Mass and angular momentum at the quasi-local level in general relativity

2006 ◽  
pp. 23-30
Author(s):  
Roger Penrose
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Local Level

Angular momentum in general relativity I. Definition and asymptotic behaviour

1977 ◽  
Vol 354 (1679) ◽  
pp. 379-405 ◽  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Asymptotic Behaviour ◽  
Event Horizon ◽  
Conservation Law ◽  
General Definition ◽  
Field Equations ◽  
Spin Coefficient ◽  
Coefficient Formalism

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

Spin-up of a rapidly rotating star by angular momentum loss - Effects of general relativity

1992 ◽  
Vol 398 ◽  
pp. 203 ◽  
Author(s):  
Gregory B. Cook ◽  
Stuart L. Shapiro ◽  
Saul A. Teukolsky
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Momentum Loss ◽  
Angular Momentum Loss ◽  
Rotating Star

Quasi-local mass and angular momentum in general relativity

1982 ◽  
Vol 381 (1780) ◽  
pp. 53-63 ◽  
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Twistor Space ◽  
New Approach ◽  
Local Mass ◽  
Bondi Mass ◽  
Definition Of

A new approach to defining energy-momentum and angular momentum in general relativity is presented which avoids some of the difficulties of previous definitions and which can be applied quasi-locally. It depends on the construction of a twistor space T α ( S ) associated with any spacelike topological 2-sphere S . Though several problems of interpretation remain to be solved, the new definition works well at I + , reproducing the Bondi-mass-momentum as four of the ten precisely determined quantities at each cut of I + . The remaining six quantities provide a definition of angular momentum which appears to be new.

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.

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