arXiv subjects

J. Martin-Martin

Publications and source records attributed to J. Martin-Martin.

4 recordsLinked to original sources

arXiv2009

Gravity as a Gauge Theory of Translations

The Poincaré group can be interpreted as the group of isometries of a minkowskian space. This point of view suggests to consider the group of isometries of a given space as the suitable group to construct a gauge theory of gravity. We extend these ideas to the case of maximally symmetric spaces to reach a realistic theory including the presence of a cosmological constant. Introducing the concept of "minimal tetrads" we deduce Einstein gravity in the vacuum as a gauge theory of translations.

gr-qc↗

arXiv2009

About the mass problem

The concept of {\it active gravitational mass}, its definition and its relation with the sources of a gravitational field, was clearly established by Tolman in 1934. On the contrary, and surprisingly in our opinion, the concept of {\it proper mass} has remained obscure in General relativity. We compare a new definition to an apparent more obvious one and discuss how each choice modifies the ratio of active to proper gravitational mass.

gr-qc↗

arXiv2006

An approximate global solution of Einstein's equations for a finite body

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic and quo-harmonic coordinates. In both cases, interior and exterior solutions are matched, in the sense of Lichnerowicz, on the surface of zero pressure to obtain a global solution. The resulting metric depends on three arbitrary constants: mass density, rotational velocity and the star radius at the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined by these three parameters. It is easy to show that this type of fluid cannot be a source of the Kerr metric

gr-qc↗

arXiv2004

An approximate global stationary axisymmetric solution of the Einstein equations

In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular velocity.

gr-qc↗