Izvorni znanstveni članak
Modelling a wormhole structure
R. Leticia Corral-Bustamante
; Department of Mechatronics Engineering, Technological Institute of Cuauhtémoc City, Tecnológico Ave. S/N, Z.P. 31500 Cuauhtémoc City, Chihuahua, MEXICO
Aaron Raul Rodríguez-Corral
; Department of Mechatronics Engineering, Technological Institute of Cuauhtémoc City, Tecnológico Ave. S/N, Z.P. 31500 Cuauhtémoc City, Chihuahua, MEXICO
Alma Reyna Rodríguez-Gutiérrez
; Department of Mechatronics Engineering, Technological Institute of Cuauhtémoc City, Tecnológico Ave. S/N, Z.P. 31500 Cuauhtémoc City, Chihuahua, MEXICO
Gilberto Irigoyen-Chávez
; Department of Mechatronics Engineering, Technological Institute of Cuauhtémoc City, Tecnológico Ave. S/N, Z.P. 31500 Cuauhtémoc City, Chihuahua, MEXICO
Jose Martín Berlanga-Reyes
; Department of Mechatronics Engineering, Technological Institute of Cuauhtémoc City, Tecnológico Ave. S/N, Z.P. 31500 Cuauhtémoc City, Chihuahua, MEXICO
Sažetak
This paper proposes a model of a hypothetical wormhole done by using non-linear equations of a high degree of complexity to obtain exact solutions. Modelling of a wormhole implies creating a particular gravitational field with a hyperbolically symmetric and static geometric body produced for a hyper-cylindrical and symmetric rest mass that
can occur in its short tunnel, and its subsequent thermodynamic study. Starting out from the metric in General Relativity, in order that a short wormhole tunnel might be modelled, it is essential to define the coordinates and covariant metric of a 4-dimensional space with three spatial coordinates and one temporal by applying the summation
convention on repeated indices in the system of four generalized coordinates. The limiting form of the line element for flat spacetime at large distances from the origin must be Lorentzian. The line element corresponding to the solution proposed here has to remain invariant under inversion of time interval. In this paper, the simplest quadratic
scalar invariant of the Riemann tensor, the Kretschmann invariant, has been taken. Furtehmore, curvilinear coordinates in which the metric tensor components that are outside the main diagonal and that have to have zero value for not having a determined direction in space have been used. The metric can be reduced to a flat metric for an observer at rest located in the “infinite” so that the effects caused by the mass in the gravitational field could be deemed negligible. The results obtained a quasi-exact solution to the Einstein’s equations that describes the gravitational field induced for a hyper-cylindrical geometry similar to a wormhole tunnel. The so-called “exotic matter” that is hypothesized to reside inside wormhole tunnels and is involved in the energy transport phenomenon has subsequently been studied.
Ključne riječi
wormhole; Einstein field equations; metric; quasi-exact solutions; hyperbolic geometry
Hrčak ID:
184915
URI
Datum izdavanja:
23.1.2014.
Posjeta: 515 *