D-Branes on Spaces Stratified Fibered Over Hyperbolic Orbifolds

We apply the methods of homology and K-theory for branes wrapping spaces stratified fibered over hyperbolic orbifolds. In addition, we discuss the algebraic K-theory of any discrete co-compact Lie group in terms of appropriate homology and Atiyah-Hirzebruch type spectral sequence with its non-trivial lift to K-homology. We emphasize the fact that the physical D-branes properties are completely transparent within the mathematical framework of K-theory. We derive criteria for D-brane stability in the case of strongly virtually negatively curved groups. We show that branes wrapping spaces stratified fibered over hyperbolic orbifolds carry charge structure and change the additive structural properties in K-homology.

On the motion of a test particle around a global monopole in a modified gravity

In this paper we suggest an approach to analyse the motion of a test particle in the spacetime of a global monopole within a $f(R)$-like modified gravity. The field equations are written in a more simplified form in terms of $F(R)=frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric problem, $F(R)$ is expressed as a radial function ${cal F}(r)equiv{F(R(r))}$. So, the choice of a specific form for $f(R)$ will be equivalent to adopt an Ansatz for ${cal F}(r)$. By choosing an explicit functional form for ${cal F}(r)$ we obtain the weak field solutions for the metric tensor, compute the time-like geodesics and analyse the motion of a massive test particle. An interesting feature is an emerging attractive force exerted by the monopole on the particle.

Gravitational Field of a Global Monopole in a Modified Gravity

In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.