, most orbits escape inwards and plunge through the horizon. On the other hand, as the energy E decreases (for fixed Lz) the outer permissible region shrinks and disappears. In the inner permissible region, chaos increases and for sufficiently small E most orbits are plunging. We find the positions of the main periodic orbits as functions of Lz and E, and their bifurcations. Around the main periodic orbit of the outer region, there are islands of stability that do not appear in the Kerr metric (integrable case). In a realistic binary system, because of the gravitational radiation, the energy E and the angular momentum Lz of an inspiraling compact object decrease and therefore the orbit of the object is nongeodesic. In fact, in an extreme mass ratio inspiraling (EMRI) system the energy E and the angular momentum Lz decrease adiabatically and therefore the motion of the inspiraling object is characterized by the fundamental frequencies which are drifting slowly in time. In the Kerr metric, the ratio of the fundamental frequencies changes strictly monotonically in time. However, in the MN metric when an orbit is trapped inside an island the ratio of the fundamental frequencies remains constant for some time. Hence, if such a phenomenon is observed this will indicate that the system is nonintegrable and therefore the central object is not a Kerr black hole.

Extremal Kerr Black Holes, Naked Singularity & Wormholes

2020 ◽  
Author(s):  
Deep Bhattacharjee
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Event Horizon ◽  
Kerr Black Hole ◽  
Naked Singularity ◽  
Kerr Metric ◽  
Spin Angular Momentum ◽  
The Way

This paper is totally based on the mathematical physics of the Black holes. In Einstein’s theory of “General Relativity”, Schwarzschild solution is the vacuum solutions of the Einstein Field Equations that describes the gravity potential from outside the body of a spherically symmetric object having zero charge, zero mass and zero cosmological constant[1]. It was discovered by Karl Schwarzschild in 1916, a little more than a month after the publication of the famous GR and the singularity is a point singularity which can be best described as a coordinate singularity rather than a real singularity, however, the drawback of this theory is that it fails to take into account the real life scenario of black holes with charge and spin angular momentum. The black hole is based on event horizon and Schwarzschild radius. However, Physicists were trying to develop a metric for the real life scenario of a black hole with a spin angular momen-tum and ultimately the exact solution of a charged rotating black hole had been discovered by Roy Kerr in 1965 as the Kerr-Newman metric[2][3]. The Kerr metric is one of the toughest metric in physics and is the extensional generalization to a rotating body of the Schwarzschild metric. The metric describes the vacuum geometry of space-time around a rotating axially-symmetric black hole with a quasipotential event horizon. In Kerr metric there are two event hori-zons (inner and outer), two ergospheres and an ergosurface. The most important effect of the Kerr metric is the frame dragging (also known as Lense-Thirring Precession) is a distinctive prediction of General relativity. The first direct observation of the collision of two Kerr Black Holes has been discovered by LIGO in 2016 hence setting up a milestone of General Relativity in the history of Physics. Here, the Kerr metric has been introduced in the Boyer-Lindquist forms and it is derived from the Schwarzschild metric using the Spin-Coefficient formalism. According to the “Cosmic Censorship Hypothesis”, a naked singularity cannot exist in nature as nature always hides the singularity via an event horizon. However, in this paper I will prove the existence of the “Naked Singularity" taking the advantage of the Ring Singularity of the Kerr Black Hole and thereby making the way to manipulate the mathematics by taking the larger root of Δ as zero and thereby vanishing the ergosphere and event horizon making the way for the naked ring singularity which can be easily connected via a cylindrical wormhole and as ‘a wormhole is a black hole without an event horizon’ therefore, this cylindrical connection paved the way for the Einstein-Rosen Bridge allowing particles or null rays to travel from one universe to another ending up in a future directed Cauchy horizon while changing constantly from spatial to temporal and again spatial paving the entrance to another Kerr Black hole (which would act as a white hole) in the other universes. I will not go in detail about the contradiction of ‘Chronology Protection Conjecture” [4]whether the Stress-Energy-Momentum Tensor can violate the ANEC (Average Null Energy Conditions) or not with the values of less than zero or greater than, equal to zero, instead I will focus definitely on the creation of the mathematical formulation of a wormhole from a Naked Ring Kerr Singularity of a Kerr Black Hole without any event horizon or ergosphere. Another important thing to mention in this paper is that I have taken the time to be imaginary[5] as because, a singularity being an eternal point of time can only be smoothen out if the time is imaginary rather than real which will allow the particle or null rays inside a wormhole to cross the singularity and making entrance to the other universe. The final conclusion would be to determine the mass-energy equivalence principle as spin angular momentum increases with a decrease in BH mass due to the vanishing event horizon and ergosphere thereby maintaining the equivalence via apparent and absolute masses in relation to spin J along the orthogonal Z axis. A ‘NAKED SINGULARITY’ alters every parameters of a BH and to include this parameters along with affine spin coefficient, it has been proved that without any spin angular momentum the generation of wormhole and vanishing of event horizon and singularity is not possible.

A NEWTONIAN INTERPRETATION OF THE PARAMETER “a” ASSOCIATED WITH THE KERR METRIC

1996 ◽  
Vol 11 (18) ◽  
pp. 1445-1451
Author(s):  
SUJAN SENGUPTA
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Electric Field ◽  
Unit Mass ◽  
Kerr Metric ◽  
Massive Object ◽  
Dipole Magnetic Field ◽  
Newtonian Case

The parameter “a” associated with the Kerr metric has been used to determine the rotationally induced quadrapole electric field outside a rotating massive object with external dipole magnetic field. A comparison of the result with that of the Newtonian case implies that the parameter “a” represents the angular momentum per unit mass of a rotating hollow object.

scholarly journals Angular momentum surface density of the Kerr metric

1993 ◽  
Vol 71 (16) ◽  
pp. 2521-2523 ◽  
Author(s):  
L. Fernández-Jambrina ◽  
F. J. Chinea
Keyword(s):  
Angular Momentum ◽  
Surface Density ◽  
Kerr Metric

scholarly journals Angular Momentum and the Kerr Metric

1968 ◽  
Vol 9 (6) ◽  
pp. 905-906 ◽  
Author(s):  
Jeffrey M. Cohen
Keyword(s):  
Angular Momentum ◽  
Kerr Metric

scholarly journals Photon boomerang in a nearly extreme Kerr metric

2021 ◽  
Author(s):  
Don N Page
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Opposite Direction ◽  
Elliptic Integral ◽  
Polar Axis ◽  
Rotation Parameter ◽  
Kerr Metric ◽  
Complete Elliptic Integral ◽  
The North ◽  
North Polar

Abstract The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate r that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of r that depends on the mass M and angular momentum J of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call ∆φ, which depends on the black hole dimensionless rotation parameter a/M = cJ/(GM2) by an equation involving a complete elliptic integral of the first kind. When the black hole has a/M ≈ 0.994 341 179 923 26, which is nearly maximally rotating, a photon sent out in a constant-r direction from the north polar axis at r ≈ 2.423 776 210 035 73 GM/c2returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

scholarly journals The Goursat problem at the horizons for the Klein–Gordon equation on the de Sitter–Kerr metric

2021 ◽  
Vol 18 (03) ◽  
pp. 609-652
Author(s):  
Pascal Millet
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Gordon Equation ◽  
Goursat Problem ◽  
Main Topic ◽  
Kerr Metric ◽  
De Sitter ◽  
Massless Field ◽  
Klein Gordon ◽  
Klein Gordon Equation

The main topic of this paper is the Goursat problem at the horizon for the Klein–Gordon equation on the De Sitter–Kerr metric when the angular momentum (per unit of mass) of the black hole is small. Indeed, we solve the Goursat problem for fixed angular momentum [Formula: see text] of the field (with the restriction that [Formula: see text] is not zero in the case of a massless field).

Angular momentum in general relativity and the Kerr metric

1972 ◽  
Vol 11 (1) ◽  
pp. 84-92 ◽  
Author(s):  
M. K. Moss ◽  
W. R. Davis
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Kerr Metric
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