Gravitational Stark effect for Ridberg atom in centrifuge

The possible way for direct observation of the quantum gravitational effects on Earth would be use of principle of equivalence and use of fast rotating centrifuges already available to create the equivalent of strong enough gravitational field.
Back in 1950 Popular mechanics magazine mentioned two commercially available record-setting centrifuges: The Sharples Corporation of Philadelphia manufactured centrifuge with 1.2 millions rotations per minute and Dr Jesse Wakefield Beams, University of Virginia reported about 166000 rotations per second.
The easiest way to observe gravitational Stark effect is to rely upon the gravitational field gradient instead of the gravitational field itself (because due to the equivalence principle both electron and nucleus will be attracted with the same force). The field gradient, however, will create the energy difference for the atom to be observed as line shift. The gradient of the gravitational field in the centrifuge is:
F=m*w*w*r
dF/dr=m*w*w
Here r is the distance from the center of the rotation, m is the mass of the object, w is the rotational angular frequency.
From the simple formula for energy in the gradient of the gravitational field:

ΔE=ΔF*a_o

Here ΔE is the energy difference due to the different gravity for the electron as it rotates around the nucleus - gravitational force is different throughout the atom, ao is the radius of the atom (the radius of Bohr orbit)

ΔF=(dF/dr)*a_o

and

ΔE=m_e*w²*a_o²=m_e*(2*π*ν)²*a_o²

here me is the mass of electron,  ν is the rotational frequency expressed in Hz , ao is the radius of the Ridberg atom (around 1 micrometer possible now). Substituting 166000 Hz as the record rotational frequency we have:

ΔE=2*10exp(-30) Joule or 1.24*10exp(-11) eV or in frequency domain the splitting would be 3021 Hz.

Such splitting between lines is possible to record. Assuming the centrifuges improved in the last 70 years the overall experiment seems feasible.

Light trapped in stars enhanced gravity: more hints from triple stars and from star clusters

The idea of the additional strong attraction force due to the light trapped inside the stars [1] should reveal itself in numerous phenomena in addition to dark matter possible explanation. The easiest way to check the hypothesis of non-Keplerian behavior of stars is to repeat Tycho Brahe work for the Milky way center: the accurate mapping of stars orbits is already on its way by Hawaii telescope and will be probably completed in 20-50 years. In addition some hints about such possibility may come from the observations of the discrepancies in stellar dynamics as computed using third Kepler law. One of the hints comes from binaries: the mass-luminosity relation seems to be wrong, actual masses of the bright stars due to the additional gravity-like force from photons should be much higher [2]
Other discrepancies which include the presence of ultra-bright young stars (those stars hypothetically have especially high amounts of trapped light inside and thus are especially strongly underweighted by usual methods). I refer to the so-called super-virial young star clusters. It is  a well established observational fact that the mass evaluation of star cluster from total luminosity and from virial theorem gives for young star clusters (full of young bright stars) the difference in 10 times. From virial theorem mass for young cluster is 10 times more compare to mass from luminosity (for old clusters, which have only old stars the masses are exactly the same) [3]. While those facts may be explained using some assumptions like binaries higher content, the explanation based on the underestimation of the effective "mass" of bright and ultra-bright stars using mass-luminosity ratio will be simpler and consistent with other facts. Indeed the young cluster is full of young short-lived stars where the amount of light trapped inside is especially high (thus making them especially "heavy"). Using the modern mass-luminosity the smaller mass is obtained. At the same time the virial distribution is created by the real forces, which are much stronger for bright stars and thus correspond to much higher spread of velocities (velocity dispersion). 10 times difference is a huge discrepancy and should be taken into the consideration. At the same time the old cluster have no or little amount of young stars (they all gone), only weak stars are left with much smaller amount of trapped light thus making such cluster closer to non-luminous objects (pure baryonic matter like planets) with more correct evaluation of mass using mass-luminosity relation.
The other hint for the problem with Keplerian mass determination comes from triple stars. Algol triple system is a close one and well investigated [4]. The problem with the mass and luminosity of Algol Aa2 star, which is close to bright main star Aa1. Because the stars may be resolved completely, the masses of them all were determined using the Kepler law and relative velocities measurements [5]. The absolute luminosity is also easy to measure. Spectral type of all three stars is confirmed after resolution of internal binary. The results gives for Aa2 star the spectral type of K0IV (whish should have luminosity of 10-42% of solar and mass below solar mass) the mass of 0.7 of solar and luminosity of 7 Suns, what is way too much for such type of the star.
However, since this star is a binary with especially bright star Aa1 (182 Suns) the additional gravitation-like force should be especially high. It means that the real masses of all three stars are much higher. For the internal pair Aa1 and Aa2 the real sum of mass is more underestimated than for the second pair (Aa1+Aa2 and Ab), because for the second pair the luminosity-related "gravity" is diluted by the presence of weak star Aa2 (the sum of bright and dim star will looks like more baryonic component). Then the masses of Aa1 and Aa2 will grow higher (say 2 times higher) compare to mass of Ab star (say 1,5 times larger), which will bring mass of Aa2 to the normal level comparable with luminosity while shifting the Ab star toward the more correct position on the mass-luminosity curve, but not throwing it off.
Modern explanation of the Algol star Aa2 as being stripped of matter due to direct mass transfer to Aa1 (too close pair) will not allow easy explanation why it is so luminous (the measurements are especially easy because all three stars may be considered as being at the same distance from Earth with high enough accuracy), and the relative measurements of luminosity should not be a problem.
Taken together, those discrepancies (mass-luminosity curve from binaries [2], supervirial young clusters and triple stars like Algol) are additional hints toward the inconsistency of present understanding of stars mass origin and to the absence of dark matter.

References.
1. https://tipikin.blogspot.com/2019/10/
2. https://tipikin.blogspot.com/2019/11/
3. https://www.aanda.org/articles/aa/full/2006/12/aa4177-05/aa4177-05.right.html
https://arxiv.org/pdf/0911.1557.pdf
4. https://en.wikipedia.org/wiki/Algol
5. https://arxiv.org/abs/1205.0754
6. https://en.wikipedia.org/wiki/K-type_main-sequence_star
http://www.solstation.com/stars3/100-ks.htm

Quantum vacuum application to gravity: the Higgs boson antigravitational particle predicted

Recent discovery of Higgs boson which has a relation to gravity but should be the boson particle with respect to the statistic poses some problems with gravitational constant origin and strength. Since boson is the antiparticle to itself, it may be created from the vacuum without any pair and since it may condense into the lowest state, the increased fluctuations of quantum vacuum near any particle will grow the final mass to infinity.
Fluctuations of quantum vacuum long ago were used to explain the origin of speed of light [1]. For the attenuation of the electric field near the charge the use of virtual dipoles from vacuum is relatively straightforward: the particle-antiparticle pair composed of fermions, which can not occupy the same state and thus can not accumulate near the charge up to infinite amounts, completely eliminating the electric field. Unfortunately, application of the same idea to the gravity fails simply because any particle has a mass and they all attract to the initial mass. While the usual particles like protons, neutrons, electrons etc will be attracted to the particle but being fermions can not accumulate infinitely, the Higgs boson can. It means that the virtual Higgs bosons will be clumping to any mass to infinity, creating infinitely heavy condensate, thus making the gravity impossible.
The plausible explanation is given in [2]: similar to the particle-antiparticle dualism, there are virtual gravitational dipoles formed by pairs matter- antigravitational matter (the mass being considered as independent quantum number, the whole set of antigravity particles should exist for both particles and antiparticles, effectively doubling the number of existing particles).
Those gravitational dipoles are formed by the particles, which may be bosons with respect to usual matter-antimatter relations but not with respect to gravity. Similar to the creation of the electron-positron pair in the intense electric field, those virtual dipoles will create pair particle - gravitational antiparticle in strong enough gravitational field (inside the dark hole, according to [2]).
Fortunately, antiparticles are formed not only in electric field, but also in any interactions of highly accelerated particles (that is how antiprotons are manufactured and separated by the electric and magnetic field). In a similar way the antigravitational particles should be formed (and may be already produced from time to time, but since the gravity is so much weaker compare to electric force, the usual separation methods in accelerators will render them unnoticed).
Using the formula derived for electric permittivity of vacuum from [1] it is even possible to estimate the mass of one component of such virtual dipole
ε_o=[(K_w²-1)^3/2/K_w]*2e²/(3π*h*c)
here ε_o - is the vacuum permittivity, e is the charge of electron, h is Planks constant, c is speed of light and K_w - is the coefficient received after the summation of all the possible fermion pairs in the vacuum near the charge.  
The gravitational constant being considered similar to Coulomb constant for vacuum permittivity:
 
k=1/(4*π*ε_o ), that is ε_o =1/(4π*k), where k=9*10exp(9) is Coulomb constant,
The equation would be (mass is instead of charge and gravitational constant instead of Coulomb constant):
1/(4π*G)=[(K_w²-1)^3/2/K_w]*2m²/(3π*h*c)
where G is gravitational constant and m is the mass of the particle- gravitational antiparticle pair.
Using value of 32 for K_w- the constant calculated in [1] the value of mass is 1.84*10exp(-9) kg or 166 GeV
Assuming the evaluations are very approximate, the only close in energy particle is Higgs boson (125 GeV).
Thus it is possible to predict that during the Higgs boson production at CERN, from time to time the antigravitational Higgs boson will be generated (like in the case with antiparticles, it will have the same mass, but of the opposite sign). It may be easily distinguished because the decay path of it will include antigravitational particles instead of normal particles and antiparticles, which would move differently at decay. The Higgs boson and antigravitational Higgs boson will be born in pairs, of course, so the total energy would be 250 GeV, but this is still well below the possible energy of BAC, which is 14 TeV.
Being discovered, such antigravitational particle would allow to justify the quantum vacuum virtual particles approach to the gravitational constant value calculations (combining approaches of [1] and [2])  thus effectively unifying electricity and gravity on the basis of quantum vacuum properties.

References.
1. https://arxiv.org/abs/1302.6165
2. https://arxiv.org/abs/1405.5792
3.

Light matter attraction as a driving force for Galaxy rotation - the energy transformed from thermonuclear to mechanical

The dark matter modern approach to the explanation of galaxies rotation has one drawback - it is still considers stars as equivalent to rocks (planets). In reality stars have one distinct difference from planets (for planets the third Kepler Law explains all the motion perfectly)  - they are generating energy by themselves. If only a small fraction of that energy is transformed through any mechanism into the mechanical energy, that may easily explain any rotation curve of the galaxy without any new hypothesis about predominant non-observable matter. Let's consider the bright star with luminocity of 1260 Sun and total inertial mass of 5.4 Sun (Polaris star). The total energy release would be 5*10exp(+29) J/s and mass would be 1.1*10exp(31) kg. If only 1% of the energy released is somehow transformed into the mechanical energy, the star may reach the rotational speed of 230000 m/s (Sun surrounding) for only 1.8 million of years (estimation done from 1/2*mV^2 formula). This is smaller than life time of the star of such initial mass (10 millions of years).
Thus the difference between the star and planet is essentially inside the star. The idea of the strongly gravitating slow light [1,2], may not only explain the too fast rotation of the stars in the galaxy (the effective gravitational mass is higher compare to the inertial mass) but also the overall dynamic of the stars in the galaxy (origin of spiral arms) and  the difference between the elliptical and spiral galaxy (why the elliptical galaxy stopped rotating).
According to the hypothesis of [1], the stars has a lot of trapped photons inside. Not only the gamma quanta from the nuclear reaction but softer light like X-ray and visible light due to bremsstrahlung scattering of electron and ions inside the fully ionized plasma inside the star. Those photons are inside the environment with enormous value of effective refraction coefficient (inside the fully conductive media) and thus are moving really slow and gravitating very strongly (similar idea is expressed in [3]). The gravity-like behavior of slow photons is demonstrated in [4] experimentally (polaritons are exactly what is expected for photons inside the stars).
The photons inside the stars are gravitating according to general relativity, of course, they are not creating the mutually reciprocal force like the baryonic matter. The slow photons are attracted to the galaxy center (and much strongly if calculated per energy compare to baryonic matter) but not creating the additional distortion of time-space themselves (except for the equivalent inertial mass they have in vacuum, from E=m*c^2). Thus they create the additional force to the bright stars, which forces them toward the center of gravity (center of galaxy). This force moves the star to the new position and according to the momentum conservation law the star is accelerating (new equilibrium position closer to the center of rotation needs higher velocity). This mechanism effectively transforms the energy of the thermonuclear fusion into the mechanical energy necessary for the accelerated rotation. Thus the energy of the nuclear fusion is transformed into the rotation energy of the whole galaxy (the effect is smaller for light stars like Sun, but stars are created and dying continuously). In this situation the rotation of the galaxy is more like dynamo phenomena than static rotation of planets around the star.
That additional force might be expressed in the following formula:
F=K*E*M/(R*R)
The force is concentrated in the star, so for the outside space it will be the central force. The 1/(R*R) law follows from the attraction formula for light and from geometry of space-time (should be similar to Newtonian law in the weak gravitational limit). The force is proportional to the inertial mass of the object which attracts the star (or to the curvature created by the inertial mass in the weak gravitation limit of general relativity), since light is "attracted" due to the curvature of space-time (similar to the deviation of light near the star). But the force does not proportional to the inertial mass of the star which attracts, but rather to the total energy of trapped light inside E (and the coefficient K depends upon the type of star, upon the effective refraction coefficient inside, which makes the whole force non-universal). When the E of trapped light is zero the force is zero only the usual gravitation exist,
For the evaluation it is possible to assume that the value of F will depend upon the luminosity I of the star (it is an idea that the amount of light still trapped inside the star should correlate with the light emitted by star every second).
F=K*I*M/(R*R)
For evaluations it is possible to assume that the force from light matter should be at least equal to the gravitational force:
K*I*M/(R*R)~G*m*M/(R*R)
and then for the stars like Sun K=3.3*10exp(-7) m*s/kg
for bright stars like Polaris K=1.46*10exp(-9) m*s/kg
and taking the average (geometric one):
K~2*10exp(-8) m*s/kg
With this force the origin of spiral arms would be the higher velocity of bright stars compare to the rest of stars: the bright stars are short lived, but they are the main driving force for the rotation of galaxy - the additional force accelerates them very much like the rotation of the skater is accelerates when he or she pulls the leg in. This acceleration of rotation transfers to the rest of stars and the galaxy starts to rotate.
The gravitational force only is seemingly not enough to sustain the rotation: the elliptical galaxies are contracting radially, not rotating. Only young galaxies, full of new stars have enough energy to start rotation and hold it at the almost constant for all galaxies speed (the energy originates from the drain of stars in the black hole, very much like the rotation of water in the tub originates from the energy of the drained water). The comparison is not really quite well because the friction is much smaller, but it was found that the vortex in bathtub also need some threshold discharge rate [5] - if the discharge is too small, water drains pure radially.
It puts the elliptical galaxies as the final evolution stage of galaxy: it starts from protogalaxy, starts to rotate around the central black hole (spiral galaxy), slowly uses all of the necessary molecular clouds - no bright stars any more - and turns into the elliptical galaxy with huge black hole and aging low luminosity stars.


References.
1. https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
2. https://tipikin.blogspot.com/2019/09/accelerated-rotation-of-star-because-of.html
3. https://arxiv.org/abs/0710.0273
4. https://funsizephysics.com/gravity-for-photons/
5.T.Kawakubo Y.Tsuchiya M. Sugaya K.Matsumura  "Formation of a vortex around a sink: a kind of phase transition in a nonequilibrium open system" // Physics Letters A, Vol.68, No1, p.p.65-66, 1978

Accelerated rotation of stars in the galaxy

Accelerated rotation of the star because of the difference between the effective gravitational mass and real inertial mass.
For baryonic matter the gravitational mass is equal for the inertial mass (Einstein's postulate). For light the inertial mass is still zero but the effective gravitational mass may be assumed (the light deviates near the star). If the enormous amount of light is trapped inside the star, the overall effective gravitational mass of the star Mg may be larger than the effective inertial mass Mi. How it will influence the rotation of the star around the galaxy center?
From Newton mechanics:

m_i*v²/R=G*m_g*M/R²  and v=[(G*M/R)*(m_g/m_i)]^1/2

where G is gravitational constant, M is effective mass of the galaxy (for simplicity), v is the linear velocity of the star around center of galaxy, m_g is the effective gravitational mass of the star,  m_i is the inertial mass of the star, R is the radius of rotation. If due to the trapped light the effective gravitational mass is much larger compare to inertial mass, so the velocity of the rotation. In this case the dark matter is not necessary for the accelerated rotation of the stars in the galaxy  

Weak equivalence principle is not valid for stars - observations of mass-luminosity relation for visual binaries

Stars are special objects in the sense of the possible gravitational deviations: they have both barionic and non-barionic matter (like trapped and slowly advancing to the surface light) inside. While for barionic matter the weak equivalence principle was established by Kepler (planets orbiting around stars) it was never checked for stars.
The good example are binaries. There are many binary stars which are visible as double stars with resolved period and axis and ratio of inertial masses (through measurements of the velocities of stars). Many parameters of such stars are published in [1]
The usual formula applied to the stars from the third Kepler Law:

T²=4π²*a³/[G(m₁+m₂)]         (1)

Here T is the period of rotation of one star around the second one, a is semi-axis, m1 and m2 are masses of the stars (assuming gravitational mass is equal to inertial mass) and G is gravitational constant.
However, the light theoretically may have much higher gravitational pull compare to the inertial mass from E=mc*c relation (it is assumed that the inertial mass of light being emitted and reabsorbed inside star is still according to E=mc*c, as it was proved by Einstein himself) [2]. The presence of slow light may modify the gravitational pull, making it much stronger for the star which has more trapped light (and other non-barionic matter). While the exact amount of trapped light is difficult to calculate (not much is known about the light content of the interior of fully ionized plasma), it is obvious that this amount is correlated with luminosity of the star - the higher the luminosity, the higher the amount of trapped light and the higher the additional gravitational pull on the star (the higher the deviation between the gravitational and inertial mass).
In the derivation of the formula (1) the gravitational masses are always comes as a product [3]:

F=G*M1*M2/r²

Here M1 and M2 are gravitational masses. Assuming the added pull is proportional to luminosity which is proportional to mass (whether gravitational or inertial) [1], it is possible to assume:

F=G*K1*K2*m1*m2/r²

Here K1 and K2 are multiplicity coefficients, the value of K may be especially high to ultra-bright star. It is important that both coefficients for binaries are always a product.
The modified third Kepler Law:

T²=4π²*a³/[G*K1*K2*(m1+m2)]

Here m1 and m2 are inertial masses. When K1=K2=1, the third Kepler Law for barionic matter is obtained.
To determine the masses from the observation of binaries we need: T, a, and ratio of masses m1/m2=n. Since the ratio of masses is determined through the Doppler shift of spectra of stars, is a ratio of inertial masses. We have two equations for masses m1, m2:

G*K1*K2*(m1+m2)=4π²*a³/T²

m1/m2=n
Then:

m2=4π²*a³/[G*T²*K1*K2*(n+1)]
m1=4π²*a³*n/[G*T²*K1*K2*(n+1)]

Suppose we decided to determine the inertial masses from the visual binaries with two distinct masses m1>>m2. How it would influence the mass-luminosity correlation (like in [1])?
It is possible to show, that contrary to the case of valid third Kepler Law the slope of the dependence will be depended upon the ratio of masses!
 Lets  consider three cases:
1.Binary m1 and m1
2.Binary m2 and m2
3.Binary m1 and m2
In the first case the value of m1 is (because n=1)
m1=m1(old)/[K1*K1], here m1(old)=4π²*a³/[G*T²*2]
Here m1(old) is real inertial mass. K1 is large and the value of m1 is shifted strongly toward smaller mass compare to real inertial mass.
In the second case the value of m2 (n is equal to 1)
m2=m2(old)/[K2*K2]
If K2 is smaller than 1 (supposedly Sun has the value of K exactly one) the mass of smaller star will shifted strongly toward larger mass
In the third case the value of m1 is
m1=m1(old)/[K1*K2], m1(old)=m1(old)=4π²*a³*n/[G*T²*(n+1)]
Since both coefficients K1 and K2 are here, one is small and one is big, the shift compare to the real inertial mass is smaller
m2=m2(old)/[K1*K2]
This idea may be immediately checked. If the mass-luminosity curve is plotted using first only stars with close masses, it will be compressed because of K1*K1 and K2*K2 coefficients along the x-axis (the slope will be larger). If the same curve is plotted using the stars with different masses (preferably with large difference, but I used what we have in [1]) it will be much more spread. I manually chose approximately half of visual binaries (17 binaries or 34 stars) from Table 1A from [1] with close masses and obtained the relation between the luminosity and mass:
Absolute luminosity= -3.2119*ln(m)+5.1264
And for the rest of the binaries (21 binaries, 42 stars) - masses are different:
Absolute luminosity = -2.495*ln(m)+5.4042
The white dwarfs were excluded, like in [1].
The scattering in the second case is much larger (as expected, because the product of coefficients K1 and K2 is highly unpredictable), but they must give much smoother curve if the coefficients are the same - the shift is larger, but it is more predictable - obviously it is some smooth function of luminosity and can not jump from star to star).
Indeed as predicted the slope is larger beyond any error for the subset of close in masses stars compare to the far in masses stars.
Since the deviation from Newton law for the barionic matter of such large scale would be noticed long ago in our Solar system (some small deviation due to GR are not considered), the only possible explanation is that the weak equivalence principle does not hold for gravitation of stars (mixture of barionic and non-barionic matter), possibly due to mechanism outlined in [2].

References.
1.George E. McCluskey, Jr, Yoji Kondo "On the mass-luminosity relation" // Astrophysics and Space Science 17 (1972), p.p.134-149
http://articles.adsabs.harvard.edu//full/1972Ap%26SS..17..134M/0000137.000.html
2.D.S.Tipikin, publication on blog
https://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html
3.http://www.astro.caltech.edu/~george/ay20/Ay20-Lec4x.pdf

Stars are full of trapped light. May this fact help to explain dark matter presence?

"Light Matter" may help to explain dark matter absence, at least partially.
Light is bended by the gravity - this is very old phenomenon, once confirmed the general theory of relativity. The Einstein formula for the light bending is:
ϒ=4*G*M/(r*c²)
where ϒ is the angle of the deviation of the light near the star, M is the mass of star, G is gravitational constant, c is speed of light and r is the shortest distance between the light and star.

From this formula it follows that the light, being traveled near the star, influenced the star, too, transferring part of its pulse to star. While for passing light this is truly negligible, what about the light trapped inside the star itself? It is well known fact, that the gamma quantum generated during the fusion in the Suns core, will spend millions of years till it is emitted by the Sun. During all this time the quantum of the light will be subject of the gravitational pull of other stars (Galaxy in general to explain the additional force added to the usual gravity which may help to explain dark matter partially). This force will mean that some kind of gravitational mass equivalent is added to the star. According to the weak equivalence principle the amount of inertial mass of the star does not change at such process.
The evaluation of the importance of such additional force from the photons back onto the barionic matter may be done as follows:
For the formal consideration (just to have the formula) the photon is treated as having mass m. Then deviation of the light near the star would be:
V_p=a*t, a=F/m, F=G*m*M_s/(r²) → a=G*M_s/(r²)
here
V_p is the perpendicular component of the velocity of the photon of formal mass m, t is time of flight near the star, a is the formal acceleration of the photon of formal mass m, M_s 

is the mass of the star, G is gravitational constant, r is the effective distance between the star and the photon, t is the effective time of flight of the photon near the star. Knowing the values of the acceleration and time it would be possible to evaluate the perpendicular component of velocity:

V_p=G*M_s*t/(r²) Evaluation of the time of flight will lead to "classical" formula for the deviation angle:
t=2r/c and
ϒ=V_p/c=G*M_s*2r/(r²*c²)=2G*M_s/(r*c²) which is exactly 2 times smaller than the Einstein results, what confirmed the general theory of relativity.

The same formal approach may be used to evaluate the influence of the galactic pull onto the all the photons inside the star (multiplying later the result by 2 to account to general theory of relativity).
The photons generated inside the star during the fusion are not leaving it immediately but essentially trapped inside for millions of years. During all this time all the numerous trapped photons are generating the pull toward the center of galaxy, which may be estimated as follows:
Using the same formal approach the formal "force" onto the photon is:

F=G*m*M/(r²)

Here G is gravitational constant, M is the effective mass of the Galaxy, r is the distance between the photon and the Galaxy center, m is the formal "mass" of the photon (the idea of such approach is that since it allows to obtain Einstein formula with accuracy of factor 2, it will allow to evaluate this pull with the same accuracy - later final formula to be multiplied by 2).
The force on the photon toward the center of Galaxy:

F=ma, a=G*M/(r²), V_p=at=G*M*Δt/(r²)

Here F is the force onto the photon toward the center of Galaxy, a is the acceleration created by such force, Vp is the perpendicular component of the velocity the photon obtained during the time Δt of its stay inside the star.

What would be the change of pulse of the photon during such stay? It may be evaluated assuming the velocity of the photon equals to   c/(n)^1/2
where n is the effective refraction coefficient for the light in the star medium (since the interior of star is enormously dense and hot plasma, this value is not 1)
The change of pulse of photon is:
Δp=V_p*n*P/c
here Δp is the change of pulse of photon, P is the total pulse of photon, Vp is the obtained perpendicular component of the velocity, c/n
is the velocity of light inside the star. The obtained velocity Vp is considered very small compare to the initial velocity - despite million of years, the photon inside the star is moving as a photon only for small time periods - it is absorbed and re-emit almost instantly. Using the formula for Vp it is possible to obtain:
Δp=G*M*Δt*n*P/(r²*c)
where Δp is the full change of pulse during time period Δt, G is the gravitational constant, M is the mass of Galaxy, n is the effective refraction coefficient, P is the full pulse of the photon, r is the distance from the star to the Galaxy center, c is speed of light.
But Δp/Δt is the effective force (toward the center of the Galaxy) expressed through pulse of photon instead of time Δt. For one photon:
F=Δp/Δt=G*M*P*n/(r²*c) Here F is the pull onto the photon toward the center of the Galaxy, M is the effective mass of the Galaxy P is the pulse of the photon, n is the effective refraction coefficient, c is speed of light, G is the gravitational constant, r is the distance from the star to the center of Galaxy.
The pulse of photon is P=n*E/c for the refracted light (Minkowski formula [1]) and:
F=Δp/Δt=G*M*e*(n)²/(r²*c²)
Where e is the energy of one photon. For the total force exhibited by all the photons this force would be:F=Δp/Δt=G*M*E*(n)²/(r²*c²)
Where E is the total energy of the photons inside the star. Now it is possible to calculate the ratio of this force to the gravitational force exhibited by the star (as derived from weak equivalence principle E=mc*c). The gravitational force

F_g=G*M_s*M/(r²) where G is gravitational constant, Ms is the mass of star, M is the mass of Galaxy, r is the distance between the star and Galaxy. The ratio of those forces

is:
F/F_g=E*(n)²/(M_s*c²)
Adding multiple 2 from Einstein's formula:
F/F_g=2*E*(n)²/(M_s*c²) This value may be somehow estimated using the data for Sun. Mass of the Sun is

2*10³⁰ kg, energy release is 3.9*10²⁶ Watt and assuming photons are trapped inside for 10 millions years ( 3.15*10¹⁴ s) the ratio would be:

F/F_g=(n)²*1.4*10^-6

which is very small if n=1. However, the star matter is relative not investigated and the effective refraction coefficient may be very high (in metals, for example it is supposed to be infinity). Essentially the light inside the Sun may be traveling very slow. If in the highly conductive full ionized plasma value of n is 100, the added force may jump to 1.4 % and become noticable
Still there is no additional gravitational pull for the Sun, which lives for billion of years. The dark matter however usually associated with the presence of young stars in the sleeves of Galaxy. For the star with the big initial mass the life time may be just 10 millions of years. It means that such star will emit the equivalent of 10^-7 of its mass per year as radiation and if the photons are still trapped inside for 10 millions of years that means that the ratio of forces

now is 2*n²

^{That means that for the star of larger mass the pull toward the center of Galaxy, associated with the light matter may be many times larger than the gravitational pull from the ordinary matter. But this trapped light still makes contribution to inertial mass E=m*c*c (according to weak equivalence principle), which would  mean that it will be rotating faster compare to pure barionic mass body like planet. This may explain the dark matter, at least partially.}

 

 

In a broad sense this idea is in today track of unification of matter and wave behavior. In addition to being full with trapped for long time quanta (pure wave), inside the star the process of tunneling of baryonic particles takes place (during the fusion). However, during the tunneling the baryonic particle is pure wave (the energy is negative, what is inconsistent with particle). Thus inside the star more energy is in wave form and waves are attracted gravitationally differently, so the overall star may have larger than possible orbital speed without presence of dark matter. More experimentation with plasma in fusion reactors may be necessary to understand the behavior of stars.

References.
1. https://en.wikipedia.org/wiki/Abraham%E2%80%93Minkowski_controversy