Gravidynamics (scalar-tensor gravitation) and the observed discrete mass spectrum of compact stellar remnants in close binary systems. Vladimir V. SOKOLOV. ( 1 ) There are two new observational facts:

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( 1 ) There are two new observational facts:

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(1) There are two new observational facts: the mass spectrum of neutron stars and black hole candidates shows an evident absence of compact objects with masses within the interval 2 - 6 solar ones, and in close binary stellar systems with a low-massive optical companion the most probable mass value (a peak in the masses distribution of black hole candidates) is close to7 masses of the Sun.

… the road test: Finn 1994; Bailyn et al. 1998; Thorsett & Chakrabarty, 1999; Kaper et al. 2006; Nice et al. 2008; Farr et al. 2011, ¨Ozel et al. 2010, 2012; Kreidberg et al. 2012; + a new paper by the SAI team: V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , Astronomicheskii zhurnal, 2014, 91, No.3, p.167

Ozel et al., ApJ, 757:55-, 2012 For the case of black holes, they used the exponential distributionwith a low mass cut-off at Mc = 6.32M⊙ and a scale of Mscale = 1.61M⊙. The solid lines representweighted mass distributions for each population, for which appropriate fitting formulae are given in the paper...

… the road test: Finn 1994; Bailyn et al. 1998; Thorsett & Chakrabarty, 1999; Kaper et al. 2006; Nice et al. 2008; Farr et al. 2011, ¨Ozel et al. 2010, 2012; Kreidberg et al. 2012; + a new paper by the SAI team: V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , Astronomicheskii zhurnal, 2014, 91, No.3, p.167

Kreidberg et al. 2012 (Particularly) on mass of compact objects In these 16 systems with a faint companion star q = Mopt / MX≈ 0.1 For such systems the optical star is a probe body:

Such a gap is puzzling in light of all theoretical studies (GR + astrophysics…) that predict acontinuousdistribution of the compact object SN remnant masses with a smooth transition from NSs to BHs

(2) In the totally non-metric field/scalar-tensor model of gravitational interaction the total mass of a compact relativistic object with extremely strong gravitational field (an analog of black holes in GR) is approximately equal to 6.7 solar masses with radius of a region filled with matter (quark-gluon plasma) approx. 10 km.

Gravidynamics: in this model of gravitational interaction (as well as in electrodynamics) the field can be described by the energy which is quite a definite part of any gravitating object mass (like the electromagnetic mass of electron). All known effects of the weak field are explained (as well as in GR), since in this case the field is mainly only the tensor one = the GR gravitation… But in the strong field of a compact object the role of the scalar component – repulsion/antigravitation – increases. Vladimir V.Sokolov,Astrophysics and Space Science, 1992, 197, p.179

A half of the total mass (6.7 Mʘ)of such an object already consists only of the field – a scalar-tensor mixture… Astrophysics and Space Science, 1993, 201, p.303, V.V.Sokolov, and S.V.Zharikov, + all references there… To what density is the field energy non-localizable ?

To what the size of the gravitational field energydensity itself can be considered non-localizable? (e. g., see in L.D. Landau & E.M.Lifshic, Vol. II, chapter XI, § 96) When the contribution of this energy should be included in the mass of a field source as it is done for electron? Where is graviton born eventually? (like photons in ED)

In GR (in Vacuum around the same bag with PQ = 1/3 (ε - 4B) the gravitational field energy nonlocalizable and nonmetering in the total mass of any compact object (e.g. NSs).

And in gravidynamics the contribution of the field energy to the total mass of a stellar collapsar should be also taken into consideration…

A collapsar in gravidynamics A half of the total mass (6.7 Mʘ)of such an object already consists only of the field – a scalar-tensor mixture… (Seemore in Astrophysics and Space Science, 1993, 201, p.303, V.V.Sokolov, and S.V.Zharikov, + all references there…)

The gauge invariance The consistent dynamic interpretation of the field equations consists in the fact that the potentials of the field Ψik (just as in ED) must be understood absolutely independently of the chosen metrics ηik. Like a vector 4-potential in ED, Ψik can be of any value by virtue of the indeterminacy of (1) This transformation for Ψik is the gauge transformation with an auxiliary 4-vector Aiand a 4-scalar Λ.

Basic equations Corresponding field equations which are relativistically and gaugeinvariant (1), will be of the form: a is determined by the choice of unit for Ψik . Tikis the EMT of point particles as was mentioned above, and

In the same linear approximation, if we base it on the interaction f ΨikTik, which one can write down in symbolic form f ΨikTik => (4) consistently adhering to the dynamical interpretation of the field Ψik we can also obtain the equations of particle motion in a given field Ψik just as it is done for an electron moving in a given ED-field.

The universality f is the same for any field -- the universality of the gravitational interaction. So, the interaction of the electromagnetic field with the given gravitational one Ψik must be in the form (5) f Ψik tik(el) => This ultimately gives the correct description of the light interaction effects in a gravitational field, such as the light deflection and radio signal lag in the field of the Sun. For the correct description of the redshift effect one must add to the interaction (5) the interaction with the spinor (e-e+) field constructed by the same rule, i.e., with the same f [Mosinsky 1950, Okun 1999].

No vector source The gauge invariance leads to a demand for sources following the strong conservation law (Neuther's identity): i.e. to the absence of a vector source. Since there is no vectorTik,k, the direct use of the gauge invariance allows excluding a vector field (corresponding to this source) contained in the symmetric tensor Ψik ( ) in the general case.

The Hilbert-Lorentz gauge condition It means that if the gauge is chosen in such a way that in the theory there is no vector constructed of two possible 4-vectors then “long” equations are transformed to the short form:

The condition Вi= 0 in the conservation of the current Tik,k = 0, retains in the theory the gravitons with two spins. So, for real gravitons there remains: And the source ofpurely scalar gravitonsis a nonzero trace of the EMT of point particles:

One can divide the field Ψikand the source Tikinto two components corresponding to by the representation of equations (10) as an equivalent system of equations for every component separately - pure scalar and tensor ones. For this it is necessary to represent the potential in such an invariant form separating explicitly the scalar and the tensor: Ψik ≡ Фik+ 1/4 ηik Ψ (14) where Фik ηik≡ 0. Here Фikdescribes only the tensor part of the field Ψikand the invariant tensor 1/4 ηik Ψ describes the purely scalar component of the same field. In exactly the same way one may manipulate Tik: where Tik(2)ηik≡ 0.

The Nonlinear GD: In accordance with the universality of gravitational interaction one must consider the field itself to be the source of gravitation (which lacks in ED). It means that in the Lagrangian, besides the term f ΨikTik, terms arise of the type: (6) fΨikθik =>

Perturbation theory -> including nonlinearities, smallness of G – the gravitational interaction constant, nonlinear corrections in Lagrangian The higher is probability, the higher is the energy density of gravitational field gravitons The correct the field energy including itself = the correct nonlinear processes including. Localizability (locality) and the energy sign thelocalprocess, the field in the first approximation m > 0 the local process, the second approximation θ00 > 0

To what the size of the gravitational field energydensity itself can be considered non-localizable? (e. g., see in L.D. Landau & E.M.Lifshic, Vol. II, chapter XI, § 96) When the contribution of this energy should be included in the mass of a field source as it is done for electron? Where is graviton born eventually? (like photons in ED)