غزوات میں رسولِ مجاہدﷺ کی جغرافیائی حکمت عملی

Allah selected Muhammad ﷺ trained by wahi provided it with all the knowledge required for any creation. Either it is any kind of Science, engineering, medical, war strategy, defense plan or any known/Unknown direction of human guidance. At last one must have to say that any precise or authentic yield of the research/effort just turn the page of Hadith or a verse of Quran no more than this. The war strategy of Muhammad ﷺ is wondering throughout the world even in such an advance time, mostly is depends upon. Initially Muhammadا started journey with the preaching of Islam, people were expecting it is too poor. How will be fruitful. It is help of Allah, constant efforts & strategy that prove whole story. This world became more stay able and more secure, was never before in the history of the mankind. Now in this age deviation from the way of Muhammadا will bring the world closer to an irreversible explosion, all the Muslim/Non-Muslim collectively believe in.

Gravitational Collapse in F R, T Modified Theory of Gravity

In this thesis, we investigate gravitational collapse in f(R, T) modified theory of gravity. We focus on the study of gravitational collapse of spherically symmetric and FriedmannRobertsonWalker(FRW) metrics for both dust and perfect fluid cases. We also explore the gravitational collapse of 5D spherically symmetric spacetime in f(R, T) gravity and extend this work to N-dimensional spherically symmetric spacetimes. Furthermore, we explore the effect of electromagnetic fields on the gravitational collapse in f(R, T) modified theory of gravity. Firstly, we discuss the gravitational collapse of spherically symmetric spacetime for both dust and perfect fluid cases in f(R, T) gravity. For this purpose, we consider the spherically symmetric spacetime as the interior region and Schwarzschild metric as the exterior region. The junction conditions between the exterior and interior regions are found by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are constant, for a particular f(R, T) = R + 2f(T) model. We calculate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is shown that the term f(R0, T0) behaves as a source of repulsive force and consequently it slows the collapse of matter. We then discuss gravitational collapse in the context of f(R, T) gravity by taking FRW metric in the interior and schwarzschild background in the exterior regions of the star. We solve the field equations by taking the assumption of constant curvature and constant trace of energy-momentum tensor. We found that the terms 2λρ0−f(R0, T0) and f(R0, T0)+2λ(p0−ρ0) behave as cosmological constant for both dust and perfect fluid cases. Next, we discuss spherically symmetric perfect fluid collapse in the frame work of f(R, T ) modified theories of gravity using a five dimensional background. For this reason we consider the five dimensional spherically symmetric metric as the interior region and a five dimensional Schwarzschild metric as an exterior region. The junction conditions between the exterior and interior regions are discussed. By taking above mentioned model, the corresponding field equations are evaluated for both marginally bound L(r) = 1 and non-marginally bound L(r) 6= 1 cases. We find the apparent horizons and their time formation for different possible cases. It has been concluded that the term involving λ plays double role: it speeds up the collapse in region where ρ0 < 4p0; and it slows down the collapsing of matter when ρ0 > 4p0. Furthermore, we extend this work to the N-dimensional case and find that the collapse process becomes faster in the region ρ0 < (n + 1)p0 and slower in the region ρ0 > (n + 1)p0. Furthermore, it is noted that our results reduce to previously published results [80] found in GR for λ = 0. Finally, we analyze the effect of electromagnetic field on the gravitational collapse in f(R, T ) modified theories of gravity by taking spherically symmetric metric in the interior region and Reissner-Nordstrom ¨ metric in the exterior region. We discuss the issue of apparent horizons. We conclude that the end state of a star, in the presence of electromagnetic fields in the f(R, T ) gravity framework, is a black hole. It is shown that the collapse is slower in the region ρc < 3pc and faster in the region ρc > 3pc. Moreover, for λ = 0, our results correspond to those of GR found previously[120].