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Negative Mass Gravity Theory(General Relativity) Garmsiri Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622 Vol. 9,Issue 9 (Series -II) September 2019, pp 20-26 RESEARCH ARTICLE OPEN ACCESS Negative mass gravity theory(general relativity). Garmsiri member of the Astrophysical Society of Bushehr Province in Persian golf, dehdashti koi hosseinieh, bushehr state. ABSTRACT: According to the theory of effective negative mass, published in the journal of physical Review letters, If force is applied to a negative mass That mass is accelerating That it accelerates unlike the direction Force applied. Therefore, based on this theory, the material can have both positive and negative masses. here we show that negative mass has negative gravity and create curvature in spacetime which basis the shape of the cosmos is after the big bang. The combination of two curves created by positive mass and negative mass basis of the orbits of the planets is around the stars….. ----------------------------------------------------------------------------------------------------------------------------- --------- Date Of Submission: 30-08-2019 Date Of Acceptance: 16-09-2019 --------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION According to the theory of effective The Fields Equation Of Negative Mass negative mass, published in the journal of physical In order to prove that the negative mass in Review letters, If force is applied to a negative spacetime produces a curvature, we know energy mass That mass is accelerating That it accelerates impact tensor must be related to the spacetime unlike the direction Force applied [1]. Therefore, curvature. We show the energy density flux with based on this theory, the material can have both the symbol ρ and the hydrostatic pressure density positive and negative masses. But the important with p symbol. Energy impact tensor thing is that the acceleration of the positive mass is is as follows: opposed to the acceleration of the negative mass, Tμv = p + ρ uμ uv + pgμv , Thus, according to the theory of general relativity, In the energy impact tensor, the energy density flux Albert Einstein, Given the two Hypothesis, he says: and the hydrostatic pressure are the result of a 1) Accelerated mass and gravitational mass are positive mass, and we call it a stress-energy tensor, both one and the same. or a material-energy, which is a positive mass. But 2) The function of the accelerator and the gravity in order to obtain a stress- negative Energy tensor, device are the same. we must have μv μ v μv Therefore, we can state the theory of gravity of T′ = pnm + ρnm u u + pnm g , negative mass It is proved with these two where μv hypotheses but for a negative mass, we must add T′ : negative energy impact Tensor, two another hypothesis, in general, with the ρnm : Energy density flux of negative mass, following three hypotheses so that: pnm : hydrostatic pressure, 1) we assume that the negative mass has a constant uμ : Four velocity vector, mass (that is, it has size, volume and radius). gμv : Metric, 2) The acceleration that the positive mass takes due Now this negative energy impact tensor to the force applied be equal to the acceleration that should have a linear relationship with the Ricci negative mass due to the same force applied. tensor. If the Covariant derivative is zero for the 3) Accelerated negative mass and gravitational negative energy impact tensor and the Ricci tensor negative mass are both one and the same. is zero, then the problem is solved. But we know 4) The function of the accelerator and the gravity that Albert Einstein in general relativity proved that device are the same. the Covariant derivative material-energy tensor is Therefore, expresses gravitational zero, but the Ricci tensor, with the help of bianchi negative mass theory that the movement of a identity, turned into the Ricci tensor and the Ricci smaller negative mass leads to a larger negative scalar In this case, the covariant derivative for this mass, It is due to the curvature that generates a tensor is zero. So, since Einstein proved that the larger negative mass in spacetime And gravity is new tensor has a zero covariant derivative, here is due to this curvature. (In this paper, for a smaller an negative energy impact tensor with the Einstein negative mass, the negative mass of the substance equalizer, and since Einstein's tensor has a is smaller and for a larger negative mass, the covariant derivative of zero, here we should only negative mass of the substrnce is larger). find the covariant derivative for the negative www.ijera.com DOI: 10.9790/9622- 0909022026 20 | P a g e Garmsiri Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622 Vol. 9,Issue 9 (Series -II) September 2019, pp 20-26 μv 1 energy impact tensor to gain. If T′ ,is an negative Rμv − gμv R = −kT′μv , energy impact tensor symbol, we have 2 (2) μv μ v μv T′ = pnm + ρnm u u + pnm g , where where ′μv μ v T :negative impact energy tensor. u u gμv = 1, In the Einstein equation, the constant k is to be μ u = (c, 0,0,0), determined. Earlier, when we obtained the −2 −c 0 0 0 Newoton’s equation in the weak and static field gμv = 0 1 0 0 , approximation, we had found that [5], 0 0 1 0 2ф 2GM g = 1 + = 1 − , 0 0 0 1 44 c2 c2r We calculate the covariant derivative for this tensor (3) is the metric and the Covariant derivative is zero The Newotonian theory in the presence of matter for the metric tensor [2] (appendix A). so, gij,k = gives poisson equation [5], 0, 2 ф = 4πGρ , i ∇ We can also the covariant derivative vector u is (4) zero [3] (appendix B). so: ui = 0, and We know that in Newton’s law of gravity so: T′μv = 0, the force of gravity between two positive masses is We want to say that, as if the mass too with the product of two masses direct proportion hight, it creates a curvature in the spacetime, the and with square of distance two masses reverse negative mass if too hight also creates a curvature ratio [6]. This law also applies for a negative mass, in spacetime. Therefore, we proved that the but to make proportions equal to that we must derivative of negative Energ impact tensor is equal multiply the negative mass gravitational constant zero, and derivative of Ricci tensor that Einstein it that’s it showing with symbol Gnm ,(appendix D) to turned to Ricci tensor and scalar Ricci is zero . so, we have so, There should be a linear relationship between Fn1 = Fn2 = Gnm (m*1) (m*2) /( r²). the tow. Therefore should a side be geometrical So, based on the first hypothesis, we can define involving the spacetime metric, Ricci tensor and Newoton’s equation for negative mass, so that we Ricci scalar, and the another side involves the had found that negative Energy-momentum tensor of the matter 2ф′ 2G (M∗) g = 1 + = 1 − nm , with negative mass fields multiplier k , Therefore 44 c2 c2r we use Einstein-Hilbert action, the difference is (5) that we here use Eistein-Hilbert action including where matter with negative mass. Gnm :gravity constant of negative mass. We know Einstein-Hilbert action including matter So, the Newotonian theory in the presence of is [4], matter with negative mass gives poisson equation 2 ′ ф′ = 4πGnm (ρnm ) , I = Ig + Im , ∇ (1) (6) Now if a matter be with negative mass equation (1) where changes to Gnm :gravity constant of negative mass. I = Ig + I(m∗) , Now we define equation (6) gravitational 2 potential of negative mass and show it with ′ ф′ Therefor in continuum mechanics, the action is the ∇ (flat) spacetime integral of a lagrangian negative ,We want to express the gravity theory with the density . so, negative mass, so that the negative mass produces a I = Ig + I(m∗) curvature in spacetime. Multiplying the equation 1 4 4 μv = −gd xR + −gd xℒ , (2) by g μ v and denoting T′ g μ v ,by T', we find R = 2k (m∗) Where k T, Then, this equation can be as 1 R = −k(T′ − g T′ ) , ℒ(m∗) , is the lagrangian negative density for μv μv 2 μv matter with negative mass, (7) We have proved that the negative impact Compare this equation with (6). We know that 4- dxμ energy tensor derivative is zero and We know that velocity uμ = .uμ (x), and also ds the Einstein tensor derivative that obtained from μ v the Ricci and Ricci scalar tensors is zero so, We gμv u u =1 ,Therefore, using the result that the use Einstein’s experience and postulate the metric gμv ,is covariantly constant, we have μ equation for matter with negative mass field g uμ uv = g uμuv + u uv = 2g uμ uv = μv ;λ μv ;λ ;λ μv ;λ (appendix C) 0. Leading to As www.ijera.com DOI: 10.9790/9622- 0909022026 21 | P a g e Garmsiri Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622 Vol. 9,Issue 9 (Series -II) September 2019, pp 20-26 v ρ ρ ρ ς ρ ς uv u;λ = 0. R μ v = ( ∂ ρ Γ μ v − ∂ v Γ μρ + Γ ςρ Γ μ v − Γ ς v Γ ρμ ) , (8) The terms involving the derivatives of Γs are μ Introduce a scalarρnm (x), so that ρnm u , gives that retained. They are, using (13): flow of matter with negative mass and negative ρ 1 ρλ ∂ρ Γμv ≃ η (∂ρ ∂μhvλ + ∂ρ ∂v hμλ − ∂ρ ∂λ hμv ) , i 4 2 density, as ρnm u −g, and ρnm u −g , (16) respectively.
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