The behavior of the dynamics of neutral and charged particles in the presence of the cosmological constant in the Schwarzschild black hole(SWBH) is presented in this article. Noether symmetries and the corresponding conservation laws are found. It is observed that the Schwarzschild metric, with non-zero cosmological constants, affects the dynamics of the particle. It is also found that for a positive value of the cosmological constant we can define a short interval in which the cosmological constant lies. This is considered a necessary ingredient for the expansion of the Universe.

The general theory of relativity has allowed a better understanding of the structure of universe. One of the fundamentals problems in the general relativity is finding exact solutions of the Einstein-Maxwell field equations. Some solutions found applications in astrophysics, cosmology and more recently in the developments inspired by string theory. In this paper, we presented a compact object model in the framework of Einstein-Gauss-Bonnet gravity (EGB) with a linear equation of state considering a metric potential proposed for Buchdahl (1959). The new obtained models satisfy all physical requirements of a physically reasonable stellar object. We analyzed the effect of the Gauss-Bonnet coupling constant α on the main physical characteristics of the model. We checked that the radial pressure, energy density and anisotropy are well defined and are regular in the interior of the star and are dependent of the values of the coupling constant.