This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope N a 25 ) is a thermometer for a ultracold gas like the dipolar gas N a 23 K 40 . So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed V in the subatomic world, one expects that the proper time of such a clock moving close to V in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called proper time dilation so that the atomic decay rate of a ultracold radioactive sample (e.g: N a 25 ) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).
We aim to investigate the theory of Lorentz violation with an invariant minimum speed called Symmetrical Special Relativity (SSR) from the viewpoint of its metric. Thus, we should explore the nature of SSR-metric in order to understand the origin of the conformal factor that appears in the metric by deforming Minkowski metric by means of an invariant minimum speed that breaks down Lorentz symmetry. So, we are able to realize that there is a similarity between SSR and a new space with variable negative curvature (−∞ < R < 0) connected to a set of infinite cosmological constants (0 < Λ < ∞), working like an extended de Sitter (dS) relativity, so that such extended dS-relativity has curvature and cosmological "constant" varying in time. We obtain a scenario that is more similar to dS-relativity given in the approximation of a slightly negative curvature for representing the current universe having a tiny cosmological constant. Finally, we show that the invariant minimum speed provides the foundation for understanding the kinematics origin of the extra dimension considered in dS-relativity in order to represent the dS-length.
Resumo O tensor de momento-energia é a entidade matemática que representa de forma unificada as fontes de momento e energia no formalismo covariante, tanto em espaços planos, como em espaços curvos. Em espaços curvos o tensor de momento-energia fica conectado a curvatura do espaço-tempo via equação de campo de Einstein. O tensor de momento-energia caracteriza os campos de matéria do sistema. Por sua vez as condições de energia estabelecidas por Hawking e Ellis classificam os diversos tipos de fluidos quanto a atratividade/repulsividade, a causalidade, interação com o vacuo e a positividade. Tambem abordamos a conservação do tensor de momento-energia via equação Tolemam-Openhaimer-Volkov(TOV), que é um importante formalismo para o estudo de estruturas e modelos estelares. Vamos estudar o tensor momento-energia nas suas versões isotrópicas e anisotrópicas, bem como a sua conservação e relação com a constante cosmológica.
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