ARTICLE 11 The General Theory of Relativity M Sc thesis :guidance Dr.K.L.Narayana

The General Theory of Relativity dissertation by Mr. Bote S R has been submitted in the year 1983 under the guidance of Dr.K.L.Narayana M.Inst.P (London) at the Department of Physics,Shivaji University, Kolhapur.We are grateful that the Vice Principal Shri Suru who has returned us back the copy of the dissertation. It has elaborated on Non symmetric Schwarschild fields, Special Metrics, Unified field theory of Einstein( Physical Review papers by Vaidhya and Krori et el have been worked out), skew symmetric metrics, and on Massive neutrino exact field solutions of Einstein-Dirac-Maxwell equations. Bote has acknowledged that Dr.K.L.Narayana had a unique way of simplifying the mathematics and has expressed gratitude for the guidance given.

This wok is actually a continuation of the earlier dissertation submitted by Mr.Anure under the guidance of Dr.K.L.Narayana on 12th April 1976 for the M.Sc degree. The problem of variations of all masses of the universe due to the gravitational influences as discussed by S. Malin in 1974 was worked out and an attempt has been made to see the possibility of even the fundamental charge variation!!. In this year we had the good fortune of Prof.McCrea's( he spoke on Angular Momentum of the Planetary system and of the origin of Moon) visit to our Department of Physics and as well to the Ind.Sci.Cong.

ARTICLE 8 : 70th B'Day volume 2009-2010 (KLN)

trusciencetrutechnology@blogspot.com
70th B’Day Volume 2009-2010 Dated 23rd October 2009.

THE SCEINCE AWARENESS ACTIVITY AT MVD HIGH SCHOOL,
Dandu Bazzar, Maharanipeta.P.O, Visakhapatnam -530002 By
Srimathi Diwakarla Surya Kumari,
Head Mistress, 50-23-2/1, TPT Colony Park, LIGF27, Visakhapatnam-530013

At our High School an activity of the Dandu Baazar Science Club was held to promote the Science awareness among the downtrodden children by way of initiating the children to write on any subject of their choice on the topic

“THE RECENT RESEARCH INVESTIGATION THAT I LIKED MOST”. An effort by the PS teacher, Sri D. Ramprasad explained vividly to the 10th Standard students about the aim of the competition in science writing and its usefulness to develop awareness of the recent developments. This has made them to submit big display-board charts with accounts of astoundingly different researches, the scientific findings and the formulations.
The competition was announced by the PET teacher Srimathi Kollabathula Thabitha on the Independence Public High School function on the 15th August 2009. Presiding the function Sri Rath, English Language teacher of the School, has said the awards would be given to the best, in memory of Late Prof Dr. K R Rao D.Sc. (Madras) D.Sc. (London) and Mrs. K. Peramma, the parents of the Chief Guest of the function.
All the teachers of the School and the administrative staff were very happy to see that their High School has conducted a Science Competition for their wards.

FIRST PRIZE has been awarded to Budathala Pratibha of 10th standarad.

The SECOND PRIZE won by Palla Leelavathi

The Antisymmetric Universe,its self-interaction,Hidden Spectroscopy & Information Technology

trusciencetrutechnology@blogspot.com Vol.2009,N0.10,Dated:11-10-2009
Time: 9hr 10min 11secs
THE ANTISYMMETRIC UNIVERSE, ITS SELF-INTERACTION, HIDDEN SPECTROSCOPY AND THE INFORMATION TECHNOLOGY
By
Prof. Dr. Kotcherlakota Lakshminarayana,
(Retd. Prof. of Physics, SU), 17-11-10, Narasimha Ashram, Official Colony, Maharanipeta. P. O, Visakhapatanm-530002, India.
Email ID: kotcherlakota_l_n@hotmail.com
Mobile: 9491902867
ABSTRACT
The General Theory of Relativity of the antisymmetric universe has been investigated with four parameters and a set of six metric tensor components. The set of 16 connection 1-forms and the 64 covariant connection coefficients of the new theory and the formalism are tabulated. The possible self-interaction of its metric components has been formulated. The universe has also been considered endowed with the two types of fine-structure constants viz. the electric type and the other magnetic type. The self-interaction refers firstly to normal and dual like terms of the metric components, akin to electromagnetic tensors and another individual Vierergruppe type of terms. These terms are just the manifestations of the antisymmetric universe metric tensor components themselves. This is the significant feature of my formulation. The interaction terms sum to the basic antisymmetric universe Riemann Tensor components. The matrix display of the Riemann Tensor components led easily for investigations on the self-interactions of the antisymmetric universe gifted with the hidden spectroscopy. Spectral eigenvectors and eigenvalues of the self-interaction of the antisymmetric universe, in the said several cases have been obtained and schematically illustrated. The idea of information technology involving the microscopic fields and the concomitant variables to carry the information around the universe is a new finding.
Subject category: Spectroscopy, Information technology, Astrophysics, Cosmology, Relativity, Mathematical Physics, Applied Physics, Differential Geometry.
Keywords: antisymmetric universe, covariant connections, fine-structure constants, spectral values, Electromagnetic like fields, asymmetric variables, hidden spectroscopy, information technology cosmos, electric-like, magnetic-like.
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trusciencetrutechnology@blogspot.com Vol.2009,N0.10,Dated:11-10-2009
Time: 9hr10min11secs
THE ANTISYMMETRIC UNIVERSE, ITS SELF-INTERACTION, HIDDEN SPECTROSCOPY AND THE INFORMATION TECHNOLOGY
By
Prof. Dr. Kotcherlakota Lakshminarayana,
(Retd. Prof. of Physics, SU), 17-11-10, Narasimha Ashram, Official Colony, Maharanipeta. P. O, Visakhapatanm-530002, India.
Email ID: kotcherlakota_l_n@hotmail.com
Mobile: 9491902867

INTRODUCTION
An asymmetric expression was first given by Minkowski for the energy-Momentum Tensor in the phenomenological electrodynamics. It led to very peculiar results which are not in contradiction with experiment. One peculiarity is that the torques derived using this expression cannot be compensated by change in the Angular momentum. Another type of asymmetry that attracted many a General Relativity specialists is the left-right asymmetry. Generally speaking the theory of General Relativity is left-right symmetric. But people argue that the nature itself is left-right asymmetric and hence it may not be bad to consider theories that incorporate the left-right asymmetry. The Ashtekar new variables are also left-right asymmetric, which have been quite readily adopted as a powerful tool in General Relativity. Penrose[1] dealing with the formalism of Twistors stated that for spin 2 the right- and left-handed twistor wave functions posses the respective homogeneities -6 and +2.
Pseudotensors like Г ^l_ik that are asymmetric govern the parallel displacement of vectors. Einstein [2] considered both the unsymmetrical Г ^l_ik and the unsymmetrical metric components g _ik to develop an Unified Theory of gravitation and Electromagnetism. The last version of geometry Einstein investigated was one which adopted torsion. Elie Cartan [3] was the first to give the concept of torsion in parallel transport of segments of small segments along each other. The resulting gaps at the ends of parallel transport of small segments of distances are determined by the skew-symmetric part of the connection coefficients. The nonsymmetric metric tensor he used was a sum of a symmetric metric tensor that would account for the distances and the other a skew-symmetric metric tensor that does not affect distances. The relation between the metric and connection coefficients was set up by him it led to nonsymmetric connection coefficients that involved the torsion. Einstein studied several geometries with the nonsymmetric metrics. R. Finkelstein used the torsion tensors with the matter possessing several types of geometric charges. He related these to the fields of mesons etc.
J. A. Schouten [4] gave a differential geometry that required the parallel transport of covariant and contravariant tensors to have different set of connection coefficients. He further showed the 27 types of differential geometries are characterized by three and only three tensors of rank three. The Riemannian geometry is the special case for which these three tensors vanish.
Another aspect of gravitation is the action-at-a-distance and the retarded and advanced effects were equivalent. Wheeler and Feynman [5] have said that the introduction of an absolute absorber in the future gives a correct account of the rest of matter in the universe which eliminates the possibility of all advanced interactions and retains only the retarded interactions in accordance with the observations of the real world in which the cause precedes effect and not vice versa. Of course, this approach of direct electromagnetic interaction contains questionable features with regard to physics of preferred direction of time i.e. the time arrow. The arrow of time and several definitions of it from thermodynamic, statistical etc. considerations have tackled the problem in their own perspective. It is well known that time symmetric Maxwell’s equations produce asymmetric results involving retarded but not advanced potentials. So fields carry information into the future but into the past, thus the time asymmetry originates most probably due to the boundary conditions adopted. Gold [6] was of the opinion that it arose in the fact that universe is expanding but not contracting. The classical theory of electrodynamics’ absorber [5] asserts that the radiative reaction on the accelerated charge arises from induced motion of other charges in the universe. Lorentz [7] has originally postulated that the radiative reaction and the concomitant loss of energy from an accelerated electron arise from the action of electron on itself. Self-action theory of electron given by Lorentz one part of an accelerated electron is influenced by the retarded potential due to the other part of electron. This indeed is the case that Maxwell time symmetry equations also allow the time reversal meaning thereby that a part of the accelerated electron can also be influenced by the advanced potential of motion of another part. Whether the advanced or the retarded radiation is emitted depends on the receipt of information from the future or the past respectively. Several models devised are based on the criteria of prohibition of information propagation into the past and such information is carried by the fields by means of retarded potential.
Some interesting properties of the full curvature tensor R _ijkm and their bearing on the behaviour of the physical fields which are not of gravitational variety was emphasized in a mathematical presentation by Lanczos [8]. In the case of four dimensions, he gave a new tensor B _ijkm involving A_ik + α_ik and G _jm= ½ (g_jm + γ_jm ) where γ_jm is an antisymmetric tensor. The α_ik is as well an antisymmetric tensor. He conceived the idea that α_ik is reminiscent of antisymmetric part of R_ik with which Einstein operated in his Unified Theory formulations. But A_ik has 10 components, the α_ik has six components and γ_jm also has six components, thus totalling about 22 components instead of just the usual 20 components of the full curvature tensor. Hence he suggested two constraint equations which, by no means are physically reasonable. He gave the equation R_ik = λ g_ik + 2 α_i ^μ α _kμ putting A_ik = λ/6 g_ik and α_ik = γ_ik . Interesting for my present formulation, is to note that Lanczos sought the α_ik have an analogy with Electromagnetic Tensor components. More over the choice made by him of λ = λ ₀ – ½ α^kμ α_kμ gives a cosmological fluid combined with Maxwell Electromagnetic field.
For the purpose of philosophy behind my research, it is to be noted that in the world of physics, the gravitational field is made up of self-interacting gravitons, which also interact with every other particle in the preferred universe.
Grand unification ideas of supersymmetry and supergravity involves the various fields of strong, weak, electroweak etc interaction are carried by “gauge entities” with respect to groups of transformations. At microscopic level i.e. scales of the order less than the Planck’s length and time intervals shorter than 10E-43 seconds, the metric tensor components and the Christoffel symbols and other geometric values would have limitations of interpretation.
The method of analysis of the General Theory of Relativity equations received imputes by the use of Cartans’ differential forms and the differential geometric approach. Misner, Thorn and Wheeler [9] specify nicely the additional armaments of (1) The concept of a vector-valued (or tensor-valued) exterior differential form; and (2) an associated generalization of the exterior derivative. The Differential forms are completely antisymmetric tensors. Cartan [3] has successfully packaged the 21 components of Riemannian Curvature tensor into just six curvature 2-forms.
The aim of the present research is to obtain The General Theory of Relativity results of a possible antisymmetric universe that is endowed with characteristic self-interactions. The section I gives The Cartan’s differential geometric method of analysis of the General Theory of Relativity Tensors and their components [9]. The section II gives certain formulae and the present theory equations derived which are very useful to solve the General theory of Relativity Matrix display of the projected Riemann Tensor components. In section III the self-interaction results and their physical significance is presented in terms of hidden spectroscopy. Section IV summarises the results obtained, new findings and the conclusions with suggestions for future research trends.
SECTION I: CONNECTION COMPUTATION
A bivector is known to be simple or decomposable if it can be expressed as a wedge product provided it satisfies a necessary and sufficient condition. The idea of purely electric or magnetic components of Electromagnetic Tensor F _αβ obey the conditions F ^αβ F _αβ <0>αβ F _αβ >0 (space-like) respectively. The general 2-form of an Electromagnetic Tensor is written as a superposition of wedge products with a factor ½. The dual form has also about six wedge products to define it. The honey-comb or the egg crate structure of electromagnetic tensor has been fully detailed by MTW [10].
The asymmetric metric form adopted by me has four wedge products. The asymmetric metric has the metric components g₁₂, g₁₃, g₁₄, g₂₃, g₂₄ and g₃₄. Parameter representation has been used by the choice of e ^a+b , e ^a+c , e ^a+p , e ^b+c e ^b+p and e ^c+p respectively. Here a, b, c, and p may be functions of the three space variables x, y, z, and the time variable t. The Cartan orthonormal frame ω ^μ is defined by the set of basis vectors that involve specifically the four metric components. The tangent vectors ω _μ dual to the 1-forms ω ^μ using the inverse set of the four metric components of the antisymmetric universe metric tensor.
The structure constants of the present formulation have been obtained by the commutation relations of the chosen basis vectors to describe the antisymmetric universe. These constants are also equivalently given by the Cartan first structure equation for the basis 1-forms.
SECTION II: CARTANS’ DIFFERENTIAL GEOMETRIC METHOD
The Cartans’ differential geometric method is a very powerful tool, to investigate the problems in the subject of Cosmology and the theory of General Relativity [9]. Misner, Thorn and Wheeler [10] have demonstrated for the computation of curvature for a pulsating star and also gave the Schwarzschild curvature forms.
I have obtained about 16 connection 1-forms that characterize the antisymmetric universe. In Table 2 the list of the sixteen connection 1-forms is given.
[Refer Table 2 for a list of 16 connection 1-forms of the present formulation]



The anholonomic system of analysis of the antisymmetric universe allowed me to compute the “covariant connection coefficients” numbering about 64. These are useful to define geodesics, covariant derivatives and parallel transport. I have retained the rule of raising or lowering a tensor index by the use of an appropriate metric tensor component.
The “covariant connection coefficients” have been all tabulated in Table1.1 through to Table1.8, which may be referred to obtain the details of their dependence on the spatial and temporal coordinates.

An immediate use of these “covariant connection coefficients” has been made to understand the results of a geodesic equation.
d ² x ^α / d λ + Г ^α _μγ d x ^μ / d λ . d x ^γ / d λ = 0
where λ is the uniformly ticking affine parameter, possibly a multiple of the particles proper time τ. Thus the set of sixty four covariant connection coefficients serve to describe how fast to turn the components of a vector to retain that vector as a constant. Some relations of the type
a_x e ^p= p _t e ^a and dx² + dx ³ = e ^a d x ¹ etc . , could be surmised.
Next the curvature 2-forms are defined, as usual, by the expression
Ω^μ_ν = d ( ω^μ_ν ) + ω^μ_α ^ ω^α _ν
The proper matrix display of the Riemann Tensor components could be easily obtained. While doing so I have specialized for a projection the 16 components corresponding to only the variables (x, t). Also I have chosen for simplicity without loss of any generality, values of the parameters as follows
a_x =-1/3 ; p _t =-1/3; a=1; p=1 and b = c = 0 also I have set a_y = a_z =0
SECTION III: HIDDEN SPECTROSCOPY AND INFORMATION TECHNOLOGY
The matrix display of the Riemann Tensor components led easily for investigations on the self-interactions of the antisymmetric universe gifted with the hidden spectroscopy. The other interaction terms could easily be incorporated to sum up with the basic matrix (designated as A and eigenvalues listed as lamA) display of the Riemann Tensor components, to obtain the modified or the new eigenvalues and the new eigenvectors.

Table3 explicitly presents the basic matrix display of the sixteen Riemann Tensor components in terms of the geometric entities a_x, p_t , a and p. Also the Table3 at the end gives the dual matrix of self-interaction of the proposed antisymmetric universe and from it one may easily surmise my model approach to have the magnetic –like and electric-like metric components of the said universe. The associated fine-structure constants are taken in the computation to get eigenvalues and the eigenvectors of the normal modes of oscillations. Some of these are found to be complex.
I have considered the interactions due to normal, dual like and the two types of Vierergruppe-like entities in terms of the metric tensor components g_ik themselves. Here I have made the choice of the normal (lamcnor) and dual tensor components (lamcdual) akin to the usual Electromagnetic Tensor. Specifically the sets (g₁₂, g₁₃, g₁₄) and (g₂₃, g₂₄, g₃₄) are found to be akin with Electromagnetic tensor physical entities and my present model and its formulation, has associated these entities with their respective fine-structure constants. This afforded a self-interacting antisymmetric universe, endowed with a hidden spectroscopy and led to the determination of its normal modes of oscillations and especially the spectral characteristics. Only for certain physical reasonability and in the light of well known quantum conditions on the electric and magnetic monopole charges I have reduced the fine-structure constant of magnetic-like terms by a factor of four. These fine-structure constants in reality refer to microscale physics.
Unlike this approach the Vierergruppe terms present a possibility of the introduction of diagonal interaction terms that was found to enhance the eigenvalues drastically. An antisymmetric universe of this kind offers a tremendous insight of the Information Technology features. The Vierergruppe has only the unit entity (diagonal) and three other entities satisfying its group multiplication table. In turn I have used the three magnetic-like and the three electric-like metric components to set up the total matrix of Riemann Tensor components summed with the interaction terms. Alternately, the two matrices thus obtained (once with the choice of magnetic-like terms of interactions and the other with electric-like terms of interactions) have both been computed to yield the eigenvalues and their corresponding eigenvectors (lamcvgr and lamcvgr1). The four different choices of the self-interaction terms adopted in computing eigenvalues and eigenvectors of the total matrix of the Riemann Tensor components (summed with the interaction terms) are illustrated in the Fig2 which presents the diagrams depicting the sets of four eigenvalues.

Note that the Fig2 actually displays only three eigenvalues since the complex conjugate eigenvalues* have been reduced to one absolute eigenvalues. In case of lamA (i.e. basic matrix) eigenvalues and the lamcvgr1 only one eigenvalues seem to be significant.

SECTION IV: RESULTS, SUMMARY AND IMPORTANT CONCLUSIONS:

The structure constants of the present formulation have been obtained by the commutation relations of the chosen basis vectors to describe the antisymmetric universe. These constants are also equivalently given by the Cartan first structure equation for the basis 1-forms. The set of 16 connection 1-forms and the 64 covariant connection coefficients of the new theory and the formalism are tabulated. These are found useful to define geodesics, covariant derivatives and parallel transport. The Differential geometric approach has been successfully implemented to investigate the antisymmetric universe endowed with self-interaction terms.
I have made the choice of the normal and dual tensor components akin to the usual Electromagnetic Tensor. Specifically the sets (g₁₂, g₁₃, g₁₄) and (g₂₃, g₂₄, g₃₄) are found to be akin with Electromagnetic tensor physical entities and my present model and its formulation, has associated these entities with their respective fine-structure constants. This afforded a self-interacting antisymmetric universe, endowed with a hidden spectroscopy. Only for certain physical reasonability and in the light of well known quantum conditions on the electric and magnetic monopole charges I have reduced the fine-structure constant of magnetic-like terms by a factor of four. These fine-structure constants in reality refer to microscale physics.
The total matrix display obtained has remarkably served to illustrate the feasible normal modes of oscillations and the spectral features of the antisymmetric universe. The eigenvalues and the eigenvectors corresponding to the four different types of self-interaction contributions to the matrix display of the Riemann Tensor components projected in the ( x, t ) frame are diagrammatically presented.
The Vierergruppe terms present a possibility of the introduction of diagonal interaction terms that was found to enhance the eigenvalues drastically. An antisymmetric universe of this kind offers a tremendous insight of the Information Technology features.

INFORMATION TECHNOLOGY OF COSMOS:

Stephen Hawking [1] sought information loss of a black hole as an extra uncertainty while Roger Penrose thought of it as a complimentary uncertainty. The later requires loss of in phase-volume which is balanced by a process of spontaneous quantum measurement in which information is gained and the phase-volume is increased. Thus quantum measurements give a different evolution (R process) viz. collapse of a wave function unlike the unitary evolution (U process) of a quantum system. The asymmetry in R arises due to boundary conditions of the cosmic entity in the future and the past. Hawking observes that there is no physical process that corresponds to the R processor it has anything to do with consciousness or quantum gravity. According to Penrose collapse of a wave function seems to introduce the CPT violation into physics. Question posed was how one perceives the world? Quantum mechanics does not do this according to Penrose. We have to solve the problem of why we perceive either a live cat or a dead cat, but never a superposition asserts Penrose. He states that philosophy is important in these matters which may not yield the answer. S. Hawking said that on a macroscopic scale things average out to be zero so one observes the cat alive or dead and not a linear combination of the two. No necessity of a new theory of measurement or the certainly doesn’t need quantum gravity.

ACKNOWLEDGMENT:

I am indebted to late Professor K. Rangadhama Rao D.Sc. (Madras) D.Sc. (London) for his constant encouragement and support of my research work. When once while I took Prof K. Rangadhama Rao driving his Ambassador car No.1482, to his research laboratories in the J. V. D. College of Science & technology, Andhra University, Waltair, he queried me whether the fine-structure constants of spectroscopy, have any relation to the space-time structures. I noted later that he mentioned in his D.Sc. thesis of Madras University that he could not get the paper published by Prof. Sommerfeld on the relativistic mass corrections to the shifts of atomic spectral lines.

REFERENCES:

1. R. Penrose , “The Nature of Space and Time”, ed.S.Hawking and R. Penrose, oxford Press, Delhi, p.114,1998
2. Albert Einstein S.B. preuss. Akad. Wiss. 1923-1925; A. Einstein and E. G. Straus Ann. Math., Princeton, (2), Vol.47, p.731, 1946 ; A. Einstein Ann. Math., Princeton, (2), Vol.46, p.538, 1945 see also W. Pauli, “Theory of Relativity”, B. I. Publications, Bombay, p.225, 1958.
3. Elie Cartan, Compt. Rend. (Paris), Vol.174, p.593, 1922.
4. J. A. Schouten,””Ricci-calculus”, Springer, Berlin, 1954.
5. J. A. Wheeler and R. Feynman, Rev. Mod. Phys. Vol.17, p.157, 1945.
6. T. Gold, Am. J. Phys, Vol.30, p.403, 1962
7. H A Lorentz “The Theory of Electron”, Dover Pub., New York, 1909
8. C. Lanczos “Recent developments in General Relativity”, p.313-321, Pergamon Press, 1962
9. Reference may be made to trusciencetrutechnology@blogspot.com previous publications by the present author.
10. C. W. Misner, Kip S. Thorn and John A. Wheeler, ”GRAVITATION” , Freeman and Company , San Francisco, 1973
• In the Petrov classification of space-times in General Relativity discussed by R. J. Adler and C. Sheffield in the article J. Math. Phys. Vol.14, No.4, p.465-469, 1973 mention has been made of matrix eigenvectors that are complex with real eigenvalues.

AN OFF-LINE ADDENDUM:
The Indian proponent of Vedas viz. Adi Sankaracharya has emphasized the Advaitha philosophy that asserts only oneness of nature in-spite of its diverse physical manifestations. Later philosophers like Madhwa and Ramanujacharya sought the Dwaitha (distinct dualism) and Vishishta advaitha ( dwaitha with an intermediate force of influence) theories of philosophy. But the full meaning of Advaitha philosophy is not grasped but the later exponents of diverse philosophical thoughts about the Nature, since Advaitha involves both the Dwaitha and Vishishta Advaitha conjectures. Generally speaking in India many people believe that the state of

Dog> + God> = Divathva is supreme instead of the state of Dog> -God>= Rakshtva.

Termed differently it is the sum totality of righteousness> and the divinity> that gives the nature a Divathva and righteousness> devoid of Divinity> becomes cruel i.e. Rakshtva. Many Epics, Puranas and Upanishads etc. go on elaborating the diverse incidents of the manifest creation of the Universe and life in the form of the super-dialogue between the Divathva and the Rakshtva.
KLN : 12/10/2009 07:58:33