Axially symmetric Petrov type II general space–time and closed timelike curves

2021 ◽  
Vol 36 (03) ◽  
pp. 2150017
Author(s):  
Bidyut Bikash Hazarika
Keyword(s):  
Vacuum Solution ◽  
Null Geodesic ◽  
Space Time ◽  
The Other ◽  
Petrov Type ◽  
Type Ii ◽  
Axially Symmetric ◽  
Closed Timelike Curves ◽  
General Space ◽  
Flat Solution

We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

scholarly journals Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Debojit Sarma ◽  
Faizuddin Ahmed ◽  
Mahadev Patgiri
Keyword(s):  
Naked Singularity ◽  
Empty Space ◽  
Space Time ◽  
Axially Symmetric ◽  
Field Equations ◽  
Closed Timelike Curves ◽  
Asymptotically Flat ◽  
Type D ◽  
Initial Hypersurface ◽  
Petrov Classification

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

scholarly journals ON THE CONSTRUCTION OF GLOBAL MODELS DESCRIBING ROTATING BODIES; UNIQUENESS OF THE EXTERIOR GRAVITATIONAL FIELD

1998 ◽  
Vol 13 (19) ◽  
pp. 1509-1519 ◽  
Author(s):  
MARC MARS ◽  
JOSÉ M. M. SENOVILLA
Keyword(s):  
Gravitational Field ◽  
Harmonic Map ◽  
Vacuum Solution ◽  
Space Time ◽  
The Body ◽  
Vacuum Field ◽  
Arbitrary Distribution ◽  
Axially Symmetric ◽  
Global Models ◽  
Rotating Bodies

The problem of constructing global models describing isolated axially symmetric rotating bodies in equilibrium is analyzed. It is claimed that, whenever the global space–time is constructed by giving boundary data on the limiting surface of the body and integrating Einstein's equations on both inside and outside the body, the problem becomes overdetermined. Similarly, when the space–time describing the interior of the body is explicitly given, the problem of finding the exterior vacuum solution becomes overdetermined. We discuss in detail the procedure to be followed in order to construct the exterior vacuum field created by a given but arbitrary distribution of matter. Finally, the uniqueness of the exterior vacuum gravitational field is proven by exploiting the harmonic map formulation of the vacuum equations and the boundary conditions prescribed from the matching.

scholarly journals Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Faizuddin Ahmed ◽  
Bidyut Bikash Hazarika ◽  
Debojit Sarma
Keyword(s):  
Cosmological Constant ◽  
Vacuum Solution ◽  
Space Time ◽  
Axially Symmetric ◽  
De Sitter ◽  
Curvature Singularity ◽  
Field Equations ◽  
Type D ◽  
Initial Space ◽  
Coulomb Type

In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

scholarly journals GLOBAL MONOPOLE AS DUAL-VACUUM SOLUTION IN KALUZA–KLEIN SPACE–TIME

1999 ◽  
Vol 14 (39) ◽  
pp. 2721-2726 ◽  
Author(s):  
NARESH DADHICH ◽  
L. K. PATEL ◽  
R. TIKEKAR
Keyword(s):  
Vacuum Solution ◽  
Flat Space ◽  
Space Time ◽  
Dimensional Euclidean Space ◽  
Global Monopole ◽  
Massless Limit ◽  
Duality Transformation ◽  
Monopole Solution ◽  
Flat Solution ◽  
Kaluza Klein

By the application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchanging Ricci and Einstein tensors), it is shown that the global monopole solution in the Kaluza–Klein space–time is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in four-dimensional Euclidean space and would have massless limit analogous to the four-dimensional dual-flat solution.

scholarly journals Progenitors and Hydrodynamics of Type II and lb Supernovae

1996 ◽  
Vol 145 ◽  
pp. 137-147
Author(s):  
S. E. Woosley ◽  
T. A. Weaver ◽  
R. G. Eastman
Keyword(s):  
Black Holes ◽  
Light Curve ◽  
Mass Loss ◽  
Massive Stars ◽  
The Other ◽  
Shock Interaction ◽  
Type Ii ◽  
Residual Hydrogen ◽  
Ordinary Type ◽  
The One

We review critical physics affecting the observational characteristics of those supernovae that occur in massive stars. Particular emphasis is given to 1) how mass loss, either to a binary companion or by a radiatively driven wind, affects the type and light curve of the supernova, and 2) the interaction of the outgoing supernova shock with regions of increasing pr3 in the stellar mantle. One conclusion is that Type II-L supernovae may occur in mass exchanging binaries very similar to the one that produced SN 1993J, but with slightly larger initial separations and residual hydrogen envelopes (∼1 Mʘ and radius ∼ several AU). The shock interaction, on the other hand, has important implications for the formation of black holes in explosions that are, near peak light, observationally indistinguishable from ordinary Type II-p and lb supernovae.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

Las mentiras en Pedro Páramo

Revue Romane ◽  
2015 ◽  
Vol 50 (1) ◽  
pp. 68-80
Author(s):  
Pol Popovic Karic
Keyword(s):  
Specific Area ◽  
Space Time ◽  
The Other ◽  
Juan Rulfo ◽  
The Novel ◽  
Pedro Paramo

Four types of lies will be analyzed in the novel Pedro Paramo by Juan Rulfo. Each one stems from a specific area: space, time, love and death. These lies are complementary; the first two permeate into the other two and these complement each other forming a circle of ambiguity and uncertainty in the narrative.

Burn-in procedures for a generalized model

2001 ◽  
Vol 38 (02) ◽  
pp. 542-553 ◽  
Author(s):  
Ji Hwan Cha
Keyword(s):  
The Other ◽  
Replacement Policy ◽  
Type I ◽  
Type Ii ◽  
Failure Model ◽  
Minimal Repair ◽  
Optimal Replacement ◽  
Complete Repair ◽  
Optimal Replacement Policy ◽  
Type Of Failure

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.

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