Mnatsakanian's research in Theoretical Astrophysics relates to areas:

I. Generalized Theory of Gravity

II. Stellar Statistics and Dynamics

III. Radiation Transfer Theory

The Annotations and publications below are given for each area separately. Principal papers are linked to their full text.

Mamikon Mnatsakanian: I. GENERALIZED THEORY OF GRAVITY

Based on extensive observational facts, V. A. Ambartsumian developed his cosmogonical conception: the birth of stars and galaxies takes place in protostellar (such as stellar associations) and protogalactic (such as active galactic nuclei) formations which are supermassive and extremely compact. They can remain stable for time periods comparable with the galactic age, at least, for billions of years. Moreover, the birth processes happen through their expansions and explosions. These facts seriously contradict Einstein's Theory of Relativity according to which massive formations should rapidly collapse and turn into black holes. To fit the observations, Einstein's General Theory of Relativity should be modified, generalized, adjusted to extreme super-gravity conditions.

Einstein himself did not believe in black holes considering them as formal mathematical consequence of his equations, which needed to be fixed. They are caused by Schwartzshild's singularity in the (external) solution for a point-mass at a distance equal its gravitational radius, at which the escape velocity of a particle equals the speed of light. As for the internal solutions, inside the massive object, gravitational forces overcome the material pressure causing a collapse.

The hypothetical collapses and black holes represent the prevailing viewpoint in modern astrophysics, so it is imperative to have an alternative theoretical basis. A possible resolution of the contradiction between observations and theory lies in Dirac's famous hypothesis of variable gravitational constant k. In fact, we have no experimental knowledge about the gravitational constant in extreme super-gravity situations, such as the Sun being compressed to 10 km, or Earth to a walnut size. It is plausible that in such extreme situations layers of mass cause 'screening' effects which weaken the internal gravitaty and stabilize the supermassive objects.

We developed 'Generalized Theory of Gravity' based on variable gravitational 'constant' k, depending on the distribution of mass. The solutions of this theory contain NO singularities, and, as a result, any large mass can be stable, inside a small size, without collapsing. As the parameter of all gravitational theories we use the compactness, w=M/R (units: c =1, k(inf.)=1, mass ~10 Msolar, size ~14 km). Newton's theory holds for w<0.01, and Einstein's for w < 0.3. The models with w >0.5, we call gravitars, all have 'similar' characteristics: the mass increases as w to 40th power, radius is M/w. The qualitative results do not depend on the state of matter, and stable models exist for all w. For example, at w~0.3, a 'barion' model has a solar mass and several kilometers in size, as in Einstein's Theory. At w ~0.6, a galactic mass can be stable inside a few parsecs, which is a perfect match with Ambartsumian's estimate.

Gravitars have extremely large gravitational mass-defects and redshifts. The light from a gravitar is greatly bent by its own gravity, so a gravitar may appear very large and less compact. We suspect that quasars are examples of gravitars. Our analyses also show that gravitars are in unstable equilibrium and a disturbance (rotation or mass losses) can lead to their expansion, rather than collapse, also in agreement with Ambartsumian's conception.

Dirac's idea was developed into theory by Jordan and Heckmann (1947), but it violated the energy conservation law; and by Brans and Dicke (1960's), but it had a crucial misinterpretation in internal solutions uncovered in [4].

Note: Our Generalized Theory involves only the combination k/c-squared, so it can perfectly serve also as a theory with variable speed of light, c.

In many ways, it sheds light on the recent discovery of accelerating expansion of the universe ( 2011 Nobel Prize in Physics ).

Publications by Mamikon Mnatsakanian: I. Generalized Theory of Gravity (Twelve papers published on this theme, originally in Russian)

1. The Relativistic Generalized Theory of Gravitation. I. (Sahakian G. S.), Astrophysics, 4, 1968, pp 567-579, English pp 234-239

2. Generalized Relativistic Theory of Gravitation. II. Baryon Configurations. (Sahakian G.S.), Astrophysics, 5, 1969, pp 555-579, English pp 271-285

3. Polytropic Models in the Relativistic Generalized Theory of Gravitation, Astrophysics, 5, 1969, pp 645-649. English pp 332-334

4. On Salmona's Paper on Models of Static Configurations (Avakian, R. M.), Astrophysics, 5, 1969, pp 169-17,. English pp 85-86

5. Models of Gravitars. Questions of the Theory of Superdense Stellar Objects, Yerevan State University, Armenia, 1984, pp 185-195

6. Generalized Newtonian Theory of Gravitation (Sahakian, G.S.), Astrophysics, 3, 1967, pp 311-323, English pp 140-144

7. Configurations of Degenerate Gas Masses in the Generalized Theory of Gravity (Sahakian G.S), International Symposium "Gravity-V", Tbilisi, Georgian SSR, 1968, p 198

8. Polytropic Models by the Nonrelativistic generalized Theory of Gravity (Avakian, R. M.), Astrophysics, 4, 1968, pp 646-650, English pp 272-275

9. Stellar Configurations of Degenerate Electron Gas (Sahakian, G. S.), Soob. Byurakan Obs., 40, 1968, pp 98-107, English Abstract

10. Nutron Configurations in the Generalized Newtonian Theory of Gravity. (Sahakian, G. S.) Astrophysics, 4, 1968, pp 181-193, English pp 62-67

11. On an Approximate Analytic Solution of the Equations of Nonrelativistic Generalized Theory of Gravity, Docl. Acad. Sci. Armenian SSR, 49, 1969, pp 78-81

12. Models of Static Configurations in Generalized Theory of Gravity, Soviet Candidate Dissertation (~Ph.D.) in Physical-Mathematical Sciences, Manuscript 169 pages and Annotations, 16 pages, Yerevan, 1969

13. Gravitars: A New Look at the Universe, Gravity Research Foundation, 2007 (submitted in 1994)

Mamikon Mnatsakanian: II. STELLAR STATISTICS AND DYNAMICS

In 1935 V. Ambarsumian solved a problem (posed by Eddington) of reconstructing the distribution of space velocities of stars based on their observed radial velocities. He obtained a 3-dimensional ellipsoidal Maxwellian distribution, using hand calculations for ~500 stars.

In 1979 a Nobel Prize in Medicine was granted to the British engineer Hounsfield and American radiobiologist Cormak for the development of computer assisted tomography. They solved, 35 years later, the same mathematical problem with dramatic applications in CAT-scans.

In 1967, I essentially simplified Ambartsumian's solution: I was able to reduce the problem for arbitrary space density distribution to a series of actually elementary solutions for spherically symmetric distributions, in fact, as many of them as the number of points in space one wants to reconstruct. This separation allows one to reconstruct only a selected 'target'-part of the object, without unnecessary computer data processing, time and memory used, for the rest of the object.

I also created a statistical enrichment method that allows me to avoid some data fluctuations, thus achieving higher accuracy (resolution). This is crucial because such inverse problems are by their nature mathematically unstable: small errors in initial data cause big errors in the solution. Numerical tests on very limited statistical data showed a success of the method [1].

In 1968 Ambartsumian asked me to try my methods to reconstucting the space distribution of flare stars in Pleiades based on data collected by Mirzoyan. The results were surprising [2-4]: there was a 'cavity' meaning no flare stars were observed in the central region of the Pleiades, in one-third of its size, although there are many flare stars projected on that region in the sky. This proves Ambarsumian's idea that flare activity is an early, but not the first, stage of a newborn star in stellar aggregates. It takes time for newborn stars to enter the flare stage, during which these stars, born via explosion, move away from the birth-center. The flare activity grows towards the end of that stage, thus showing the central "cavity", and consequently the expansion in Pleiades.

I also applied my methods to Ambartsumian's stellar associations, which are among his great discoveries. My goal was to reconstruct the space velocity distribution of stars depending on their distance from the center in space. The data used are the projections of the stars, as seen on the sky, and their radial velocities. The results [5-8] clearly demonstrate that the average space velocity of the stars increases linearly with their average space distance from the 'birth-center' (similar to Hubble's Law). This fact is in perfect agreement with an explosive nature of star-birth processes in stellar associations: the faster they move at the moment of explosion, the further they get from the center of explosion (forces of gravity in such systems are negligible). These results allowed me also to evaluate the ages of the associations, which were again in perfect agreement with Ambartsumian's estimates.

I've also solved a double-tomography problem such that the distribution of stars' any characteristics can be reconstructed in space together with the positions and velocities. Later I developed another statistical method [9] for predicting the flare activity in time, to the future or retrospectively back, based on Ambartsumian's challenging idea of a possible evaluation of the total number of flare stars in the aggregates. We combined it with the 'enrichment' method and reconstructed the flare-activity frequency as a function of distance in space. The results [10-12] show no flare-activity, a cavity, around the center in the Pleiades, with estimated total 750 flare stars. It also proves that predictions are impossible into more than the already observed past time.

In 1977 Ambartsumian asked me to write a review on pulsars for 'Astrophysics' magazine. I did [12], and in it I also created a new statistical method for reconstructing the distribution of the initial 'at-birth' pulsation periods of the pulsars, based on their currently known pulsing periods.

It showed that pulsars are not born with initial zero-period pulsation as it was commonly accepted but with two uniform distributions, in two distinct intervals of the period, and that there are two types of pulsars essentially different by their nature according to these two intervals. This clarification allowed me to reduce (by an order of magnitude) the characteristic ages of the pulsars and to remove the existing contradiction between them and the kinematical ages of pulsars. These results are important especially for theoreticians investigating possible models and evolution of pulsars.

Publications by Mamikon Mnatsakanian: II. Stellar Statistics and Dynamics. Sixteen papers published on this theme originally in Russian

1. On the Question of Finding the Distribution of Stars in Poor Globular Clusters. Docl. Acad. Sci. Armenian SSR, 49, 1969, pp 33-37

2. Unusual Distribution of Flare Stars in Pleiades. (Mirzoyan, L.V.). Comission 27 IAU Inform. Bulletin of Variable Stars, No. 528, 1971. English

3. On the Space Distribution of Flare Stars in Pleiades. (Mirzoyan, L.V.). Comission 27 IAU Inf. Bulletin of Variable Stars, No. 604, 1971. English

4. Space Distribution of Flare Stars in the Pleiades Aggregate. (Mirzoyan L.V., Oganian, G.B.). Conf. 'Flare Stars, Fuors, Herbig-Haro Objects', Yerevan, 1980, pp 113-121, English Abstract

5. On the Distribution of Space Velocities of OB Stars. (Mirzoyan, L. V.). Sym 38, The Spiral Structure of Our Galaxy IAU, 56, 1970, pp 295-296, English

6. A Study of Velocity Distribution of O-B Stars in Associations. (Mirzoyan, L. V.). Asrophysics, 6, 1970, pp 411-429. English pp 221-231

7. Dynamic Stability of the khi and h Persei Association. (Mirzoyan, L.V.). Astrophysics, 6, 1970, pp 337-340. English pp 175-176

8. Distribution of Space Velocities in the Associations Cepheus OB2 and OB3. (Akhundova, G.V, Ivanova, N.L.). Soob. Byrakan Obs., 49, 1976, pp 71-74, English Abstract

9. On the Distribution of the Frequency of Stellar Flares in Stellar Aggregates. Astrophysics, 24, 1986, pp 621-623, English Abstract

10. Prediction of Flare Activity of Stellar Aggregates. I. Theoretical Part. (Mirzoyan, A. L.). Astrophysics, 29, 1988, pp. 32-43. English pp 423-430

11. A Prediction of Flare Activity of Stellar Aggregates. (Mirzoyan, A. L.). Flare Stars in Star Clusters/Assoc., IAU, Netherlands, 1990, pp 113-116, English

12. Pulsars. Survey of Observational Data. Astrophysics, 15, 1979, pp. 515-532, English pp 342-352

13. On the Problem of Reconstruction of Space Distributions. Soob. Byurakan Obs., 57, 1985, p 45, English Abstract

14. On the Determination of the Star Distributions in Stellar Clusters. Soob. Byurakan Obs., 49, 1969, pp 81-86, English Abstract

15. Dynamical Evolution and Instability of the Trapezium Type Systems. (Mirzoyan, L.V.). Astrophysics, 11, 1975, pp. 551-553. English pp 367-368

16. On Two Possible Groups of Flare Stars in Pleiades. (Mirzoyan, A.L.). IAU Sym. No. 137, 1990, pp 77-80, English

17. On the Analytical Representation of the Photomaterials Characteristic Curve (Sarkissian, R.A., Karapetian, M.S.) Astron. Tsirculyar, 1544, May 1990, 35

Mamikon Mnatsakanian: III. RADIATION TRANSFER THEORY

V. Ambartsumian is the father of Soviet Theoretical Astrophysics, whose main subject is 'Radiation Transfer Theory' (RTT). It is used to analyze the properties of planetary and stellar atmospheres based on the transformed information carried to us through light radiation.

In 1941, Ambartsumian introduced his 'principle of invariance' and used it to solve some basic theoretical problems. Later it was deeply explored by Sobolev, Ivanov, and others, at Leningrad University, USSR, and Chandrasekhar, Bellman, Kalaba, and others in the USA.

In 1972 I solved the same problems by a simpler method, reducing them to linear instead of the classical nonlinear integral equations [1-3]. Thus, for problems in finite thickness layers, instead of principle of invariance, I introduced a reduction method - reducing them' to a particular, much simpler and solvable even analytically, case for a semi-infinite layer. For the latter case only, I modified Ambartsumian's principle into a general 'apparatus' of invariance [5]. The reduction method can also be applied to solve similar pure mathematical problems [4].

My method is extremely efficient both for numerical calculations and for analytic solutions of very high accuracy [6-10]. With hand calculations, I obtained Chandrasekhar's numeric computer solutions published in several volumes in Ap. J. Suppl, with three digits accuracy which fully suffices for practical applications considering that the problems in question are idealized compared to the real ones. In a very special case, Yamamoto's puzzling intuitive solution follows.

My methods were successfully applied furter to solve both numerically and analytically the problems with an anisotropic scattering [9, 21] using Chandrasekhar's idea of pseudo-indicatrix and Sobolev's transformations, as well as my simple geometric-probabilistic interpretation of pseudo-indicatrix. They were also extended to problems with non-monochromatic scatterings [10-12], in particular, with complete frequency redistribition law of scattering (for Doppler, Lorenz, etc., profiles).

In 1978 I have also solved a non-linear transfer problem [5]. Soon, I was invited to 'Joint Institute of Nuclear Research' in Dubna, because I actually approached a problematic issue in Quantum Field Theory in an elementary manner, with simple geometric considerations, The solution is mathematically equivalent to important Gell-Mann and Low equation in Quantum Electrodynamics (QED). My approach established analogies between Semi-Groups intoduced in [5,13] in nonlinear RTT and the Renormalization Group in QED, in the frames of Shirkov's Functional Self-Similarity.

In a series of papers [13-17], I established both formal and physical parallels between Ambartsumian's invariance principle presented in a form of diagrams for elementary light scattering acts, and Feynman's famous diagrams in QED, 'Milne's solution' and 'naked charge' in QED, the 'critical thickness' and 'ghost pole', 'infrared catastrophee' the 'semi-infinite non-linear solution' and the 'asymptotic freedom', and more. These are one-to-one analogies, which allow one to use the solutions in nonlinear RTT to draw certain conclusions in the corresponding counterpart problems of QED and other sciences.

In 1981, I organized International Symposium 'Principle Invariance and its Applications', at Byurakan Observatory. Was editor of its Proceedings. My work on RTT was nominated in 1985 to Soviet State Prize by Marchuk, the President of the USSR Academy of Sciences. It was the topic of my Doctoral Dissertation [21]. In 1984-88, at Ambartsumian's suggestion, I lectured on this work at Yerevan State University, Armenia.

Publications by Mamikon Mnatsakanian: III. Radiation Transfer Theory. Twenty two papers are published on this theme, originally in Russian.

1. On the Solution of One-Dimentional Transport Problem, Soob. Byurakan Obs., 46, 1975, pp 93-100, English Abstract

2. On the Reduction of Radiative Transfer Problem in a Finite Layer to the Problem for a Half Space, Docl. Acad. Sci. USSR , 225, No. 5, 1975, pp 1049-1052, English pp 833-835

3. On the Solution of the Light Diffusion Problem in Optically Finite Shell (Danielian, E. Kh.). Soob. Byurakan Obs., 46, 1975, pp 101-114, English Abstract

4. On the Linear Problems of Transfer (Yengibarian, N.B.), Docl. Acad. Sci. USSR, Math., 217, No.3, 1974, pp 533-535

5. On the Solution of Radiative Transfer Problems in Semi-Infinite Media, Soob. Byurakan. Obs., 50, 1978, pp 59-78, English Abstract

6. The Quasiasymptotic Solutions of the Radiative Transfer Problem in an Optically Finite Shell. I. Conservative Scattering. Astrophysics, 11, 1975, 659-678, English pp 434-448

7. The Quasiasymptotic Solutions of the Radiative Transfer Problem in an Optically Finite Shell. II. Non-Conservative Scattering. Astrophysics, 12, 1976, 451-473, English pp 295-311

8. Analytic Solutions of High Accuracy to the Problem of Monochromatic Scattering of Light in a Plane Layer. Astrophysics, 16, No.3, 1980, pp 513-533, English pp 271-285

9. On the Theory of Anisotropic Scattering in a Plane Layer. High-Accuracy Analytic Solutions. Int. Sym. 1981 'Principle Invariance and its Applications', Eds. Mnatsakanian, Pikichian Yerevan, Acad. Sci. Armenian SSR, 1988, pp 445-456, English Abstract

10. Solution of Radiative Transfer Problem in a Plane Layer for the Model of Complete Frequency Redistribution. I. One-Dimensional Medium. (Gabrielian, R.G., Mkrtchian, A.R., Kotandjian, Kh.V.) Astrophysics, 28, 1988, pp 193-204, English pp 112-119

11. Solution of Radiative Transfer Problem in a Plane Layer for the Model of Complete Frequency Redistribution. II. Three Dimensional Medium. (Gabrielian, R.G., Mkrtchian, A.R., Kotandjian, Kh.V.) Astrophysics, 28, 1988, pp 443-454, English pp 262-268

12. Nearly Exact Analytical Solutions of the Problem of Radiation Transfer in a Plane Layer for the Model of Complete Frequency Redistribution. (Gabrielian, R. G., Mkrtchian, A. R., Kotandjian, Kh.V.). Izv. Ac. Sci. Arm., 22, No.4, 1987, pp 191-197, English Abstract

13. Non-linear Tranfer Problems and the Renormalization Group. Docl. Acad. Sci. USSR, 262, No.4, 1982, pp 856-860, English pp 262-856

14. Renorm-Group Analogies in Astrophysics. Int. Conf. 'Renormalization Group-86', Dubna, USSR, 26-29 August 1986, World Sci. Publ., pp. 437-465, in English

15. On the Solution of a Non-Linear Reflection Problem. (Melikian, A.O.). Soviet Conf. Young Astrophys., Yerevan, Acad. Sci. Arm, 1979, p. 22

16. On Analogies Between the Problems of Non-Linear Transfer Theory and the Theory of Interacting Quantized Fields. Int. Sym. Modern Problems of Quantum Field Theory, Alushta, 1981, Uspekhi Phys. Sci., 136, No.3, 1982, pp 542-543

17. Non-Linear Tranfer Problems and the Problems of the Theory of Quantized Fields. Int. Sym. 1981 'Principle Invariance and its Applications', Eds. Mnatsakanian, M. A., Pikichian, O.V., Yerevan, Acad. Sci. Armenian SSR, 1988, pp 445-456, English Abstract

18. On the Problem of Random Walk on Lattice. Int. Sym. 1981 'Principle of Invariance and its Applications', Eds. Mnatsakanian M. A., Pikichian, O. V., Yerevan, 1988, pp 445-456, English Abstract

19. On Some Representations of the Source Function. Soob. Byurakan Obs., 61, 1975, pp 113-116, English Abstract

20. About One Peculiarity of the Solution of Conservative Anisotropic Scattering Problems. Astrophysics, 17, 1981, pp 179-183, English Abstract

21. New Apparatus of Transfer Theory in a Plane Layer. Soviet Doctoral Dissertation in Theoretical and Mathematical Physics/Astrophysics; Manuscript, Yerevan, 1983, 320 pages; Annotations, Byurakan, 1984, 32 pages