arXiv subjects

G. Cruz

Publications and source records attributed to G. Cruz.

3 recordsLinked to original sources

arXiv2024

Lovelock type brane gravity from a minimal surface perspective

We explore the correspondence between the parallel surfaces framework, and the minimal surfaces framework, to uncover and apply new aspects of the geometrical and mechanical content behind the so-called Lovelock-type brane gravity (LBG). We show how this type of brane gravity emerges naturally from a Dirac-Nambu-Goto (DNG) action functional built up from the volume element associated with a world volume shifted a distance $\alpha$ along the normal vector of a germinal world volume, and provide all known geometric structures for such a theory. Our development highlights the dependence of the geometry for the displaced world volume on the fundamental forms, as well as on certain conserved tensors, defined on the outset world volume. Based on this, LBG represents a natural and elegant generalization of the DNG theory to higher dimensions. Moreover, our development allows for exploring disformal transformations in Lovelock brane gravity and analyzing their relations with scalar-tensor theories defined on the brane trajectory. Likewise, this geometrical correspondence would enable us to establish contact with tractable Hamiltonian approximations for this brane gravity theory, by exploiting the linkage with a DNG model, and thus start building a suitable quantum version.

hep-th↗

arXiv2024

Dark energy as a geometrical effect in geodetic brane gravity

Within the framework of the modified geodetic brane gravity, conformed by the Regge-Teitelboim model and enhanced with a linear term in the extrinsic curvature of the brane, the possibility that under an FRW geometry this theory emulates the so-called dark energy is discussed. The cosmological behavior of this model displays a self-(non-self)-accelerated expansion of this universe which is caused by a combination of usual matter and gravitational geometric effects controlled by a $\beta$ parameter that accompanies the correction $K$ term. Indeed, the self-accelerated branch, provided by the trace $K$ model raises the question of whether the extrinsic curvature correction terms might be suitable for dark energy candidates. We discuss the analytical expression obtained for $\rd$ in addition to the main cosmological parameters such as the state parameter $\omega_{\text{\tiny eff}}$ and the deceleration parameter $q$. Moreover, when we call for the contribution of dark radiation-like energy to be switched off, $\Odr \to 0$, we find the same acceleration behavior, as well as the same dark energy content provided by the DGP theory. The relationship of our findings to the analysis for $\rd$ performed by Davidson and Gurwich within the unified brane cosmology is briefly discussed.

gr-qc↗

arXiv2001

Quantum Collapse of a Small Dust Shell

The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Háj{\'ı}ček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self adjoint momentum operator in the space of the shell motion which is confined to a half line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

gr-qc↗