From the cosmological Friedmann model, which has been considered function lapse N(t) and the scaling function a(t), it is determined the scalar curvature of Ricci tensor extrinsic curvature, and from this the total formed by the gravitational Lagrangian Lagrangian and the matter is determined; and from conjugates Finally time, the Hamiltonian of the cosmological model is built.

In this article we explain the relativistic eects in the Global Positioning System (GPS); Corrections due to Special Relativity and General Relativity are analyzed. Although the gravitational effects are weak and the speeds are small, they nevertheless generate signicant relativistic efects. If these eects are not taken into account, errors would occur in the measurement of time and in the position of the GPS device (in the order of 11.5 km).

In this work a basic introduction is made about the space-time of Sitter and Anti-Sitter. For the Sitter space, two equivalent metrics are calculated, one using static coordinates and the other using Friedmann- Lemaître-Robertson-Walker coordinates (FLRW). In the case of the Anti-Sitter space, the condition that the cosmological constant must meet is determined to be a solution of Einstein's equations and nally, using global coordinates, its metric is determined.

A revision of the standard model of cosmology is presented with an emphasis on the Friedmann equation. A summary of the evidence for the accelerated expansion of the universe is shown; In order to explain such an acceleration in expansion, the characteristics of some dark energy models such as the cosmological constant, the quintessence, the K-essence and the Chaplygin gas are described and reviewed.

Recent discoveries determine that the universe is expanding rapidly. In order to explain this acceleration,a component of dark energy called quintessence has been proposed. In this article it is proposed tointroduce quintessence in Schwarzschild space-time. The Einstein eld equations for the Schwarzschilmetric are solved with an energy-moment tensor, whose components are the variables that dene thequintessence model.

In this work, the deduction of Friedmann's equations is presented in the context of modified gravity theories f(R); it has been considered to present them as a function of the constant k associated with the curvature of the hypersurface. To deduce it, a revision of the Lagrangian formulation of General Relativity and the modified gravity theories f (R) as well as the deduction of the field equation in the environment of the theories f(R) is previously made.

The space-time metric AdS will be determined and based on it the cosmological constant will be calculated as a function of the radius of the space AdS, using this cosmological constant the Einstein equations will be solved in order to find a metric based on from the radial coordinate of the event horizon, then some thermodynamic properties of black holes in spacetime AdS such as temperature, area and entropy will be calculated.

In this work, the shadow of the Schwarzschild black hole is studied analytically. The shadow of an object is understood as the shape that said object has in space, seen by an observer when only the properties of space-time are considered. To nd the analytical solution we use the Hamilton-Jacobi equation, the separation of variables method and the introduction of a conserved Carter-type quantity. For the determination of the orbits of constant radius, the impact parameters and the celestial coordinates will be used.

In this article, initially, a review of some classical aspects of bosonic string theory is made. In addition, the light cone coordinates are analyzed, as a covariant quantization method related to these coordinates with the proper coordinates through an appropriate transformation. This work aims to show an alternative way to deduce the solutions of string dynamic equation. For that, it starts transforming the light-cone coordinates by means of an arbitrary variable parameter, and by applying it into the Polyakov's action leads to equivalent solutions to the ones obtained using Fourier's series method.

This article presents a review about the cosmological constant, the Friedmann-Lemaitre-Roberson-Walker cosmological model and its relationship with Einstein's gravitational theory and with Friedmann's equations. The observational evidence is evaluated and the experimental results of the accelerated expansion of the Universe are analyzed. Finally, the physical nature of the cosmological constant is described as a possibility of dark energy.