تفسیر نجوم الفرقان کے فقہی طرز استدلال کا تجزیاتی مطالعہ

The jurisprudence is the essence of Islamic teachings. It is the summary of Qurʼān and the soul of Messenger’s (on whom be peace and greetings) sunnah. In general, it represents the sharīaʻh and the path to follow for Islamic lifestyle. Therefore, the significance of its importance is clear in Islamic Studies. The scholars have been kept solving ummah problems through religious principles and will keep solving the problems till the day of judgement. Whenever there arises a new problem, the scholars provide the solution in the lights of Qurʼān and Hadith and set the rules till the day of judgement. Allama ʻAbdul Razzāq Bhutrālwī also presented the solutions to different problem using the same principle i.e. He interprets a Quranic verse in such a way that provide the implied solution for paying ransom to poor against fasting for traveler and patient. Allama ʻAbdul Razzāq Bhutrālwī discussed about the permission for women to visit graveyard by following the orders of Prophet (on whom be peace and greetings), when it was prohibited for everyone to go to graveyards but later on the permission was granted for the same act. In the same way Allama ʻAbdul Razzāq Bhutrālwī presented his argument about the burning or sinking into the water or burying the shabby pages the Holy Qurʼān based on an order of Hazrat Uthman Ghani to burn all the copies of the Holy Qurʼān except Qurat-e-Quraish to bring uniformity

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].