Quantization and Assessment of the Gravitational Waves

General Relativity describes the movement of bodies in strong gravitational fields with the geometrical structure of the dynamical space-time continuum. Accelerating objects produce changes in the curvature which propagate outwards at the speed of light in a wave-like manner which transport energy as gravitational radiation and this phenomenon are known as gravitational waves.

Gravitational waves are ripples in the structure of space-time which propagate as waves and travels outward from the source. One of the vital properties of this wave is that it transports energy as gravitational radiation and this radiation or energy creates the distortion of the medium (Ohanian and Ruffini, 1994). In General theory of relativity, this radiation known as gravity which is connected to space-time curvature (Narlikar, 1978;Max, B. Einsteins's, 1964;Clarke, 1929;Hughston and Tod, 1990;Foster, 1994; and Biressa and Pacheco, 2011). Heavy mass creates this curvature (Weinberg, 1972).

Identifying of Gravitational waves
The LIGO (Laser Interferometer Gravitational-Wave Observatory) scientific collaboration announce on 11 February 2016 the identifying of gravitational waves which is known as quadruple wave which uses the space-time as a medium (Ohanian and Ruffini, 1994). By the expansion and contraction of the space it spreads out through the medium. The character of quadruple wave is that if it contracts the space to the horizon, the space will be expansion to the upright at the same time and vice-versa (Caroll, 2019).
By the ultimate slice of a minimum time of the unification, it released over force than fifty times that of all the heavenly body in the notice able united cosmos. The single picks up the high place between the vibration of 35 and 250 Hz. By rotating two dead massive stars a black hole is created which creates distortion over the space time known as gravitational waves (Ohanian and Ruffini, 1994). This wave has two vital and singular characters. Primarily, it is need not to present the substance for creating of the waves by a dual system of zero charged black holes, which would transmit no electromagnetic diffusion. stars may be enclosed out by stellar pollen, while gravitational waves will cross originally unhindered (Ohanian and Ruffini, 1994). By these two modes this waves bear information about astronomical occurrence never before noticed by humans.

Plane-Wave Solutions and the Transverse Traceless (TT) Gauge
The Linearized field eq. in empty space is given by With the flat wave solutions, Where is fixed, symmetric, rank-2, and ≡ is a fixed four-vector familiar to the wave vector in the approach of extension and Re stands for "real part". Putting (2) into (1), we have the condition (Wapstra and Nijgh, 1955).
Then the amplitude tensor has 10 different (complex) components, but the condition (4) [ is orthogonal (transverse) to ] gives four conditions on these, cutting their number down to 6. The gauge condition.
Let the solution of (6) as Where, are constants? We have In the new gauge (7) becomes From which, using (7), we obtain Since exp( ′ ′) differs from exp( ) by only a first-order quantity (Banu et al., 2021). We conveniently choose constants as follows: So that 0 ′ 0 ′ = 0 ′ 1 ′ = 0 ′ 2 ′ = 0 and 1 ′ 1 = − 2 ′ 2 ′ On dropping primes the matrix of amplitude tensor and this wave in this gauge travelling in the 3 direction, the two components 11 and 12 completely characterize the wave. In this gauge ≡ = 0 00 = 33 = 0 and 11 = − 22 It then follows that ℎ = 0 so that there is no difference between ℎ and : Because of ℎ = = 0 the gauge is called traceless, and because of ℎ 0 = 0 = 0 It is called transverse.

Gravitational Waves Propagate through Empty Space-time with Light velocity
Maxwell's equations are second order differential equation under a suitable gauge condition (Richard, 1983). We have the Minkowskian metric is of the form (Stephani, 2004;Wapstra and Nijgh, 1955 So, the Ricci tensor is The field equations implies (Weinberg's, 1972).
Introducing the new variables We further simplify (11) by a gauge transformation defined by ′ ≡ + ( ) Now the matrix element is given by We find Neglecting products of small quantities it leads on rearranging to Contracting with it yields Also, Then, the linearized Einstein equations (20) becomes The remaining gauge freedom → + preserves the gauge condition provided satisfies Evidently equation (23) represents a wave equation with source term In empty space equation (23) reduces to It shows that these waves approach through null space-time having light velocity .

Gravitational Waves and Quantum Mechanics
We know earth emits 0.005 watt energy during rotating about the sun. Dirac was able to quantize the field equations and showed that gravitation-quanta or gravitation is the multiple of plank constant ℎ like as photon; although the spin of gravitation is twice number of photon. Now, we would explain a plane wave solution, with wave vector and helicity ±2, as consisting of gravitations: quanta with energy momentum vector = ћ and rotation quantities in the direction of speed ±2ћ (Gott et al., 1974).
We consider that the number consistency of gravitons with helicity ±2 in a plane wave is The gravitational radiation by any system as giving the rate Γ of emitting gravitons of energy ћ into the solid angle Ω is By observation equation (29) is mostly overwhelmed for the frequencies which indicate the number of gravity.

CONCLUSION:
We can summarize that gravitation is the manifestation of space-time curvature and the waves created by heavy mass is dynamic with the velocity of light (Stephani, 2004). We have also arises the plane wave solution for quantum theory of gravi-tational waves by energy momentum tensor which implies the wave like manner and particle manner.

ACKNOWLEDGEMENT:
Authors thanks to the authority of the Department of Computer Science and Engineering, NWU, for supporting with the proper support to conduct the successful study.

CONFLICTS OF INTEREST:
The authors declare there are no potential conflicts of interest to publish it under the current issue.