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Nasr Ahmed

Publications and source records attributed to Nasr Ahmed.

31 records · Page 2Linked to original sources
arXiv2019

Space-time singularities and the theory of retracts

In previous publications, we have started investigating some possible applications to the retraction theory in gravitational physics and showed that it can be very useful in providing proofs and explaining the topological bases. In the current work, we investigate the role of the retraction theory in the mathematical study of space-time singularities and suggest a topological restriction on the formation of singularities. Although we present a toy model using a 5D cosmological metric as an example, the current study applies for any collapsing system under the influence of gravity such as a massive star or the whole universe. After showing that the cosmological space-time $M$ can be retracted into lower dimensional circles $S_i \subset M $, we prove the existence of a homotopy between this retraction and the identity map which defines a deformation retract on $M$. Since a circle doesn't deformation retract onto a point but it does retract to a point, the defined deformation retract stops any circle $S_i$ from retracting into a point which means no singularity is formed. The paper underlines the role of algebraic topology in the mathematical study of space-time singularities and represents a new application of the retraction theory in mathematical physics.

physics.gen-ph↗
arXiv2019

A Cyclic Universe With Varying Cosmological Constant in $f(R,T)$ gravity

A new kind of evolution for cyclic models in which the Hubble parameter oscillates and keeps positive has been explored in a specific $f(R,T)$ gravity reconstruction. A singularity-free cyclic universe with negative varying cosmological constant has been obtained which supports the role suggested for negative $Λ$ in stopping the eternal acceleration. The cosmological solutions have been obtained for the case of a flat universe, supported by observations. The cosmic pressure grows without singular values, it is positive during the early-time decelerated expansion and negative during the late-time accelerating epoch. The time varying EoS parameter $ω(t)$ shows a quintom behavior and is restricted to the range $-2.25 \leq ω(t) \lesssim \frac{1}{3}$. The validity of the classical linear energy conditions and the sound speed causality condition has been studied. The non-conventional mechanism of negative cosmological constant that are expected to address the late-time acceleration has been discussed.

gr-qc↗
arXiv2018

On the existence of deformations and dimensional reduction in wormholes and black holes

The deformation retract is, by definition, a homotopy between a retraction and the identity map. We show that applying this topological concept to Ricci-flat wormholes/black holes implies that such objects can get deformed and reduced to lower dimensions. The homotopy theory can provide a rigorous proof to the existence of black holes/wormholes deformations and explain the topological origin. The current work discusses such possible deformations and dimensional reductions from a global topological point of view, it also represents a new application of the homotopy theory and deformation retract in astrophysics and quantum gravity.

physics.gen-ph↗
arXiv2018

A stable flat universe with variable Cosmological constant in f(R,T) Gravity

In this paper, a general FRW cosmological model has been constructed in $f(R,T)$ gravity reconstruction with variable cosmological constant. A number of solutions to the field equations has been generated by utilizing a form for the Hubble parameter that leads to Berman's law of constant deceleration parameter $q=m-1$. The possible decelerating and accelerating solutions have been investigated. For ($q>0$) we get a stable flat decelerating radiation-dominated universe at $q=1$. For ($q<0$) we get a stable accelerating solution describing a flat universe with positive energy density and negative cosmological constant. Nonconventional mechanisms that are expected to address the late-time acceleration with negative cosmological constant have been discussed.

gr-qc↗
arXiv2018

Topological Origin of Holographic Principle: Application to wormholes

In this paper, we suggest a mathematical representation to the holographic principle through the theory topological retracts. We found that the topological retraction is the mathematical analogs of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five dimensional (5D) wormhole space-time $W$ which we found it can retract to lower dimensional circles $S_i \subset W$. In terms of the holographic principle, the description of this volume of space-time $W$ is encoded on the lower-dimensional circle which is the region boundary.

gr-qc↗
arXiv2015

Fluid sphere: stability problem and dimensional constraint

We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vectors. The solutions of the Einstein field equations examined specifically for five different set of spacetime. We calculate the active gravitational mass and impose stability conditions of the fluid sphere. The analysis thus carried out immediately indicates that at $4$-dimension only one can get a stable configuration for any spherically symmetric stellar system and any other dimensions, lower or higher, becomes untenable as far as the stability of a system is concerned.

gr-qc↗
arXiv2015

Deformation Retract and Folding of the 5D Schwarzchild Field

In this article we introduce some types of the deformtion retracts of the $5D$ Schwarzchild space making use of Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The relation between folding and deformation retract of this space has been achieved. A relation for energy conservation similar to the one obtained in four dimensions has been obtained for the five dimensional case.

physics.gen-ph↗
arXiv2014

Bianchi Type-$V$ cosmology in $f(R,T)$ gravity with $Λ(T)$

A new class of cosmological models in $f(R, T)$ modified theories of gravity proposed by Harko et al. (2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar $R$ and the trace of the stress-energy tensor $T$, have been investigated for a specific choice of $f(R, T) = f_{1}(R) + f_{2}(T)$ by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(αt)$, where $n$ and $α$ are positive constants. For $0 < n \leq 1$, this generates a class of accelerating models while for $n > 1$, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct $f(R,T)$ models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant $Λ$ as a function of the trace of the stress energy-momentum-tensor, and dub such a model "$Λ(T)$ gravity" where we have specified a certain form of $Λ(T)$. Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair $\{r,s\}$ parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.

physics.gen-ph↗
arXiv2014

On the Masses of the Universal hypermultiplets in heterotic M-theory

The reduced 5D Heterotic M-theory has a deeply rich structure. For every Calabi-yau compactification, there exists a gravitational hypermultiplet $(g_{μν},ψ_μ,A_μ)$ and a universal hypermultiplet. In this paper we derive the formulae for the masses of the scalar sector of the universal hypermultiplet $(V,σ,ζ,\barζ)$ in the framework of 5D Heterotic M-theory.

hep-th↗
arXiv2014

Nonommutative wormholes in $f(R)$ gravity

This paper discusses several new exact solutions of static wormholes in $f(R)$ gravity with a noncommutative-geometry background, which replaces point-like structures by smeared objects. In the first part of the paper we assume the power-law form $f(R)=aR^n$ and discuss several solutions corresponding to different values of the exponent. The second part of the paper assumes a particular form of the shape function that also yields a viable solution. This investigation generalizes some of our previous work in $f(R)$ gravity, as well as in noncommutative geometry.

gr-qc↗
arXiv2010

Balancing the vacuum energy in heterotic $M$-theory

Moduli stabilisation is explored in the context of low-energy heterotic $M$-theory to show that a small value of the cosmological constant can result from a balance between the negative potential energy left over from stabilising the moduli and a positive Casimir energy from the higher dimensions. Supersymmetry breaking is induced by the fermion boundary conditions on the two branes in the theory. An explicit calculation of the Casimir energy for the gravitino reveals that the energy has the correct sign, although the size of the contribution is close to the edge of the parameter range for which the calculation is valid.

hep-th↗
arXiv2008

Gaugino condensation in an improved heterotic M-theory

Gaugino condensation is discussed in the context of a consistent new version of low energy heterotic M-theory. The four dimensional reduction of the theory is described, based on simple boson and fermion backgrounds. This is generalised to include gaugino condenstates and various background fluxes, some with non-trivial topology. It is found that condensate and quantised flux contributions to the four-dimensional superpotential contain no corrections due to the warping of the higher dimensional metric.

hep-th↗