Oral comunication
T. B. Gonçalves, J. P. Mimoso
Abstract
We modulate the Minkowski metric with constant spatial curvature. By doing so, we dissociate it into three possibilities:
the standard flat Minkowski spacetime, a static metric with constant positive curvature, and a static metric with constant
negative curvature. The flat case is vacuum, and corresponds to the spacetime of the special theory of relativity, which
holds locally. On the other hand, the curved cases require exotic matter, with $
ho+3p =0$, and are related to the
geometry of the Einstein static universe and the Lobatchevksi geometry, respectively. The interest of these metrics is their
being at the core of the FLRW metric commonly used nowadays. In other words, the FLRW line element results from a
conformal transformation (by a time varying scale factor) of the metrics studied here. We also explore the de Sitter universe
model, for which the metric is also static (the metric functions do not depend on time), and the spacetime geometry is
determined by a single cosmologically constant parameter, $Lambda$. We note that a correspondence can be drawn with
the three cases of the curvature modulation of Minkowski, depending on the sign of $Lambda$. The distinction is that the
de Sitter case has instead $
ho+p =0$. Furthermore, we also modulate the Schwarzschild metric with constant spatial
curvature, and study the Tolman-Oppenheimer-Volkov equation for static equilibrium in these conditions. This work has
both a pedagogical interest as the metrics studied here form the basis of FLRW models used nowadays in cosmology and
Schwarzschild models of stars and black holes, and also an interest in the formal study of the impact of nested conformal
transformations.
18th Iberian Cosmology Meeting (IberiCOS2024)
Salamanca, Spain
2024 March
