scholarly journals Axial gravitational waves in Bianchi I universe

2020 ◽  
pp. 2050116
Author(s):  
Sarbari Guha ◽  
Sucheta Datta
Keyword(s):  
Gravitational Waves ◽  
Separation Of Variables ◽  
Azimuthal Velocity ◽  
Perturbation Parameter ◽  
Matter Field ◽  
Field Equations ◽  
Bianchi I ◽  
Expansion Scalar ◽  
Special Cases ◽  
Axial Waves

In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge–Wheeler gauge. In this gauge, there are only two nonzero components of [Formula: see text] in the case of axial waves: [Formula: see text] and [Formula: see text]. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar [Formula: see text] to be proportional to the shear scalar [Formula: see text] (so that [Formula: see text], where [Formula: see text], [Formula: see text] are the metric coefficients and [Formula: see text] is an arbitrary constant), and the wave equation for the perturbation parameter [Formula: see text] has been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined [Formula: see text]. We then discuss a few special cases to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum [Formula: see text]. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.

Cosmological constant Λ in f(R,T) modified gravity

2016 ◽  
Vol 13 (05) ◽  
pp. 1650058 ◽  
Author(s):  
Gyan Prakash Singh ◽  
Binaya Kumar Bishi ◽  
Pradyumn Kumar Sahoo
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Modified Gravity ◽  
Bianchi Type ◽  
Field Equations ◽  
Type Iii ◽  
Expansion Scalar ◽  
Modified Theory Of Gravity ◽  
Shear Scalar ◽  
Modified Theory

In this paper, we have studied the Bianchi type-III cosmological model in the presence of cosmological constant in the context of [Formula: see text] modified theory of gravity. Here, we have discussed two classes of [Formula: see text] gravity, i.e. [Formula: see text] and [Formula: see text]. In both classes, the modified field equations are solved by the relation expansion scalar [Formula: see text] that is proportional to shear scalar [Formula: see text] which gives [Formula: see text], where [Formula: see text] and [Formula: see text] are metric potentials. Also we have discussed some physical and kinematical properties of the models.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

scholarly journals An Analysis of Gravitational waves

2021 ◽  
Author(s):  
Vaibhav Kalvakota
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Mathematical Structure ◽  
Gauge Condition ◽  
Field Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Wave Detector ◽  
The Masses

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

scholarly journals Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Genly Leon ◽  
Sebastián Cuéllar ◽  
Esteban González ◽  
Samuel Lepe ◽  
Claudio Michea ◽  
...  
Keyword(s):  
Scalar Field ◽  
Nonlinear Dynamical Systems ◽  
Perturbation Parameter ◽  
Time Dependent ◽  
Late Time ◽  
De Sitter ◽  
Time Dynamics ◽  
Locally Rotationally Symmetric ◽  
Bianchi I ◽  
Rotationally Symmetric

AbstractScalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic equation of state (EoS) with barotropic index $$\gamma $$ γ for the locally rotationally symmetric (LRS) Bianchi I and flat Friedmann–Lemaître–Robertson–Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $$\gamma $$ γ , the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter H – acting as time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.

scholarly journals How a projectively flat geometry regulates F(R)-gravity theory?

2021 ◽  
Author(s):  
Tee-How Loo ◽  
Avik De ◽  
Sanjay Mandal ◽  
P. K. Sahoo
Keyword(s):  
Matter Field ◽  
Gravity Theory ◽  
Gravity Models ◽  
Spacetime Geometry ◽  
Projectively Flat ◽  
Expansion Scalar ◽  
Isotropic Pressure ◽  
Constant Energy Density ◽  
Projective Flatness

Abstract In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

scholarly journals SPECTRUM OF GRAVITATIONAL WAVES IN KREIN SPACE QUANTIZATION

2011 ◽  
Vol 26 (36) ◽  
pp. 2697-2702 ◽  
Author(s):  
M. MOHSENZADEH ◽  
A. SOJASI ◽  
E. YUSOFI
Keyword(s):  
Gravitational Waves ◽  
Krein Space ◽  
Slow Roll ◽  
Primordial Power Spectrum ◽  
Alternative Approach ◽  
Special Cases ◽  
Kreĭn Space ◽  
Field Quantization ◽  
Krein Space Quantization ◽  
Scalar Perturbations

The main goal of this paper is to derive the primordial power spectrum for the scalar perturbations generated as a result of quantum fluctuations during an inflationary period by an alternative approach of field quantization.1–3 Formulas are derived for the gravitational waves, special cases of which include power law inflation and inflation in the slow roll approximation, in Krein space quantization.

scholarly journals SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

On uniqueness in dynamic poroelasticity

1963 ◽  
Vol 53 (4) ◽  
pp. 783-788 ◽  
Author(s):  
H. Deresiewicz ◽  
R. Skalak
Keyword(s):  
Porous Media ◽  
Liquid Medium ◽  
Uniqueness Theorem ◽  
Dissimilar Materials ◽  
Elastic Solid ◽  
Porous Solid ◽  
Uniqueness Of Solution ◽  
Biot’S Theory ◽  
Field Equations ◽  
Special Cases

Abstract Conditions are derived sufficient for uniqueness of solution of the field equations of Biot's theory of liquid-filled porous media, particular attention being paid to continuity requirements at an interface between two such dissimilar materials. It is found that at an interface two distinct sets of conditions will satisfy the demands of the mathematical uniqueness theorem, one of them being discarded on physical grounds. The permissible set is then discussed in relation to a number of possible models of the structure of a pair of elements in contact. The special cases of an impermeable elastic solid or a liquid medium in contact with a saturated porous solid are also examined.

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