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.

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 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.

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

Particles dynamics around time conformal quintessential Schwarzschild black hole

2020 ◽  
Vol 29 (13) ◽  
pp. 2050095
Author(s):  
Israr Ali Khan ◽  
Amir Sultan Khan ◽  
Saeed Islam ◽  
Farhad Ali
Keyword(s):  
Black Hole ◽  
Small Parameter ◽  
Conservation Laws ◽  
Charged Particles ◽  
Conformal Factor ◽  
Noether Symmetries ◽  
Schwarzschild Black Hole ◽  
Approximate Symmetries ◽  
Particles Dynamics ◽  
General Time

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

scholarly journals Black hole superradiance as a probe of ultra-light new particles

2016 ◽  
Vol 12 (S324) ◽  
pp. 273-278
Author(s):  
Robert Lasenby
Keyword(s):  
Beyond Standard Model ◽  
Black Holes ◽  
Black Hole ◽  
Standard Model ◽  
Gravitational Wave ◽  
Exponential Growth ◽  
Gravitational Radiation ◽  
Bound States ◽  
Penrose Process ◽  
Energy And Momentum

AbstractBosonic fields around a spinning black hole can be amplified via ‘superradiance’, a wave analogue of the Penrose process, which extracts energy and momentum from the black hole. For hypothetical ultra-light bosons, with Compton wavelengths on ≳ km scales, such a process can lead to the exponential growth of gravitationally bound states around astrophysical Kerr black holes. If such particles exist, as predicted in many theories of beyond Standard Model physics, then these bosonic clouds give rise to a number of potentially-observable signals. Among the most promising are monochromatic gravitational radiation signals which could be detected at Advanced LIGO and future gravitational wave observatories.

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
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