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 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 Photon regions and shadows of accelerated black holes

2015 ◽  
Vol 24 (09) ◽  
pp. 1542024 ◽  
Author(s):  
Arne Grenzebach ◽  
Volker Perlick ◽  
Claus Lämmerzahl
Keyword(s):  
Black Holes ◽  
Cosmological Constant ◽  
Boundary Curve ◽  
Kerr Metric ◽  
Axially Symmetric ◽  
De Sitter ◽  
Acceleration Parameter ◽  
Type D ◽  
Analytical Formulas ◽  
Photon Regions

In an earlier paper, we have analytically determined the photon regions and the shadows of black holes of the Plebański class of metrics which are also known as the Kerr–Newman–NUT–(anti-)de Sitter metrics. These metrics are characterized by six parameters: Mass, spin, electric and magnetic charges, gravitomagnetic NUT charge and the cosmological constant. Here, we extend this analysis to the Plebański–Demiański class of metrics which contains, in addition to these six parameters, the so-called acceleration parameter. All these metrics are axially symmetric and stationary type D solutions to the Einstein–Maxwell equations with a cosmological constant. We derive analytical formulas for the photon regions (i.e. for the regions that contain spherical lightlike geodesics) and for the boundary curve of the shadow as it is seen by an observer at Boyer–Lindquist coordinates (rO, ϑO) in the domain of outer communication. Whereas all relevant formulas are derived for the whole Plebański–Demiański class, we concentrate on the accelerated Kerr metric (i.e. only mass, spin and acceleration parameter are different from zero) when discussing the influence of the acceleration parameter on the photon region and on the shadow in terms of pictures. The accelerated Kerr metric is also known as the rotating C-metric. We discuss how our analytical formulas can be used for calculating the horizontal and vertical angular diameters of the shadow and we estimate these values for the black holes at the center of our Galaxy and at the center of M87.

scholarly journals Cylindrically Symmetric, Asymptotically Flat, Petrov Type D Spacetime with a Naked Curvature Singularity and Matter Collapse

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Cosmic Time ◽  
Petrov Type ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Curvature Singularity ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Type D ◽  
Cylindrically Symmetric ◽  
Petrov Type D

We present a cylindrically symmetric, Petrov type D, nonexpanding, shear-free, and vorticity-free solution of Einstein’s field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy-momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals Exact Axially Symmetric Solution inf(T)Gravity Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Vacuum Solution ◽  
Gravity Theory ◽  
Kerr Metric ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Kerr Spacetime ◽  
Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

Wormhole solutions in embedding class 1 space–time

2021 ◽  
Vol 36 (02) ◽  
pp. 2150015
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Safiqul Islam
Keyword(s):  
Dimensional Space ◽  
Vacuum Solution ◽  
Energy Condition ◽  
Radial Distance ◽  
Space Time ◽  
Exotic Matter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Class 1

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an [Formula: see text]-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance [Formula: see text], the Schwarzschild radius, and match to the external vacuum solution.

scholarly journals Cosmological model favored by the holographic principle

2016 ◽  
Vol 41 ◽  
pp. 1660127
Author(s):  
Irina Dymnikova ◽  
Anna Dobosz ◽  
Bożena Sołtysek
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Space Time ◽  
Holographic Principle ◽  
Einstein Equations ◽  
Energy Tensor ◽  
De Sitter ◽  
Quantum Evaporation ◽  
Stress Energy ◽  
De Sitter Vacua

We present a regular spherically symmetric cosmological model of the Lemaitre class distinguished by the holographic principle as the thermodynamically stable end-point of quantum evaporation of the cosmological horizon. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. Global structure of space-time is the same as for the de Sitter space-time. Cosmological evolution goes from a big initial value of the cosmological constant towards its presently observed value.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

INHOMOGENEOUS DUST COLLAPSE WITH COSMOLOGICAL CONSTANT

2005 ◽  
Vol 14 (03n04) ◽  
pp. 707-715 ◽  
Author(s):  
S. G. GHOSH
Keyword(s):  
Cosmological Constant ◽  
Gravitational Collapse ◽  
Dust Cloud ◽  
Cosmic Censorship ◽  
Space Time ◽  
De Sitter ◽  
Naked Singularities ◽  
Asymptotic Flatness ◽  
Sitter Background ◽  
Strong Curvature

We investigate the occurrence of naked singularities in the gravitational collapse of an inhomogeneous dust cloud in an expanding de Sitter background — a piece of Tolman–Bondi–de Sitter space–time. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. Our result unambiguously support the fact that the asymptotic flatness of space–time is not a necessary ingredient for the development of naked singularities.

scholarly journals Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Gravitational Lensing ◽  
Cosmic Time ◽  
Naked Singularity ◽  
Space Time ◽  
Axially Symmetric ◽  
Time Machine ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Closed Orbits ◽  
Group A

We present a gravitational collapse null dust solution of the Einstein field equations. The space-time is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near the singularity and the gravitational lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that this solution depends on the local gravitational field consisting of two components with amplitudes Ψ2 and Ψ4.

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