SOME NONCONFORMAL ACCELERATING PERFECT FLUID PLATES OF EMBEDDING CLASS 1 USING SIMILARITY TRANSFORMATIONS

2010 ◽  
Vol 25 (09) ◽  
pp. 1863-1879 ◽  
Author(s):  
Y. K. GUPTA ◽  
PRATIBHA ◽  
SACHIN KUMAR
Keyword(s):  
Perfect Fluid ◽  
Flat Space ◽  
Space Time ◽  
Explicit Solutions ◽  
Field Equations ◽  
Similarity Transformations ◽  
Higher Dimensional ◽  
Class 1 ◽  
Brane Theory ◽  
Respective Category

In view of renewed interest in the space–time embedded in higher-dimensional flat space which are useful in extrinsic gravity, string and brane theory, a set of six explicit solutions to Einstein's field equations for nonconformally flat accelerating and shearing perfect fluid plates is obtained using similarity transformations method by considering a five-dimensional flat metric. All the solutions thus obtained are analyzed physically. All the solutions are new in their respective category as far as authors are aware.

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 HIGHER DIMENSIONAL SZEKERES' SPACE–TIME IN BRANS–DICKE SCALAR TENSOR THEORY

2004 ◽  
Vol 13 (06) ◽  
pp. 1073-1083
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Turning Point ◽  
Coupling Parameter ◽  
Big Bang ◽  
Space Time ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Higher Dimensional ◽  
Theory Of Gravitation ◽  
The Big Bang

The generalized Szekeres family of solution for quasi-spherical space–time of higher dimensions are obtained in the scalar tensor theory of gravitation. Brans–Dicke field equations expressed in Dicke's revised units are exhaustively solved for all the subfamilies of the said family. A particular group of solutions may also be interpreted as due to the presence of the so-called C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter. The models show either expansion from a big bang type of singularity or a collapse with the turning point at a lower bound. There is one particular case which starts from the big bang, reaches a maximum and collapses with the in course of time to a crunch.

scholarly journals SPIN-3/2 FERMIONS IN TWISTOR FORMALISM

2001 ◽  
Vol 16 (32) ◽  
pp. 2103-2113 ◽  
Author(s):  
MITSUO J. HAYASHI
Keyword(s):  
Twistor Space ◽  
Integrability Condition ◽  
Local Existence ◽  
Flat Space ◽  
Space Time ◽  
Necessary Condition ◽  
Field Equations ◽  
Weyl Spinor ◽  
Cartan Theory ◽  
The Right

Consistency conditions for the local existence of massless spin-3/2 fields have been explored to find the facts that the field equations for massless helicity-3/2 particles are consistent if the space–time is Ricci-flat, and that in Minkowski space–time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity-3/2 fields, we show in flat space–time that the charges of spin-3/2 fields, defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space–time that the (anti-)self-duality of the space–time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space–time to that with torsion (Einstein–Cartan theory), and investigate the consistency of existence of spin-3/2 fields in this theory. A simple solution to this consistency problem is found: The space–time has to be conformally (anti-)self-dual, left-(or right-) torsion-free. The integrability condition on α-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed torsion.

scholarly journals Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Sanjay Oli
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Space Time ◽  
Time Dependent ◽  
Field Equations ◽  
Current Observation ◽  
Kinematical Parameters ◽  
Kaluza Klein

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

Perfect fluid in a conformally flat space time

1980 ◽  
Vol 13 (1) ◽  
pp. 191-197 ◽  
Author(s):  
M M Som ◽  
N O Santos
Keyword(s):  
Perfect Fluid ◽  
Flat Space ◽  
Space Time ◽  
Conformally Flat

A Class of Energetically Rigid Gravitational Fields

1974 ◽  
Vol 29 (11) ◽  
pp. 1527-1530 ◽  
Author(s):  
H. Goenner
Keyword(s):  
Flat Space ◽  
Second Fundamental Form ◽  
Momentum Tensor ◽  
Space Time ◽  
Curved Space ◽  
Geometrical Properties ◽  
Gravitational Fields ◽  
The Second Fundamental Form ◽  
Perfect Fluids ◽  
Higher Dimensional

In Einstein's theory, the physics of gravitational fields is reflected by the geometry of the curved space-time manifold. One of the methods for a study of the geometrical properties of space-time consists in regarding it, locally, as embedded in a higher-dimensional flat space. In this paper, metrics admitting a 3-parameter group of motion are considered which form a generalization of spherically symmetric gravitational fields. A subclass of such metrics can be embedded into a five- dimensional flat space. It is shown that the second fundamental form governing the embedding can be expressed entirely by the energy-momentum tensor of matter and the cosmological constant. Such gravitational fields are called energetically rigid. As an application gravitating perfect fluids are discussed.

scholarly journals TACHYON MONOPOLE

2005 ◽  
Vol 20 (23) ◽  
pp. 5491-5499 ◽  
Author(s):  
XIN-ZHOU LI ◽  
DAO-JUN LIU
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Tachyon Field ◽  
Field Equations ◽  
Monopole Solution ◽  
Static Space

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.

Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

2018 ◽  
Vol 33 (12) ◽  
pp. 1850065 ◽  
Author(s):  
Suhail Khan ◽  
Muhammad Shoaib Khan ◽  
Amjad Ali
Keyword(s):  
Perfect Fluid ◽  
Outer Region ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Higher Dimensional ◽  
Stress Energy ◽  
Inner Region ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress–energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

NON-MINIMAL COUPLING, VARIABLE SPEED OF LIGHT AND COSMOLOGY

2002 ◽  
Vol 17 (20) ◽  
pp. 2777-2777
Author(s):  
P. TEYSSANDIER
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Space Time ◽  
Variable Speed ◽  
Speed Of Light ◽  
Field Equations ◽  
Minimal Coupling ◽  
Structural Constant ◽  
Dimensional Space Time ◽  
Photon Gas

Presently, there exists some renewed interest in time varying speed of light theories as possible solutions of the major cosmological problems1. It is often believed that the local Lorentzian invariance is broken if the speed of light in a vacuum is not a constant. We point out that this belief is not necessarily founded and that a variable speed of light is perfectly consistent with general relativity under the assumption of non-minimal coupling between electromagnetism and curvature. Two kinds of arguments may be invoked in favour of such an assumption. First, a theorem due to Horndeski2 shows that in a four-dimensional space-time the Einstein-Maxwell field equations are not the only second-order vector potential field equations which stem from a Lagrangian scalar density, are consistent with the charge conservation and reduce to Maxwell's equations in a flat space-time (see also3). Second, according to QED4,5, vacuum polarization induces tidal gravitational effects which imply that photons propagating in a curved space-time have velocities exceeding the value of the "Lorentzian structural constant" c. The modified electromagnetic field equations given by Horndeski2 are studied here in the geometrical optics limit. Considering the case of Friedmann-Robertson-Walker cosmological models, we find the value of the speed of light as a function of the energetic content of the universe. We deduce from this result a new equation of state for a photon gas and we discuss the consequences of this equation on the evolution of the scale factor during the radiation-dominated era.

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