Declaration I, Sagar Dey, declare that the work embodied in this thesis is my own bona fide work and carried out by me under the supervision of Prof. (Dr.) Bikash Chandra Paul from June 2017 to June 2022 at the Department of Physics, University of North Bengal, Darjeeling, Siliguri. The matter embodied in this thesis has not been submitted for the award of any other degree/diploma. I declare that I have faithfully acknowledged and given credits to the research workers whenever and wherever their works have been cited in my work in this thesis. I further declare that I have not will fully copied any others’ work, paragraphs, text, data, results, etc., reported in journals, books, magazines, reports dissertations, thesis, etc., or available at websites and have not included them in this thesis and have not cited as my own work. Date Signature Place (Sagar Dey) Acknowledgements The road to my Ph. D. was full of twists and turns, which made the experience even more unforgettable. It would have been difficult to convey my research findings in my thesis without the help of numerous people who were always there for me when I needed them. I owe a debt of thanks to a number of people for the work shown here, and I’d want to use this time to express my heartfelt gratitude to them for making this thesis possible. First and foremost, I convey my heartfelt gratitude to my supervisor, Dr. Bikash Chandra Paul, Professor, Department of Physics, University of North Bengal for his unwavering encouragement and support throughout my Ph.D. programme. In spite of his busy schedule of the academic and administrative responsibility as a Dean, PG Faculty of Science, NBU, he inspired me to carry out research work in new areas of theoretical astrophysics with great enthusiasm. To me, the most motivating source is his talent and persistence to execute any task with the utmost care. I owe him a debt of gratitude for teaching me the fundamentals of astrophysics and cosmology. Despite the fact that I was not a very gifted student, I was fortunate in that he allowed me to pursue my ambition under his direction and pushed me to pursue this line of research throughout my Ph.D. period. I have made several mistakes, and he, like a parent, has helped me understand my faults and conquer the difficulties. He is my philosopher and mentor in the best meaning of the word. My grand mother Late Rama Dey deserved special recognition for her unwavering support and unequivocal motivation that she had provided me throughout my life, as long as she was alive. This list would be incomplete without acknowledging my grand father Late Badal Dey, my father Mr. Biplab Dey, mother Mrs. Mita Dey, my pisi Mrs. Papri Dutta and cousins Ms. Payel Dutta and Mr. Sayan Dutta who are the sole pillars in my life and deserve all of the credit for all I have accomplished so far. A constant support from my parents made my path smooth in the difficult time. Mr. Anirban Chanda, a childhood friend who always advised me whenever I confronted a difficulty in my research work or official work, and always stood with me as a brother, deserves my deepest appreciation. I like to thank my senior researchers Dr. Arindam Saha, Dr. Souvik Ghosh, and my colleague Dr. Binay Rai for their invaluable assistance and support whenever I needed. I want to express my gratitude to Bibhas, Prabir and Bikash, my vi younger research scholars, for their assistance and valuable discussions. I am grateful to one of my didi, Dr. Prajnamita Dasgupta, and dadas, Dr. Shounak Ghosh and Dr. Amit Das, for their constant assistance, constructive recommendations and talks at various times, as well as collaboration and helps. I also like to thank all other friends, seniors and juniors of Physics Department whose names are not mentioned here to make the acknowledgement too lengthy one! I like to offer my profound gratitude to my teachers of the Physics Department, NBU for their advice. I like to thank my sir Mr. Dipesh Chanda and m’am Mrs. Basabdatta Bose, Physics Department, Siliguri College, for successfully instigating my inner desire to purse for ad- vance study when I was a graduate student. I acknowledge the help in learning mathematical procedures and calculations from Dr. Pradip Chattopadhyay of Cooch Behar Panchanan Barma University, Dr. Shyam Das of Malda College and Dr. Tamal Sarkar of North Bengal University. I’d also like to thank Rajesh Pradhan with computer-related technical issues. Non-teaching employees of the department namely Sarita di, Lubai da, Sudip da, Ayub da, late Rana and others, helped me lot during my Ph.D. A special mention and thank is due to Dr. Abhijit Deb of Cooch Behar Panchanan Barma University, Mr. Anirban Biswas and Mr. Sudeep Basu from University of North Bengal, Dr. Santanu Das from Surya Sen College, Dr. Suprakash Roy for their encouragement and valuable suggestions as seniors in my life. I am thankful to IUCAA Centre for Astronomy Research Development (ICARD), NBU for extending research facilities. I like to express my heartfelt gratitude to my friends Anup Das, Biswadip Roy Choudhury, Sudipta Das, Palash Basak, Arup Das, and Gourav Ghosh for their unconditional love, con- stant support and help during the journey. IUCAA, Pune brought another turning point in my research career. I did some of my research work in that august institution. I still cherish the warm welcome and facilities they had provided to me when I was a part of the IUCAA Visitor Student Program. IUCAA is a fantastic site to do research because of its calm and tranquil setting, as well as its modern facilities. I also want to express my gratitude to the University Grant Commission for award- ing UGC-NET fellowship. I appreciate the Almighty for providing me with the quality and tolerance to labour for these many years, allowing me to stand become now. I am heartily thankful to Mr. Utpal Paul, my school teacher of Physics, who made me realize the beauty of Physics through their wonderful teaching skill and make me more passionate about Physics in different stage of my study. During my M.Sc. and Ph.D. programmes, I will always cherish the beautiful scenery and environment-friendly lush green campus of North Bengal University, as well as the moments vii I spent here with my friends, seniors, and juniors. The affection of Rocky, my pet sprinkled to me is inexpressible in words. His unconditional love helped a lot when I used to become exhausted. Without all of them, this accomplishment would not have been possible. Obviously, thanking them is insufficient, but this is the simplest method for me to express my deep thanks! List of figures 1.1 Source: Hertzsprung–Russell diagram (HR Diagram) of Stars from "https: //www.eso.org/public/images/eso0728c/" . . . . . . . . . . . . . . . . . . . 2 2.1 Radial variation of E2 at the stellar interior of the pulsar Her X-1 for D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . 28 2.2 Radial variation of s at the stellar interior of the pulsar Her X-1 for D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . 29 2.3 Radial variation of energy-density (r) in Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) in the unit of GD (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Radial variation of pr in Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) in units of GD (considering a = 0.5) . . . . . . . 30 2.5 Radial variation of p? in Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) in units of GD (considering a = 0.5) . . . . . . . 30 2.6 Radial variation of D at the stellar interior of the pulsar Her X-1 for D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . 31 2.7 Variation of E2 (Black) and D (Red) inside Her X-1 with a for D = 5 (Solid Line), D = 6 (Dashed) and D = 7 (Dot Dashed) (considering b = 7.7 km.) . 31 2.8 Radial variation of v2 r at the stellar interior of the pulsar Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) 32 2.9 Radial variation of v2 ? at the stellar interior of the pulsar Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) 32 2.10 Behaviour of Gr at the stellar interior of the pulsar Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . 33 2.11 Behaviour of G? at the stellar interior of the pulsar Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . 34 2.12 Behaviour of NEC inside Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . . . . . . . . . . 34 List of figures xvi 2.13 Behaviour of WEC1 inside Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . . . . . . . . . . 35 2.14 Behaviour of WEC2 inside Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . . . . . . . . . . 35 2.15 Behaviour of SEC inside Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) for a = 0.5 . . . . . . . . . . . . . . . . . . . . 36 2.16 Radial variation of mass inside Her X-1 for D = 4 (Red), D = 5 (Black), D = 6 (Blue) and D = 7 (Green) (considering a = 0.5) . . . . . . . . . . . 36 2.17 Curve fitting of p⇤r with r⇤ in Her X-1 for D = 4 (Black), D = 5 (Red) . . . 39 2.18 Curve fitting of p⇤r with r⇤ in Her X-1 for D = 6 (Blue), D = 7 (Green) . . 40 3.1 Radial variation of energy-density of PSR J0348+0432 for b = 1 (Red), b = 2 (Black) and b = 3 (Blue) for a = 0.4 . . . . . . . . . . . . . . . . . 50 3.2 Variation of radial pressure with r of PSR J0348+0432 for b = 1 (Red), b = 2 (Black) and b = 3 (Blue) for a = 0.4 . . . . . . . . . . . . . . . . . 50 3.3 Variation of radial pressure with r of PSR J0348+0432 for a = 0 (Dot Dashed) and a 6= 0 (Red) . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Variation of transverse pressure with r of PSR J0348+0432 for b = 1 (Red), b = 2 (Black) and b = 3 (Blue) for a = 0.4 . . . . . . . . . . . . . . . . . 51 3.5 Variation of pr (solid line) and p? (dot dashed) with r of PSR J0348+0432 for b = 1 for a = 0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.6 Variation of the anisotropic parameter of PSR J0348+0432 for a = 0.4 . . . 52 3.7 Radial variation of v2 sr of PSR J0348+0432 . . . . . . . . . . . . . . . . . 53 3.8 Radial variation of v2 st of PSR J0348+0432 . . . . . . . . . . . . . . . . . 53 3.9 Radial variation of |v2 st � v2 sr| of PSR J0348+0432 . . . . . . . . . . . . . . 54 3.10 Variation of the mass function at the interior of a stellar object with r for PSR J0348+0432 with b = 1 and b1 = 0 . . . . . . . . . . . . . . . . . . 54 3.11 Variation of pr with r for PSR J0348+0432 with b = 1 (The Red solid line denotes quadratic fitting and the Blue dashed line denotes linear fitting) . . 55 3.12 Variation of energy-density (rc) with r for PSR J0348+0432 considering b = 1 and matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.13 Variation of radial pressure (prc) with r for PSR J0348+0432 considering b = 1 and matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.14 Variation of v2 rc with r for PSR J0348+0432 considering b = 1 and matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) . . 59 List of figures xvii 3.15 Variation of v2 tc with r for PSR J0348+0432 considering b = 1 and matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) . . 59 3.16 Variation of |v2 tc � v2 rc| with r for PSR J0348+0432 considering b = 1 and matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) 60 3.17 Variation of the anisotropic parameter (Dc) of PSR J0348+0432 with matter distribution following Chaplygin EoS for a = 0 (Blue) and a 6= 0 (Red) . . 60 4.1 Radial variation of energy-density (r) in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2 Radial variation of radial pressure (pr) in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3 Radial variation of radial pressure (pr) in PSR J0348+0432 for a = 0 (Gray), a = 0.1 (Yellow), a = 0.2 (Pink), a = 0.3 (Cyan), a = 0.4 (Brown) and a = 0.5 (Red) for c = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.4 Radial variation of transverse pressure (p?) in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.5 Radial variation of transverse pressure (p?) in PSR J0348+0432 for a = 0 (Gray), a = 0.1 (Yellow), a = 0.2 (Pink), a = 0.3 (Cyan), a = 0.4 (Brown) and a = 0.5 (Red) for c = 1 . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.6 Radial variation of anisotropy parameter (D) in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.7 Radial variation of v2 r in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . 75 4.8 Radial variation of v2 ? in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . 75 4.9 Radial variation of |v2 ?� v2 r | in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.10 Radial variation of Gr in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple), c = 10 (Black), c = 1 (Red, Dotted) and c = 3 (Blue, Dotted) for a = 0.5 [Sky Blue Line for 4 3 limit] . . . . . . . . 76 List of figures xviii 4.11 Radial variation of G? in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple), c = 10 (Black),c = 1 (Red, Dotted) and c = 3 (Blue, Dotted) for a = 0.5 [Brown Line for 4 3 limit] . . . . . . . . . 77 4.12 WEC 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.13 WEC 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.14 DEC 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.15 DEC 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.16 SEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.17 Mass - Radius relation in PSR J0348+0432 c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . 79 4.18 EoS in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5) . . . . . . . . . . 81 4.19 Mass - Radius relation in PSR J0348+0432 for c = 1 (Blue) and c = 3 (Green), c = 5 (Black), c = 7 (Red), c = 10 (Grey) taking a = 0.5 [Here, in Lower portion: Fg (Solid), Fc (Dot Dashed) and in Upper portion: Fa (Dashed), Fh (Dotted)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.20 Compactification factor in PSR J0348+0432 for c = 1 (Red), c = 3 (Blue), c = 5 (Green), c = 7 (Purple) and c = 10 (Black) (considering a = 0.5,Brown Line for Buchdahl limit) . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.1 Variation of r in PSR J0348+0432 for different a values taking Bg = 60 MeV/fm3 (a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2 Variation of pr in PSR J0348+0432 for different a values taking Bg = 60 MeV/fm3 (a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3 Radial variation of anisotropic stress factor in PSR J0348+0432 for different a values taking Bg = 60MeV/ f m3 (a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . 92 5.4 Radial variation of radial speed of sound v2 r (dashed line) and transverse speed of sound v2 ? (solid line, dotted line) in PSR J0348+0432 for different a values taking Bg = 60MeV/ f m3 (a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . 93 List of figures xix 5.5 Radial variation of |v2 ?�v2 r | in PSR J0348+0432 for different a values taking Bg = 60MeV/ f m3 (a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.6 Radial variation of G for different a in PSR J0348+0432 taking Bg = 60MeV/ f m3 in D = 5 dimensions.(a = 0 (Blue) , a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)). . . . . . . . . . . . . . . . . . . . . . . . 94 5.7 WECr (Upper left), WEC? (Upper Middle), SEC (Upper right), DECr (Lower left) DEC? (Upper middle) for different a in PSR J0348+0432 taking Bg = 60MeV/ f m3 in D = 5 dimensions. (a = 0 (Blue), a = 0.5 (Black), a = 1.0 (Red), a = 3.0 (Green), a =�0.5 (Black, Dotted), a =�1.0 (Red, Dotted) and a =�3.0 (Green, Dotted)) . . . . . . . . . . . . . . . . . . . 95 5.8 TOV relation in PSR J0348+0432. The blue, black, red and green line for a = 0, a = 0.5, a = 1.0 and a = 3.0, respectively for Bg = 60MeV/ f m3 with different values of R given in Table 1 [Here, Fg (DotDashed), Fa (Soild) and Fh (Dashed)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.9 Radial variation of Mass. The purple, blue, red, black and green line for a = 0, a = 0.01, a = 0.5, a = 1.0 and a = 3.0, a =�0.5 (Black, Dotted), a = �1.0 (Red, Dotted) and a = �3.0 (Green, Dotted) respectively for Bg = 60 MeV/ f m3 with different values of R taken form Table I . . . . . . 96 6.1 Shadow cast by Lovelock black hole at qi = p/2 for different dimensions (D) taking a 0 = 1 and µ = 0.35 without plasma (k = 0). . . . . . . . . . . . . 111 6.2 Shadow cast by Lovelock black hole at qi = p/2 for different dimensions (D) taking a 0 = 1 and µ = 0.35 with plasma (k 6= 0). . . . . . . . . . . . . . . 112 6.3 Shadow cast by Lovelock black hole at qi = p/2 for different mass parameter (µ) taking a 0 = 1 in D = 6 dimensions without plasma (k = 0). . . . . . . . 113 6.4 Shadow cast by Lovelock black hole at qi = p/2 for different mass parameter (µ) taking a 0 = 1 in D = 6 dimensions with plasma (k 6= 0). . . . . . . . . 114 6.5 Shadow cast by Lovelock black hole at qi = p/2 for different Lovelock parameter (a 0) taking µ = 0.4 in D = 6 dimensions without plasma (k = 0). 115 6.6 Shadow cast by Lovelock black hole at qi = p/2 for different Lovelock parameter (a 0) taking µ = 0.4 in D = 6 dimensions with plasma (k 6= 0). . 116 6.7 Variation of energy emission rate with frequency (w) for different dimensions117 6.8 Variation of energy emission rate with frequency (w) with plasma (k 6= 0) and without plasma (k = 0) in D = 6 dimensions. . . . . . . . . . . . . . . 118 List of tables 2.1 Different values of parameters A, B, C for Her X-1 (considering a = 0.5) . 37 2.2 Different values of parameters A, B, C for PSR J0348+0432 (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3 Different values of parameters A, B, C in D = 4 and D = 5 for pulsar Her X-1 (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4 Different values of parameters A, B, C in D= 4 and D= 5 for PSR J0348+0432 (considering a = 0.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5 Predicted EoS for Her X-1 in different dimensions (considering a = 0.5) . 39 3.1 Parameter values for different known compact objects with a = 0.4 and b = 1 62 3.2 Values of different physical parameters considring different values of the model parameter b for PSR J0348+0432 . . . . . . . . . . . . . . . . . . 62 3.3 Parameter values for different known compact objects for matter distribution following Chaplygin EoS for a 6= 0 ( b = 1, b1 = 0 and g = 1) . . . . . . 62 3.4 Parameter values for different known compact objects for matter distribution following Chaplygin EoS for a = 0 ( b = 1, b1 = 0 and g = 1) . . . . . . 63 4.1 Different model parameters for a variation of compactness factor of PSR J0348+0432 in modified gravity taking c = 1 and a = 0.5 . . . . . . . . . 79 4.2 Physical parameters for PSR J0348+0432 in f (R,T ) gravity for different c values with best fitted C = 0.009664 and a = 0.5. . . . . . . . . . . . . . . 80 4.3 Best fitted values of model parameters for different known compact object taking a = 0.5 and c = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.1 Numerical values of the physical parameters for the strange star candidate PSR J0348+0432 having mass 2.01±0.04 M� due to the different values of a in D = 5 dimensions where R is the metric parameter. . . . . . . . . . . . 97 5.2 Numerical values of the physical parameters for PSR J0348+0432 having mass 2.01±0.04 M� with a < 0 in D = 6 dimensions . . . . . . . . . . . . 97 List of tables xxi 5.3 Best fitted values of model parameters for different known compact object in D = 5 dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.1 Radius of the black hole shadow (Rs) and photon sphere radius (rp) for different dimensions (D) in Lovelock black holes. . . . . . . . . . . . . . . 119