Department of Mathematics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/21
Browse
7 results
Search Results
Item Extension of Isotropic Solutions into Anisotropic Domain Via Gravitational Decoupling Approach(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) MOBEEN AMIN; CIIT/FA19-RMT-048/LHR; Dr. Muhammad Zubair; LHR TP 7437In this thesis, we study known charged and uncharged isotropic Heintzmann solution and Durgapal IV solution and extend it to its well anisotropic domain by manipulating gravitational decoupling through extended geometric defor- mation (EGD) approach. We employ linear transformation on both metric po- tentials and convert the single set of EFEs into two less-complicated subsys- tems. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. The matching con- ditions at the stellar surface are discussed in detail, where outer geometry is represented by Reissner-Nordstrom solution in the presence and schwarzschild solution in the absence of charge and also evaluate the expressions for ther- modynamical quantities ρtot, ptot r and ptot t using mimic constraint and equation of state (EoS).We discuss the physical properties of the stellar model. Physical analysis is carried out using different physical indicators i.e, energy conditions, equilibrium equation, casualty condition, Herrera’s cracking concept, adiabatic index, compactness and surface redshift. In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3652, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e., γ = 0, 0.2 and 0.3 and also evaluate the graphical behavior of compact star PSRJ1614 − 2230 against different values of γ = 0.25, 0.55 and 0.75 for different model.Item 4D Black Holes and Their Parameters(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Sania sobedar; SP23-RMT-036; Dr. Muhammad Zubair; LHR TP 9576Black holes are among the most enigmatic objects in the universe, characterized by their immense gravitational pull and profound influence on surrounding matter. In this thesis we considered Dyonic Modmax black hole, which is static and we apply Newman-Janis Algorithm to make the black hole rotating. The rotating metric then explored to study parametric constraints and frequencies of black hole by using the Quasi-Periodic Oscilla tions. Moreover, we investigated the effective potential. We also find the orbital frequency (or Keplerian frequency) of Dyonic ModMax black hole. It is the frequency of a particle which is orbiting around the BH. In general, it is function containing charge and radial distance of a particle from BH.Item Existence and Stability of Neutron Stars in Minimally Coupled Gravity(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Fahad Hainf; FA22-RMT-042; Dr. Muhammad Zubair; LHR TP 9378Relativistic stars’ equilibrium and stability evolved as an exciting aspect in both modified theories of gravity and GR. When these systems reflect movements and make an effort to maintain stability, they attract a lot of attention. The dynamical analysis of gravitating systems plays key role in structure formation that is why astrophysicists and cosmologists pay great attention in the discussion of stability range of gravitating sources.Here, we shall analyze the stability of NSs by analyzing the evolution of hydrostatic equilibrium configu ration for the choice of EoS p = ω(ρ4B), with ω = 1 3 and B represents Bag constant. In this scheme we pick the minimally coupled F(R,T) gravity of the form F(R,T) = R+2λT, λ stands as the coupling parameter. We will compare our results with recent observational data.Item An Anisotropic Version of Tolman VII Solution in Rastall Theory of Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Dawood Falik Sher; FA18-RMT-022; LHR TP 6457; Dr. Muhammad ZubairIn our research, we worked for self gravitating system to evaluate stellar in- terior’s possibilities. For this we describe an anisotropic matter distribution , which is based on the Rastall’s theory of gravity with the help of minimal geo- metric deformation approach. As the minimal coupling matter principle is bro- ken down by the Rastall’s gravity, hence we have to provide an exhaustive ex- planation. This explanation deals with Israel-Darmois junction conditions and how it works in this pattern. Further, we have obtained the deformed space- time and use the procedure of mimic constraints. For checking the viability of any proposal, the results has been applied to any well known solution. So as we do. We use famous Tolman VII solution, to check the viability. The whole description of thermodynamical effects presented by the additional sources in mentioned. In addition, we have compared the results with their similes in the shadow of pure general relativity, pure Rastall’s gravity and, also in the struc- ture of general relativity which includes "gravitational decoupling". For mathe- matical and graphical analysis we take α i.e., gravitational decoupling constant and λ i.e., parameter of Rastall as free parameter. The compactness factor which describes the general relativity is taken as 0.2. Besides, in order to get more realistic picture, it requires to bound the parameters α and λ both through the use of real observational data to get the limits of the theory under this model. This methodology suggested to study the applications of neutron and quark stars. Our work also deals with the extended minimal geometric deformation. ixIn this section we check how temporal component effects the value of total en- ergy density, total redial and tangential pressure, anisotropy of pressure, energy conditions and stability conditions. For this we again use famous Tolman VII solution for the values of ν and µ and check the results. The metric potential of this solution is in the form of exponent, hence we use the rules function (ln) to get the suitable values of components. This section show very interesting results as we will discuss in chapter 3 in detail.Item Dynamical Analysis of Self-gravitating Cylindrical Objects in f (R, T ) Gravity(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Hina Azmat; FA15-RMT-010; Dr. Muhammad Zubair; LHR TP 6823The exploration of stability or instability range in modified theories provide deep insight of gravitational interaction in current era which is based on the ex pansion of the universe. In this thesis, we have analyzed cylindrically symmet ric self-gravitating objects for stability analysis within the framework of f(R,T) gravity. This alternative theory provides substitute to dark energy (DE) which assumes high negative pressure and is considered to be responsible for cosmic expansion. In this discussion, we have considered cylindrically symmetric systems with anisotropic matter distribution. The modified field equations and dynamical equations are constructed in f(R,T) theory of gravity. First order perturbation is applied on the modified field equations and dynamical equations which facil itates the construction of the collapse equation. Instability ranges are explored in both Newtonian(N)andpost-Newtonian(pN)eraswiththehelpofadiabetic index Γ which measures the pressure variation with changing energy density. Some conditions are imposed on material variables that are required for stable configuration. Cylindrically symmetric sources evolving under expansion-free condition are analyzed with locally anisotropic distribution . The collapse equation of cylin drical star is obtained by adopting perturbation approach for general solutions of gravitational field equations and conservation equations. Dynamical insta bility is discussed in N and pN regimes, stability constraints have also been ix developed. The adiabatic index ‘Γ’ is found to be meaningless for the discus sion of stability of gravitating sources carrying expansion-free condition, while stability variations are determined by physical properties of the fluid. Stability analysis for shearing viscous anisotropic fluid with cylindrical symmetry has also been made in f(R,T) theoryItem Stellar Structures in modified gravity based on Karmarkar Condition(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Allah Ditta; FA18-RMT-045; LHR TP 6025; Dr. Muhammad ZubairUniverse expansion has been a hot topic of discussion since the last decade. Not long ago, it remained in discussion under ways of interest like, radiation era ( early-time expansion) also known inflationary (rapid expansion) era, late time cosmic expansion (dark energy) era etc. Thesis understudy discusses the acceleration phenomenon of the Universe in cosmology by narrating different configurations of compactobjects bytakingintoaccountthefluidofanisotropic. Here we use f(T) gravity, which is originally a real and approximate modifica tion of TEGR. We carry our study with a well-known models f(T) = βTn and f(T) = T − α (T 6 )m1 + β(T 6 )m2 of f(T) gravity where T is torsion scalar, α, β are real constant, and n,m1,m2 are integers greater or equal to 2. For the con struction of stellar structures, we use spherically symmetric space-time as it is considerably near to nature. Embedding class one approach which is famous as Karmarkar condition is a useful technique to evaluate the metric components. This techniquelinks bothofthepotentialcomponentsofthemetricfunctioninto a unified differential equation. We assume the grr component of the space-time with the required potential. Using the Karmarker condition, one can fond the gtt component of metric function by solving the differential equation which links the gravitational metric potentials. We calculate the values of constants used in modeling by comparison of interior and exterior space-times through junc tion condition. For this motive, we utilize the observed data of compact star PSRJ1614-2230 for values of radius and mass. We ensure the stability and vi ability of our model through a detailed and comprehensive inspection of TOV ix equation, EOS, speeds of sound, casualty conditions, Redshift, compactness, and mass function graphically.Item Deviation of Rotating Black Hole in Loop Quantum Gravity from Kerr Black Hole(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) MADIHA KANWAL; CIIT/FA20-BSM-041/LHR; Dr. Muhammad Zubair; LHR TP 9916First and foremost, I would like to thank ALLAH Almighty (the most beneficent and most merciful) for giving me the strength, knowledge, ability and opportunity to undertake this research study and to preserve and complete it satisfactorily. My heartiest gratitude to Hazrat Muhammad (S.A.W) for His guidance to humanity and for material and spiritual uplift. I would like to express my deepest gratitude to my supervisor Dr. Muhammad Zubair, for his excellent guidance, interest, patience, and for providing me a decent atmo- sphere for the research. It was not an easy task but his extraordinary support made it so. I am also thankful to my senior research fellow Muhammad Ali Raza (PhD student) who always taught me with his humble attitude and with whom I collaborated and learned many things. Lastly, I would like to thank my parents and siblings, who always supported me and prayed for my success. Without their support, love and efforts, I would have not achieved all this. They gave me wings to fly.