scholarly journals The Second-Order Correction to the Energy and Momentum in Plane Symmetric Gravitational Waves Like Spacetimes

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 220 ◽  
Author(s):  
Mutahir Ali ◽  
Farhad Ali ◽  
Abdus Saboor ◽  
M. Ghafar ◽  
Amir Khan
Keyword(s):  
Gravitational Waves ◽  
Energy Content ◽  
Conformal Factor ◽  
Second Order ◽  
Noether Symmetries ◽  
Noether Theorem ◽  
Plane Symmetric ◽  
Energy And Momentum ◽  
Symmetric Spacetime ◽  
Conformal Plane

This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves.

scholarly journals Approximate Noether symmetries from geodetic Lagrangian for plane symmetric spacetimes

2015 ◽  
Vol 12 (10) ◽  
pp. 1550124 ◽  
Author(s):  
Farhad Ali ◽  
Tooba Feroze
Keyword(s):  
Conformal Factor ◽  
Noether Symmetries ◽  
Plane Symmetric ◽  
First Order ◽  
Symmetric Spacetimes ◽  
General Plane ◽  
Symmetric Spacetime ◽  
Conformal Plane ◽  
General Time

Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time-conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed,5–6 where they obtained approximate Noether symmetries from Lagrangian for a particular plane symmetric static spacetime. In the present paper, the most general plane symmetric static spacetime is considered and perturbed it by introducing a general time-conformal factor eϵf(t), where ϵ is very small which causes the perturbation in the spacetime. Taking the perturbation up to the first-order, we find all Lagrangian for plane symmetric spacetimes for which approximate Noether symmetries exist.

Correction to the conservation laws in plane symmetric gravitational wave-like spacetimes

2018 ◽  
Vol 33 (21) ◽  
pp. 1850123 ◽  
Author(s):  
Farhad Ali ◽  
Wali Khan Mashwani ◽  
Muhammad Asif Jan
Keyword(s):  
Conservation Laws ◽  
Gravitational Wave ◽  
Conformal Factor ◽  
Time Dependent ◽  
Noether Symmetries ◽  
Plane Symmetric ◽  
Energy And Momentum ◽  
Symmetric Spacetime

This paper discusses the approximate Noether symmetries of the action of plane symmetric spacetime. A time-dependent conformal factor is introduced in the plane symmetric metric in such a way so as to obtain the same number of Noether symmetries as for the exact plane symmetric spacetime. The corresponding approximate conservation is obtained to discuss the conservation laws of the energy and momentum during the formation of gravitational wave.

scholarly journals Killing and Noether Symmetries of Plane Symmetric Spacetime

2013 ◽  
Vol 52 (9) ◽  
pp. 3106-3117 ◽  
Author(s):  
M. Farasat Shamir ◽  
Adil Jhangeer ◽  
Akhlaq Ahmad Bhatti
Keyword(s):  
Noether Symmetries ◽  
Plane Symmetric ◽  
Symmetric Spacetime

Noether symmetry analysis for novel gravitational wave-like spacetimes and their conservation laws

2020 ◽  
Vol 35 (28) ◽  
pp. 2050234
Author(s):  
Amir Sultan Khan ◽  
Israr Ali Khan ◽  
Saeed Islam ◽  
Farhad Ali
Keyword(s):  
Black Holes ◽  
Conservation Laws ◽  
Neutron Stars ◽  
Gravitational Wave ◽  
Hawking Radiation ◽  
Conformal Factor ◽  
Noether Symmetries ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Symmetric Structure

The phenomena-like Hawking radiation, the collapse of black holes, and neutron stars decrease the curvature of spacetime continuously with the passage of time. The time conformal factor adds some curvature to nonstatic spacetime. In this article, some novel classes of nonstatic plane-symmetric spacetimes are explored by introducing a time conformal factor in the exact plane-symmetric spacetimes in such a way that their symmetric structure remains conserved. This technique re-scales the energy contents of the corresponding spacetimes, which comes with a re-scaled part in each spacetime. The invariant quantities corresponding to the Noether symmetries are also calculated.

scholarly journals The Physical Significance of Time Conformal Minkowski Spacetime

2020 ◽  
Vol 39 (2) ◽  
pp. 365-370
Author(s):  
Farhad Ali ◽  
Muhammad Asif Jan ◽  
Wali Khan Mashwani ◽  
Rashida Adeeb Khanum ◽  
Hidayat Ullah Khan
Keyword(s):  
Cosmological Constant ◽  
Energy Content ◽  
Einstein Field Equation ◽  
Minkowski Spacetime ◽  
Conformal Factor ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Einstein Field Equations ◽  
Field Equations ◽  
General Time

The Minkowsiki spacetime is flat and there is no source of gravitation. The time conformal factor is adding some cuvature to this spacetime which introduces some source of gravitation to the spacetime. For the Minkowski spacetime the Einstein Field equation tells nothing, because all the components of the Ricci curvature tensor are zero, but for the time conformal Minkowski spacetime some of them are non zero. Calculating the components of the Ricci tensor and using the Einstein field equations, expressions for the cosmological constant are cacultaed. These expressions give some information for the cosmological constant. Generally, the Noether symmetry generator corresponding to the energy content in the spacetime disapeares by introducing the time conformal factor, but our investigations in this paper reveals that it appears somewhere with some re-scale factor. The appearance of the time like isometry along with some re-scaling factor will rescale the energy content in the corresponding particular time conformal Minkowski spacetime. A time conformal factor of the form () is introduced in the Minkowski spacetime for the invistigation of the cosmological constant. The Noether symmetry equation is used for the Lagrangian of general time conformal Minkowski spacetime to find all those particular Minkowski spacetimes that admit the time conformal factor. Besides the Noether symmetries the cosmology constant is calculated in the corresponding spacetimes.

Energy and momentum of cylindrical gravitational waves

1993 ◽  
Vol 25 (4) ◽  
pp. 429-433 ◽  
Author(s):  
Nathan Rosen ◽  
K. S. Virbhadra
Keyword(s):  
Gravitational Waves ◽  
Energy And Momentum

scholarly journals Propagation of Scalar Fields in a Plane Symmetric Spacetime

2016 ◽  
Vol 46 (6) ◽  
pp. 784-792 ◽  
Author(s):  
Juliana Celestino ◽  
Márcio E. S. Alves ◽  
F. A. Barone
Keyword(s):  
Scalar Fields ◽  
Plane Symmetric ◽  
Symmetric Spacetime

scholarly journals ENERGY–MOMENTUM DENSITY OF GRAVITATIONAL WAVES

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4569-4577 ◽  
Author(s):  
AMIR M. ABBASSI ◽  
SAEED MIRSHEKARI
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Momentum Density ◽  
Energy And Momentum ◽  
Energy And Momentum Densities

In this paper, we elaborate the problem of energy–momentum in general relativity by energy–momentum prescriptions theory. Our aim is to calculate energy and momentum densities for the general form of gravitational waves. In this connection, we have extended the previous works by using the prescriptions of Bergmann and Tolman. It is shown that they are finite and reasonable. In addition, using Tolman prescription, exactly, leads to the same results that have been obtained by Einstein and Papapetrou prescriptions.

Noether symmetries of vacuum classes of pp-waves and the wave equation

2016 ◽  
Vol 13 (09) ◽  
pp. 1650109 ◽  
Author(s):  
Sameerah Jamal ◽  
Ghulam Shabbir
Keyword(s):  
Wave Equation ◽  
Gravitational Waves ◽  
Wave Equations ◽  
Noether Symmetry ◽  
Symmetry Groups ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Metric Functions ◽  
Symmetry Algebras

The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.

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