Related papers: Klein-Gordon equation for a particle in brane mode…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
We study the Klein-Gordon equation in one spatial and one temporal dimension. Physically, this equation describes the wave function of a relativistic spinless boson with positive rest mass. Mathematically, this is the most elementary…
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
The $N$-branching Brownian motion with selection ($N$-BBM) is a particle system consisting of $N$ independent particles that diffuse as Brownian motions in $\mathbb{R}$, branch at rate one, and whose size is kept constant by removing the…
The main cosmological models on the brane are presented. A generic equation is given, from which the Friedmann equations of the Randall-Sundrum, induced gravity, Gauss-Bonnet and the combined induced gravity and Gauss-Bonnet cosmological…
Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form…
The effective four-dimensional, linearised gravity of a brane world model with one extra dimension and a single brane is analysed. The model includes higher order curvature terms (such as the Gauss-Bonnet term) and a conformally coupled…
Recently, path equations have been obtained for charged, spinning objects in brane world models, using a modified Bazanski Lagrangian. In this study, path deviation equations of extended objects are derived. The significance of moving…
In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first…
Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated.…
The behavior of the angular velocity of a test particle moving in a stable circular orbit in the vacuum on the brane is considered. In the brane world scenario, the four dimensional effective Einstein equation acquire extra terms, called…
It is shown that for a specific choice of a particular solution of the relativistic wave equation, it falls into the Helmholtz equation and the Klein -Gordon equation. In this case, the squares of the rest masses of the particle with the…
If the observable universe is a braneworld of Randall-Sundrum type, then particle interactions at high energies will produce 5-dimensional gravitons that escape into the bulk. As a result, the Weyl energy density on the brane does not…
Recently, it was argued that the spacetime dynamics can be understood by calculating the difference between the degrees of freedom on the boundary and in the bulk in a region of space. In this Letter, we apply this new idea to braneworld…
In the study of three-brane cosmological models, an unusual law of cosmological expansion on the brane has been reported. According to this law, the energy density of matter on the brane quadratically enters the right-hand side of the new…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
In this paper we investigate the Klein-Gordon equation in the past causal domain of a De Sitter brane imbedded in a Anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed…
We derive exact solutions of the Einstein equations in the context of the Randall-Sundrum model with matter both on the brane and in the bulk. The bulk metric is a generalization of the static metrics describing the interior of stellar…
We show that a four-dimensional equation of state for a cosmological constant term arises from a perfect fluid in the bulk in the context of a gravity model where the scalar curvature is non-minimally coupled to the perfect fluid Lagrangian…
A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of the Chaplygin gas with the modified equation of state such as $p=A\rho-B/\rho$. Initially…