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A Lagrangian model for gravitation and electromagnetism. (English) Zbl 0708.53057
The starting point in this model is a generalized Lagrange space \(\overset \circ M^ n=(M,g_{ij}(x,y))\) in which \(g_{ij}(x,y)=\gamma_{ij}(x)+(1/c^ 2)y_ iy_ j,\) where \(\gamma_{ij}\) is a Riemannian metric on the base manifold \(M,y_ i=\gamma_{ij}(x)y^ j\) and \((x^ i,y^ i)\) are local coordinates on TM. The authors assume that there exists an electromagnetic field \(A_ i(x)\) and postulate that this field is unified to \(g_{ij}(x,y)\) by the nonlinear connection \(N=\overset \circ N-F\), where N is the canonical connection of \(\overset \circ M^ n\) and F is the tensor field \(F^ i_ j=(\phi /mc)\gamma^{ik}(\partial_ kA_ j-\partial_ jA_ k).\) Thus the pair \(M^ n=(M^ n,N)\) is a generalized Lagrange space which furnishes the desired model. The Einstein equations as well as the Maxwell equations are deduced and studied by means of the geometry of \(M^ n\).
Reviewer: M.Anastasiei

53C80 Applications of global differential geometry to the sciences
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories