AbstractThe polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.
A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called `basis rhombicity' which is the sum of the absolute values of the elements of the metric tensor associated with the basis. The levels of reduction are quite similar to those obtained with the Lenstra–Lenstra–Lovász (LLL) algorithm, at least up to the moderate dimensions that have been tested (lower than 20). The method can be used to reduce unit cells attached to given hyperplanes.
Solutions of unified theory equations of gravity and electromagnetism has to satisfy Einstein-Maxwellequation. Specially, solution of the unified theory is generally Kerr-Newman solution in vacuum. We finallyfound the revised Einstein gravity tensor equation with new term (2-order contravariant metric tensor two timesproduct and the constant matrix) is right in Kerr-Newman solution.
Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein-Maxwellequation. Hence, solutions of the unified theory is Reissner-Nordstrom solution in vacuum. We found inrevised Einstein gravity tensor equation, the condition is satisfied by 2-order contravariant metric tensor twotimes product, the constant matrix.
Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein-Maxwellequation. Hence, solutions of the unified theory is Reissner-Nodstrom solution in vacuum. We found in revisedEinstein gravity tensor equation, the condition is satisfied by 2-order contravariant metric tensor two timesproduct.
Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein-Maxwellequation. Hence, solutions of the unified theory is Reissner-Nordstrom solution in vacuum. We found inrevised Einstein gravity tensor equation, the condition is satisfied by 2-order contravariant metric tensor twotimes product and Gauss symbol.
Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein-Maxwellequation. Hence, solutions of the unified theory is Reissner-Nordstrom solution in vacuum. We found in revisedEinstein gravity tensor equation, the condition is satisfied by 2-order contravariant metric tensor two timesproduct. In theory, the problem that the special Ricci tensor have two value term is solved by two orientationof rotating (right hand and left hand).
Solutions of unified theory equations of gravity and electromagnetism satisfy Einstein-Maxwellequation. Hence, solutions of the unified theory is Reissner-Nordstrom solution, Kerr-Newman solution invacuum. In this careful point, Einstein gravity field equation’s energy-momentum tensor has two sign.Therefore, according to the solution, the sign is treated. We found in revised Einstein gravity tensor equation,the condition is satisfied by 2-order contravariant metric tensor two times product and Gauss symbol..
Aspects of the polynomial affine model of gravity in three dimensions
