General relativistic analogue solutions for the Yang-Mills theory (original) (raw)
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Yang-Mills inspired solutions for general relativity
Physics Letters A, 1996
Several exact, cylindrically symmetric solutions to Einstein's vacuum equations are given. These solutions were found using the connection between Yang-Mills theory and general relativity. Taking known solutions of the Yang-Mills equations (e.g. the topological BPS monopole solutions) it is possible to construct exact solutions to the general relativistic field equations. Although the general relativistic solutions were found starting from known solutions of Yang-Mills theory they have different physical characteristics.
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The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.
Generalized Yang-Mills theory and gravity
Physical Review D, 2016
We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.
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Geometry of the Einstein and Yang-Mills equations
International Journal of Theoretical Physics, 1997
It is shown that the Einstein and Yang-Mills equations arise from the conditions for the space-time to be a submanifold of a pseudo-Euclidean space with dimension greater than 5. Some possible applications to cosmology, spin-2 fields, and geometrodynamics are discussed.
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