arXiv subjects
Publications and source records attributed to Safiqul Islam.
In this paper, we introduce the concept of ideal on CL-algebra. It is proved that this concept generalizes the notion of ideal on Residuated Lattices. Prime ideal on CL-algebra are defined and few interesting properties are obtained. It has been shown that quotient algebra corresponding to CL-algebra is formed with the help of ideal is also a CL-algebra.
We intend to study a new class of cosmological models in $f(R, T)$ modified theories of gravity, hence define the cosmological constant $Λ$ as a function of the trace of the stress energy-momentum-tensor $T$ and the Ricci scalar $R$, and name such a model "$Λ(R, T)$ gravity" where we have specified a certain form of $Λ(R, T)$. $Λ(R, T)$ is also defined in the perfect fluid and dust case. Some physical and geometric properties of the model are also discussed. The pressure, density and energy conditions are studied both when $Λ$ is a positive constant and when $Λ=Λ(t)$, i.e a function of cosmological time, t. We study the behaviour of some cosmological quantities such as Hubble and deceleration parameters. The model is innovative in the sense that it has been described in terms of both $R$ and $T$ and display a better understanding of the cosmological observations.
In this paper, we introduce the concept of filter on IL-algebra. It is proved that this concept generalizes the notion of filter on Residuated Lattices. Prime filters on IL-algebra are defined and few interesting properties are obtained. It has been shown that quotient algebra corresponding to IL-algebra is formed with the help of filters also an IL-algebra.
We present the interior solutions of distributions of magnetised fluid inside a sphere in $f(R,T)$ gravity. The magnetised sphere is embedded in an exterior Reissner-Nordström metric. We assume that all physical quantities are in static equilibrium. The perfect fluid matter is studied under a particular form of the Lagrangian density $f(R,T)$. The magnetic field profile in modified gravity is calculated. Observational data of neutron stars are used to plot suitable models of magnetised compact objects. We reveal the effect of $f(R,T)$ gravity on the magnetic field profile, with application to neutron stars, especially highly magnetized neutron stars found in X-ray pulsar systems. Finally the effective potential $V_{\rm eff}$ and innermost stable circular orbits, arising out of motion of a test particle of negligible mass influenced by attraction or repulsion from the massive center, are discussed.
We provide a 2-fluid immiscible matter source that supplies fuel to construct wormhole spacetime. The exact wormhole solutions are found in the model having, besides real matter or ordinary matter, some quintessence matter along with charge distribution. We intend to derive a general metric of a charged wormhole under some density profiles of galaxies that is also consistent with the observational profile of rotation curve of galaxies. We have shown that the effective mass remains positive as well as the wormhole physics violate the null energy conditions. Some physical features are briefly discussed.
In static and spherically symmetric spacetime, we solve the Einstein Maxwell equations. The effective gravitational potential and the electric field for charged anisotropic fluid are defined in terms of two free parameters. For such configuration, the mass of the star as a function of stellar radius is found in terms of two aforementioned parameters, subjected to certain stability criteria. For various values of these two parameters one finds that such mass radius relationship can model stellar objects located at various regions of Hertzsprung-Russel diagram.
A new model of gravastar is obtained in $D$-dimensional Einstein gravity. This class of solutions includes the gravastar as an alternative to D-dimensional versions of the Schwarzschild-Tangherlini black hole. The configuration of this new gravastar consists of three different regions with different equations of state: [I] Interior: 0 \leq r < r_1, ρ= -p; [II] Shell: r_1 \leq r < r_2, ρ= p; [III] Exterior: r_2 < r, ρ= p =0. The outer region of this gravastar corresponds to a higher dimensional Schwarzschild-Tangherlini black hole.
We provide a new matter source that supplies fuel to construct wormhole spacetime. The exact wormhole solutions are found in the model having, besides real matter, an anisotropic dark energy. We have shown that the exotic matters that are the necessary ingredients for wormhole physics violate null and weak energy conditions but obey strong energy condition marginally. Though the wormhole comprises of exotic matters yet the effective mass remains positive. We have calculated the effective mass of the wormhole up to 8 km from the throat (assuming throat radius as 4 km) as $1.3559M_\odot $. Some physical features are briefly discussed.
Noncommutative geometry, an offshoot of string theory, replaces point-like structures with smeared objects and has recently been extended to higher dimensions. The purpose of this letter is to obtain wormhole solutions with this extended noncommutative geometry as a background. It is found through this investigation that wormhole solutions exist in the usual four, as well as in five dimensions, but they do not exist in higher-dimensional spacetimes.
This is a continuation and generalization of our earlier work on {\it gravastar} in (2+1) anti-de Sitter space-time to 2+1 dimensional solution of charged gravastar. Morphologically this gravastar contains three regions namely: (i) charged interior, (ii) charged shell and (iii) electrovacuum exterior. We have studied different characteristics in terms of Length and Energy, Entropy, and Junction conditions of the spherical charged distribution. It is shown that the present model of charged gravastar is non-singular and represents itself an alternative of Black Hole.
We propose a new model of a gravastar in (2+1) anti-de Sitter space-time. This new three dimensional configuration has three different regions with different equations of state: [I] Interior: 0 \leq r < r_1, ρ= -p ; [II] Shell: r_1 \leq r < r_2, ρ= p; [III] Exterior: r_2 < r, ρ= p =0. The outer region of this gravastar corresponds to the exterior (2+1) anti-de Sitter space-time, popularly known as the BTZ space-time. Like BTZ model, Λis taken to be negative, which at the junction turns out to be positive as required by stability of gravastar and mathematical consistency. After investigating the Interior space-time, Shell and Exterior space-time we have highlighted different physical features in terms of Length and Energy, Entropy, and Junction conditions of the spherical distribution. It is shown that the present model of charge-free gravastar in connection to the exterior (2+1) anti-de Sitter space-time or the BTZ space-time is stable and non-singular.