Narrow Results

This paper deals with the dynamics of charged plane symmetric collapse with dissipative fluid distribution in the framework of energy–momentum squared gravity. For this purpose, we consider non-static plane symmetric spacetime in the inner and static charged Vaidya spacetime in the outer regions of a star. We use Darmois junction conditions to match the interior and exterior geometries and find that masses of both spacetimes are identical if and only if their correspondence charges are same. To investigate the dynamics of the system, we apply Misner–Sharp and Müler–Israel–Stewart approaches to formulate dynamical as well as transport equations, respectively. We then couple these equations to analyze the effect of physical quantities and modified terms on the collapse rate. A relation among Weyl tensor, electromagnetic field and fluid variables, is also developed. Due to the influence of charge, anisotropic pressure and modified terms, the spacetime is not conformally flat. Further, we assume isotropic fluid and ignore the impact of electromagnetic field which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the presence of a charge, effective pressure, heat flux and additional terms of this gravity.

This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation.

We study the five-dimensional spherical collapse of an inhomogeneous dust in the presence of a positive cosmological constant. The general interior solutions, in the closed form, of the Einstein field equations, i.e. the 5D Tolman–Bondi–de Sitter, is obtained which in turn is matched to the exterior 5D Schwarzschild–de Sitter. It turns out that the collapse proceeds in the same way as in the Minkowski background, i.e. the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. A brief discussion on the causal structure singularities and horizons is also given.

We attempt to construct the braneworld analog of the cheese slice universe, an inhomogeneous cosmology constructed from alternating layers of Kasner and FLRW space–times. This construction is possible in four dimensions and we find that the energy conditions can be satisfied in the braneworld context. However, an extension into the bulk becomes more problematic. We use a 3 + 1 + 1 decomposition inspired by the ADM decompositions to show that structure is required in the bulk to support an inhomogeneous brane.

In this paper, metric-affine theories in which the gravity Lagrangian is built using (projectively invariant) contractions of the Ricci tensor with itself and with the metric (Ricci-based gravity theories, or RBGs for short) are reviewed. The goal is to provide a contextualized and coherent presentation of some recent results. In particular, we focus on the correspondence that exists between the field equations of these theories and those of general relativity, and comment on how this can be used to build new solutions of physical interest. We also discuss the formalism of junction conditions in the $f(R)$ case, and provide a brief summary on current experimental and observational bounds on model parameters.

The purpose of this paper is to study the feasibility and the appearance of charged thin-shell wormholes using generalized Chaplygin gas under the influence of minimally coupled $f(R,T)$ gravitational theory. Here, $f$ is a generic function of the scalar curvature $R$ and the trace of stress-energy tensor $T$. We explore different components of Lanczos equations in the context of a specific $f(R,T)$ functional form, i.e. $f(R,T)=R+2\lambda T$, by applying junction conditions on field equations. We study static stable solutions using radial perturbation and the generalized Chaplygin gas equation of state (EoS) with the isotropic environment. We investigate the stable (unstable) static wormhole solutions for various physical parametric values and illustrate them graphically.

Propagating shock-waves can be discussed in terms of junction conditions between space-time regions separated by a hypersurface. Recent observations of gravitational waves and their electromagnetic counterparts established that the former also propagate with the speed of light. Hence energetic gravitational waves could be perceived as shock-waves on null hypersurfaces. The most generic scalar-tensor theories with at most second order dynamics, the Horndeski-theories were severely constrained. We derive junction conditions across a null hypersurface for the subclass of allowed Horndeski-theories with linear kinetic term dependence, exploring a formalism based on a transverse null vector. We obtain a 2+1 decomposed generalised Lanczos equation, with the jump of the transverse curvature induced by both the distributional energy-momentum tensor of the wavefront of the shock-wave, and by the jump in the transverse derivative of the scalar. The surface density, current and pressure of the distributional light-like shock-wave and the transverse derivative of the scalar are also constrained by a scalar junction equation.

We review some applications of relativistic shells that are relevant in the context of quantum gravity/quantum cosmology. Using a recently developed approach, the stationary states of this general relativistic system can be determined in the semiclassical approximation. We suggest that this technique might be of phenomenological relevance in the context of the brane-world scenario and we draw a picture of the general set-up and of the possible developments.

The effects of isotropic pressure and adiabatic index on the instability regions of collapsing self-gravitating cylindrical objects are studied. After constructing collapse equation through perturbation scheme, instability limits are evaluated for Newtonian and post-Newtonian eras.