arXiv subjects
Publications and source records attributed to Xavier Jaén.
We propose a novel approach to detect gravitational waves based on a semi-rigid detector. The approach relies upon the time delay that the light takes to travel from a fixed mirror at the end of a rigid bar to a nearby free mirror. We show that the dimensions of the experimental device can be shortened in comparison to the conventional ones based on two free mirrors.
For a given space-time and for an arbitrary time-like geodesic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigid covariant. We then apply these conditions to linear plane gravitational waves.
The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlevé--Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.
Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when the latter is interpreted as the geodesic velocity field. The results are closely related to spacetimes that admit Painlevé--Gullstrand synchronization.
We consider the homothetic motion group. We construct a homothetic covariant Newtonian gravitation theory which unifies inertial homothetic forces and gravitational fields. This is achieved through an equivalence principle based on a local homothetic frame of motion. As a consequence, we can obtain a coherent Newtonian cosmology which admits a cosmological principle and leads to the Friedman equations for a dust universe. Finally we prove that this gravity theory can be obtained as the non-relativistic limit of a class of metrics in General Relativity. The Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) metric and its limit are also studied.
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally we find the non-relativistic limit of the Einstein's equations for the space--time metric derived from the Newtonian theory.