Browsing by Author "Dr. Muhammad Zubair"

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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 9576
Black 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.
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 Zubair
In 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.
Constraining the Newly Reconstructed f (Q, T ) Gravity Models Under the Recent Cosmic Domains
(Library Information Services, CUI Lahore, 2023) Muhammad Muzammal Khan; CIIT/FA21-RMT-070/LHR; Dr. Muhammad Zubair
The modified gravitational theories commonly known as MGTs performed very signifi- cant role in studying the sped-up stage of our Universe over past several decades. There have been several techniques which are proposed in modified theories to resolve the cosmic problem. Considering the Weyl geometry, we investigated the f (Q, T ) gravity, where Q is a non-metricity scalar and T as trace of energy momentum tensor (EMT). In this research we took into account the models of f (Q, T ) theory that are described as f (Q, T ) = β[(1 − α) + (1 + z)(α + zβ )] involving arbitrary parameters α, β and redshift z. Moreover, we studied the existence of their analytical solutions. In addi- tion, we determine the behavior of effective equation of state (EoS) parameter ω for every reconstructed solution of the models and examine the quintessence region of the Universe for ω
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 9916
First 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.
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 6823
The 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) theory
Dynamics of Stellar Structures in Curvature Based Gravitational Theories
(Library Information Services, CUI Lahore, 2022) Hina Azmat; FA18-PMT-002; Dr. Muhammad Zubair
The main objective of this thesis is to explore different astrophysical structures in the background of general relativity as well as in the framework of modified theories. Firstly, we discuss the minimal geometric deformation (MGD) decoupling approach to develop new exact anisotropic solutions for compact stellar systems in the absence as well as in the presence of the electromagnetic field. We consider two well-known solutions, namely Tolman V and charged Durgapal V, and extend them to anisotropic domains by transforming their radial metric functions. The physical analysis of the new interior anisotropic solutions is performed by examining the graphical behavior of energy conditions, equilibrium condition, causality condition, adiabatic index and gravitational redshift for different compact star candidates. Secondly, we develop two analytical models of ultra-compact stellar configurations with non-uniform anisotropic features in the framework of 𝑓(𝑅, 𝑇) theory. In order to introduce anisotropy in the system, we again consider gravitational decoupling by means of MGD and obtain two families of interior solutions for both charged and uncharged scenarios. Dark energy EoS is considered in the interior of the configuration. In the exterior region, we consider both standard vacuum and conformally deformed black hole solutions. The junction conditions at the stellar boundary for both charged and uncharged stellar sources are presented in detail. Some fundamental properties of a stable configuration including regularity at the center, positive energy density with monotonically decreasing behavior from the center outwards, and non-uniform pressure with the monotonic profile are checked for the new anisotropic solutions. Finally, the complexity analysis of non-static spherically and cylindrically symmetric self-gravitating sources surrounding in the locally anisotropic environment and suffering dissipation in the form of heat flux is presented in the light of 𝑓(𝑅, 𝑇) gravity. Our study is based on the definition of complexity for dynamical self-gravitating sources, proposed by Herrera et al. [68]. The scalar functions through the orthogonal splitting of the Riemann tensor are defined in 𝑓(𝑅, 𝑇) gravity, and structure scalars are worked out for both geometries. Our main objective is to analyze the behavior of
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 9378
Relativistic 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.
Exploring the Existence of Non-Commutative Wormholes in Scalar Tensor Theories
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) TAHREEM GHAFFAR; CIIT/SP20-RMT-008/LHR; Dr. Muhammad Zubair; LHR TP 7645
Scalar tensor theories appear as handy candidate to analyze the stellar objects like compact stars and wormholes. In this thesis, we have discussed about the non commutative spherically symmetric wormhole solutions in f(R, Φ) gravity. For this purpose, we consider two different frameworks such as Gaussian distri- bution as well as Lorentzian distribution non commutative geometry. With the help of Gaussian and Lorentzian distribution we have found the exact and nu- merical solutions of the non commutative wormhole’s in f(R, Φ) gravity. By con- sidering suitable values of the unknown parameters, we analyse the different characteristics of the wormhole’s models analytically as well as graphically.It has been observed that without involving any exotic material it is feasible to acquire wormhole’s solution in this theory.For this purpose ﬁrstly we consid- ered the different categories of ﬂuids i.e an isotropic, anisotropic and barotropic ﬂuids. For all these ﬂuids we analyzed the energy conditions to examine the f(R, Φ) gravity. To check the energy conditions we have calculated b(r) numer- ically as well as graphically in order to check whether the wormhole solutions exist or not. It has been concluded that the solution we obtained is idealistic. We have also analyzed the energy conditions (NEC and WEC) in detail. We have concluded that for the existence of non commutative wormhole’s solution these energy conditions are valid. And also for these cases, we observed that for anisotropic ﬂuid, realistic wormhole geometries can be constructed that satisfy the energy conditions. We ﬁnd the shape function which protects the worm- hole throat and enables us to discuss the requirement of exotic matter. We also analyze the energy constraints using the graphical schemes.
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 7437
In 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.
Generalized Study of Horizons, Photon Sphere and its Shadows in Rotating Black Holes
(Library Information Services, CUI Lahore, 2023) Eiman Maqsood; CIIT/FA21-RMT-025/LHR; Dr. Muhammad Zubair
In this thesis, we considered two static black holes, one in Kalb-Ramond gravity and the other in Bopp–Podolsky Electrodynamics. The metrics of the black holes have been discussed in a nutshell. The radius of photon sphere of both black holes have also been discussed. The photon sphere radius of hairy black hole in Bopp-Podolsky Electrodynamics is further used to study the linear radius of the black hole shadow, angular velocity and Lyapunov exponent. The center of mass energy of two colliding particles is then investigated. We converted the static black holes into rotating black holes by using Newman-Janis algorithm. These rotating metrics are then explored to study horizon structure using the numerical technique. Moreover, we construct the null geodesic equations and effective potential is investigated. In addition, a mathematical scheme is derived from the effective potential for calculating and plotting the shadows. The numerical results obtained for the shadows are used to study the distortion and energy emission rate. We obtained some interesting results and analyzed the effect of black hole parameters on the above mentioned properties. We find that the parameters corresponding to both black holes have a significant effect on the different properties mentioned above, especially, the shadow. Lastly, the parametric constraints are obtained for the black hole in Kalb-Ramond gravity.
Particle Creation with Adiabatic Transformation Through Thermodynamic Perspective in Modified Theories
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Mubashira Rasheed; FA17-RMT -014; Dr. Muhammad Zubair; LHR TP 5651
Modified gravitational theories play significant role to discuss many con stituent of the accelerated phase of our universe for last few decades. A large numberofdifferent techniques in modified theories are proposed to sort out the cosmological problem. Weanalyzedopenirreversiblethermodynamicsinthescenarioofparticle cre ation for modified theory of gravity known as f(G,T) gravity theory, in which the generic function defines the coupling between GB invariant G and trace of the EMT with non-zero divergence. We discussed the generalized conser vation equation which involves additional contribution from matter geome try coupling for irreversible matter creation process with the help of general ized "second law of thermodynamics" in the light of the “Friedmann-Lematre Robertson-Walker" FLRW space time. Particle creation rate, number of particle creation, creation pressure, entropy production rate, and temperature for this theory have been formulated by choosing some particular model of f(G,T), which help us to explore the particle creation in a significant way. We also discussed non-minimal F(R,T,Q) theory of gravity where (R, T, Q are ricci scalar, trace of EMT and interaction of Ricci tensor and non-minimal coupling of Ricci scalar respectively, and Q = RαβTαβ) is the interaction of Ricci tensor and EMT. Due to the non-minimal coupling of gravity and geometry an extra force present which is perpendicular to four velocity. We also formulated some explicit results of created particle from gravitational field to the created ix matter such as particle creation rate, pressure of created particle and entropy with respect to time variation through irreversible thermodynamics interrelated with adiabatic transformation in the context of FLRW space time. We consid ered the dust universe i.e., P = 0 and the scale factor by power law a(t) = tm to precise our results. It is observed that in this procedure a large amount of co-moving entropy has been generated
Some Cosmological Implications Of Extended Scalar
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Farzana Kousar; SP13-PmAth-006; Dr. Muhammad Zubair; LHR TP 5607
This thesis is devoted to explore some cosmological implications in gravity and generalized reconstruction of gravity. Initially, we discuss the cosmological theory (where , and represent the Ricci scalar, scalar invariant and scalar field) corresponding to power law and de Sitter evolution in the framework of FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some known forms of these conditions in general relativity, and theories. We also present the general constraints in terms of recent values of snap, jerk, deceleration and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively. First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in gravity. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for ̂ ̂ , where ̂ is an extra entropy term because of the non-equilibrium presentation of the equations and ̂ for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR, and gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters. Moreover, we examine static spherically symmetric wormhole solutions in generalized gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. From our results, one can conclude that for all three cases of fluids stable and realistic wormhole solutions can be constructed. Further, we have considered action which is non-minimally coupled to the x scalar field. In this context, we obtain the exact analytical solutions for inflationary era as well as find a graceful exit condition from inflation. We calculate the perturbed parameters, i.e., number of e-folds, slow-roll parameters, scalar and tensor power spectra, corresponding spectral indices and ultimately tensor to scalar ratio. It is showed that the power spectra lead to blue-tilt for this model. The trajectories of the perturbed parameters are plotted to compare the results with recent observations. Finally, we will discuss cosmological models using Bianchi type I for anisotropic fluid in theory of gravity which involves scalar potential. For this purpose, we consider power law assumptions of coupling function and scalar field along with the proportionality condition of expansion and shear scalars. We choose two models and obtain exact solutions of field equations in both cases. For these constructed models, the behavior of different physical quantities like EoS parameter, self-interacting potential as well as deceleration and skewness parameters is explored and illustrated graphically for the feasible ranges of free parameters. It is concluded that anisotropic fluid approaches to isotropy in later cosmic times for both models which is compatible with the observational data.
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 Zubair
Universe 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.