arXiv subjects
Publications and source records attributed to E. C. de Rey Neto.
We compute analytically the tidal field and polarizations of an exact gravitational wave generated by a cylindrical beam of null matter of finite width and length in quadratic curvature gravity. We propose that this wave can represent the gravitational wave that keep up with the high energy photons produced in a gamma ray burst (GRB) source.
In the present work we approximate an ultrarelativistic jet by a homogeneous beam of null matter with finite width. Then, we study the influence of this beam over the space-time metric in the framework of higher-derivative gravity. We find an exact shock wave solution of the quadratic gravity field equations and compare it with the solution to Einstein's gravity. We show that the effect of higher-curvature gravity becomes negligible at large distances from the beam axis. We also observe that only the Ricci-squared term contribute to modify the Einstein's gravity prediction. Furthermore, we note that this higher-curvature term contribute to regularize the discontinuities associated to the solution to Einstein's general relativity.
We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + ε( 3 α_1 u^2 u_x + 3α_2 uu_{xx} + 3α_3 u_x^2 + α_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order ε, to a linearizable equation if the condition $3α_1 - 3α_3 - 3/2 α_2 + 3/2 α_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.