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.

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 A class of axially symmetric stationary exact solutions of Einstein's vacuum field equations

1978 ◽  
Vol 20 (3) ◽  
pp. 344-351
Author(s):  
M. D. Patel
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Coordinate System ◽  
Stationary Distribution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
System A ◽  
Oblate Spheroidal

AbstractEinstein's vacuum field equations of an axially symmetric stationary rotating source are studied. Using the oblate spheroidal coordinate system, a class of asymptotically fiat solutions representing the exterior gravitational field of a stationary rotating oblate spheroidal source is obtained. Also it is proved that an analytic axisymmetric and stationary distribution of dust cannot be the source for the gravitational field described by the axisymmetric stationary metric.

scholarly journals Geometric properties of the Bertotti–Kasner space-time

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
H.M. Manjunatha ◽  
S.K. Narasimhamurthy ◽  
Zohreh Nekouee
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Design Methodology ◽  
Vacuum Solution ◽  
Space Time ◽  
Field Equations ◽  
Geometric Properties ◽  
Content Type ◽  
Insight Into ◽  
Weyl Invariants

PurposeThe purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.Design/methodology/approachThis paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.FindingsThe Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.Originality/valueThe findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

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 Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

2015 ◽  
Vol 24 (02) ◽  
pp. 1530006 ◽  
Author(s):  
Christian Heinicke ◽  
Friedrich W. Hehl
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Symmetric Solution ◽  
Gravitational Theory ◽  
Vacuum Field ◽  
Kerr Solution ◽  
Spherically Symmetric ◽  
Axially Symmetric ◽  
Schwarzschild Solution ◽  
Spherically Symmetric Solution

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(–Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

The spin-zero Duffin-Kemmer-Petiau equation in a cosmic-string space-time with the Cornell interaction

2016 ◽  
Vol 31 (36) ◽  
pp. 1650191 ◽  
Author(s):  
M. de Montigny ◽  
M. Hosseinpour ◽  
H. Hassanabadi
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Cosmic String ◽  
Topological Defects ◽  
Space Time ◽  
Dkp Equation

In this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time and consider the interaction of a DKP field with the gravitational field produced by topological defects in order to examine the influence of topology on this system. We solve the spin-zero DKP oscillator in the presence of the Cornell interaction with a rotating coordinate system in an exact analytical manner for nodeless and one-node states by proposing a proper ansatz solution.

Rotating elliptic cylinders in a viscous fluid at rest or in a parallel stream

1977 ◽  
Vol 79 (1) ◽  
pp. 127-156 ◽  
Author(s):  
Hans J. Lugt ◽  
Samuel Ohring
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Elliptic Cylinder ◽  
The Body ◽  
Oscillatory Behaviour ◽  
Incompressible Fluid Flow ◽  
Transient Period ◽  
Parallel Stream ◽  
Rotating Bodies

Numerical solutions are presented for laminar incompressible fluid flow past a rotating thin elliptic cylinder either in a medium at rest at infinity or in a parallel stream. The transient period from the abrupt start of the body to some later time (at which the flow may be steady or periodic) is studied by means of streamlines and equi-vorticity lines and by means of drag, lift and moment coefficients. For purely rotating cylinders oscillatory behaviour from a certain Reynolds number on is observed and explained. Rotating bodies in a parallel stream are studied for two cases: (i) when the vortex developing at the retreating edge of the thin ellipse is in front of the edge and (ii) when it is behind the edge.

THREE DIMENSIONAL INTERPRETATION OF GRAVITATIONAL ANOMALIES

Geophysics ◽  
1952 ◽  
Vol 17 (2) ◽  
pp. 344-364 ◽  
Author(s):  
Fraser S. Grant
Keyword(s):  
Gravitational Field ◽  
Mass Distribution ◽  
Three Dimensional ◽  
Relaxation Method ◽  
The Body ◽  
Multipole Moments ◽  
Size And Shape ◽  
Surface Field ◽  
Derivatives Of

A method is developed for determining the approximate size and shape of the three‐dimensional mass distribution that is required to produce a given gravitational field. The first few reduced multipole moments of the distribution are calculated from the derivatives of the surface field, and the approximative structure is determined from the values of these moments and a knowledge of the density contrast between the body and its surroundings. A system of classification of problems by symmetry is introduced and its practical usage discussed. A relaxation method is described which may be used to adjust the initial solution systematically to give agreement over the whole field. A descriptive discussion is appended.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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