The kinematics of particles moving in rainbow spacetime

The kinematics of particles moving in rainbow spacetime is studied in this paper. In particular the geodesics of a massive particle in rainbow flat spacetime is obtained when the semi-classical effect of its own energy on the background is taken into account. We show that in general the trajectory of a freely falling particle remains unchanged which is still a straight line as in the flat spacetime. The implication to the Unruh effect in rainbow flat spacetime is also discussed.Comment: 5 page

On the cone eigenvalue complementarity problem for higher-order tensors

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we given an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound of cone eigenvalues of tensors. Moreover, some new results concerning the bounds of number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.Comment: 26 pages, 2 figures, 3 table