Relativistic hyperbolic motion and its higher order kinematic quantities



Título del documento: Relativistic hyperbolic motion and its higher order kinematic quantities
Revista: Revista mexicana de física
Base de datos: PERIÓDICA
Número de sistema: 000460541
ISSN: 0035-001X
Autores: 1
1
Instituciones: 1Instituto Potosino de Investigación Científica y Tecnológica, San Luis Potosí. México
Año:
Periodo: Nov-Dic
Volumen: 68
Número: 6
País: México
Idioma: Inglés
Tipo de documento: Artículo
Enfoque: Analítico, teórico
Resumen en inglés We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1 + 1 and 1 + 3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1 + 3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities
Disciplinas: Física y astronomía
Palabras clave: Física,
Movimiento hiperbólico,
Jerk,
Snap,
Espacio-tiempo de Minkowski,
Hipérbolas de Rindler modificadas
Keyword: Physics,
Hyperbolic motion,
Jerk,
Snap,
Minkowski spacetime,
Modified Rindler hyperbolas
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