Complex Spacetimes and the Newman-Janis Trick

2021 ◽  
Author(s):  
◽  
Del Rajan

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

2021 ◽  
Author(s):  
◽  
Del Rajan

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>


2014 ◽  
Vol 92 (1) ◽  
pp. 46-50
Author(s):  
De-Jiang Qi

Recently, via adiabatic invariance, Majhi and Vagenas quantized the horizon area of the general class of a static spherically symmetric space–time. Very recently, applying the period of the gravity system with respect to the Euclidean time, Zeng and Liu derived area spectra of a Schwarzschild black hole and a Kerr black hole. It is noteworthy that the preceding methods are not useful for the quasi-normal modes. In this paper, based on those works, and as a further study, adopting near horizon approximation, applying the laws of black hole thermodynamics, we would like to investigate the black hole spectroscopy from a class of Plebański and Demiański space–times by using two different methods. The result shows that the area spectrum of the black hole is [Formula: see text], which confirms the initial proposal of Bekenstein, and the result is consistent with that already obtained by Maggiore with quasi-normal modes.


2021 ◽  
Vol 2081 (1) ◽  
pp. 012005
Author(s):  
A C Gutiérrez-Piñeres ◽  
N H Beltrán ◽  
C S López-Monsalvo

Abstract A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to generate solutions to the Einstein field equation inspired by the mention problems. We present a collection of independent classes of exact interior solutions of the Einstein equation describing rotating fluids with anisotropic pressures. Furthermore, we will elaborate on some obtained solutions by alluding to rotating wormholes.


2020 ◽  
Author(s):  
Deep Bhattacharjee

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.


2019 ◽  
Vol 28 (03) ◽  
pp. 1950048 ◽  
Author(s):  
R. V. Maluf ◽  
Juliano C. S. Neves

Bardeen regular black hole is commonly considered as a solution of general relativity coupled to a nonlinear electrodynamics. In this paper, it is shown that the Bardeen solution may be interpreted as a quantum-corrected Schwarzschild black hole. This new interpretation is obtained by means of a generalized uncertainty principle applied to the Hawking temperature. Moreover, using the regular black hole of Bardeen, it is possible to evaluate the quantum gravity parameter of the generalized uncertainty principle or, assuming the recent upper bounds for such a parameter, to verify an enormous discrepancy between a cosmological constant and that measured by recent cosmological observations [Formula: see text].


1997 ◽  
Vol 12 (35) ◽  
pp. 2683-2689 ◽  
Author(s):  
W. Kummer ◽  
H. Liebl ◽  
D. V. Vassilevich

It is well known that spherically symmetric reduction of general relativity (SSG) leads to non-minimally coupled scalar matter. We generalize (and correct) recent results to Hawking radiation for a class of dilaton models which share with the Schwarzschild black hole non-minimal coupling of scalar fields and the basic global structure. An inherent ambiguity of such models (if they differ from SSG) is discussed. However, for SSG we obtain the rather disquieting result of a negative Hawking flux at infinity, if the usual recipe for such calculations is applied.


Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordström black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordström black-holes they derive from the potential barriers surrounding them belonging to a special class.


2016 ◽  
Vol 25 (09) ◽  
pp. 1641001
Author(s):  
Paolo Pani ◽  
Leonardo Gualtieri ◽  
Andrea Maselli ◽  
Valeria Ferrari

We review recent work on the theory of tidal deformability and the tidal Love numbers of a slowly spinning compact object within general relativity. Angular momentum introduces couplings between distortions of different parity and new classes of spin-induced, tidal Love numbers emerge. Due to spin-tidal effects, a rotating object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second-order in the spin. The tidal Love numbers depend strongly on the object’s internal structure. All tidal Love numbers of a Kerr black hole (BH) were proved to be exactly zero to first-order in the spin and also to second-order in the spin, at least in the axisymmetric case. For a binary system close to the merger, various components of the tidal field become relevant. Preliminary results suggest that spin-tidal couplings can introduce important corrections to the gravitational waveforms of spinning neutron star (NS) binaries approaching the merger.


2016 ◽  
Vol 12 (S324) ◽  
pp. 45-46
Author(s):  
Vojtěch Witzany ◽  
Claus Lämmerzahl

AbstractSince the first investigations into accretion onto black holes, astrophysicists have proposed effective Newtonian-like potentials to mimic the strong-field behavior of matter near a Schwarzschild or Kerr black hole. On the other hand, the fields of neutron stars or black holes in many of the alternative gravity theories differ from the idealized Schwarzschild or Kerr field which would require a number of new potentials. To resolve this, we give a Newtonian-like Hamiltonian which almost perfectly mimics the behavior of test particles in any given stationary space-time. The properties of the Hamiltonian are excellent in static space-times such as the Schwarzschild black hole, but become worse for space-times with gravito-magnetic or dragging effects such as near the Kerr black hole.


2018 ◽  
Vol 73 (11) ◽  
pp. 1061-1073 ◽  
Author(s):  
N.A. Hussein ◽  
D.A. Eisa ◽  
T.A.S. Ibrahim

AbstractThis paper aims to obtain the thermodynamic variables (temperature, thermodynamic volume, angular velocity, electrostatic potential, and heat capacity) corresponding to the Schwarzschild black hole, Reissner-Nordstrom black hole, Kerr black hole and Kerr-Newman-Anti-de Sitter black hole. We also obtained the free energy for black holes by using three different methods. We obtained the equation of state for rotating Banados, Teitelboim and Zanelli black holes. Finally, we used the quantum correction of the partition function to obtain the heat capacity and entropy in the quantum sense.


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