Home Page of Prof G S Khadekar

1. Research: General Relativity and Cosmology, high energy physics in

various dimensions and Alternative theories of Gravitation

A. General Relativity:

(i) Higher dimensional problems in general Relativity

(ii) Dark energy, conformal motion, stars model

B. Cosmology:

(i) Cosmological Models of the Universe: RW, Banchi type –I , II and V model with Kantowski –

Sachs model of the Universe

C. Other theories:

(i) Bimetric theory of Relativity

(II) Kaluza-Klein theory of gravitation

(iii) Variable speed light theory (VSL theory)

(iv) (2+1) –dimensional Gravity

Current Position

Professor and Head at Post graduate

Teaching Department of Mathematics.

Rashtrasant Tukadoji Maharaj, Nagpur

University, Nagpur

Postal: Post graduate Teaching Department of

Mathematics. Rashtrasant Tukadoji Maharaj, Nagpur

University, Mahatama Jyotiba Phule Educational

Campus, Amravati Road, Nagpur-44-0033 (M.S.),

India

Email: gkhadekar@yahoo.com,

gkhadekar@rediffmail.com, gkhadekar@gmail.com

Phone: (Cell) 09011323123, (office): 0712-

2042089,(home):0712-2239461

Dr. G S Khadekar

Professor and Head

My main area of research is the study of some cosmological model in an alternatives theories of

gravitation. The universe is accelerating, but the truth of the matter is that we don't know exactly what

the rate of acceleration is. As time goes on, distant galaxies will recede from us (and us from them) at

an exponentially expanding rate. A cosmological constant (w=-1) will change the universe as a whole,

but on the individual galaxy scale, nothing particularly terrible will happen for a very long time. From

the last three year we are working on future singularity in the universe. In our current understanding,

there are four fundamental interactions (“forces”) in nature: Electromagnetism, weak and strong

nuclear forces, and gravity. Unification has also give rise to predictions successfully verified by

experiments. This is the case of electromagnetism and the weak nuclear force, once formulated in terms

of the electroweak model of Weinberg and Salam. Thus, pursuing this strategy so as to include the

remaining interactions has been a guide to propose new models in theoretical physics.

A particularly interesting proposal, as old as General Relativity, concerns the unification of

electromagnetism and gravity, so that electromagnetism appears as “the shadow” of a single

gravitational field formulated in a higher-dimensional space-time. In this model, the extra dimensions

are supposed to be extremely curled up in such a way that one cannot perceive them in daily

experience, as it is hard to distinguish an extremely thin cylinder (of two-dimensions) from one-

dimensional line. Even though this proposal runs into conflict with observation, its aesthetic appeal has

recently received serious consideration in different seemingly consistent scenarios.

Currently we are working on Freidmen equations by considering the a universe media as a bulk

viscosity described by modified equation of sate and going to build the dark energy and dark matter

model of the universe.

Our universe filled with viscosity media, therefore the cosmological problems based on imperfect fluid

is proposed reasonably due to the observed cosmic accelerating expansion. We emphasize that the

perfect fluid is just a limit of a general viscosity media that is more practical in astrophysics sense.

Because viscosity media seems to relate the matter sector to the geometric gravity side via the Einstein

field equations. With the available and recently up-coming high quality and increasingly large amount

of astrophysical observational data, specially the good low red-shift SNe Ia data sets with less

uncertainty for possible errors we except the one decade old mysterious dark energy problem will be

compared with the long time standing unsolved dark matter and mystery.

In particular we calculated the problems related to the Big Rip, sudden and generalized sudden

singularity in the universe in the framework of Kaluza-Klein theory of gravitation.

2. Teaching experience 28 years

I have taught virtually all the basic courses in Mathematics for B.Sc. Level at Kamal Nehru

Mahavidyalaya, Nagpur during 1988-1990. I have also taught Engineering Mathematics, Numerical

Methods, Probability theory during 1999-2000, at PCOE, Nagpur and VNIT, Nagpur. I have currently

taught General Relativity and Cosmology and Mathematical Methods, Classical Mechanics for post

graduate students at RTM Nagpur University, Nagpur from 2000 to still date.

3. Ph.D. Supervisor: In two discipline (i) Mathematics and Theoretical Physics

4. Ph.D. Produced: 16 [12 in Mathematics and (4) in Theoretical Physics]

5. M.Phil. :03

5. Research Project Completed: (3) Three

6. Coordinator: Mathematics, RTM Nagpur University, Nagpur

7. Member of Learned Societies:

Indian Society of Technical Education, New Delhi (Life Member No.M 37867 since 22/9/1993

Board of Studies of Mathematics Amravati, University, Amravati Since 1995

Board of Studies of Mathematics RTM Nagpur University, Nagpur Since 2006

Nagpur University Teachers Organization

Indian Academy of Mathematics, Indor, INDIA

International Society of General Relativity and Gravitation (U.K)

Internal Quality Assurance Cells (IQAC) RTM Nagpur University, Nagpur

Interconnectivity under UGC info net programme RTM Nagpur University, Nagpur

University with Potential Excellence (UPE), RTM Nagpur University, Nagpur

NAAC, RTM Nagpur University, Nagpur

Statistical Cell, RTM Nagpur University, Nagpur

Research Recognition Committee (RRC), Swami Ramanand Trirth Marathwada University

(SRTM), Nanded (M.S.)

Academic Council, RTM Nagpur University, Nagpur

Research Recognition Committee (RRC), RTM Nagpur University, Nagpur

9. Visiting Fellow: (i) International Center for Theoretical Physics, Trieste, Italy

(ii) IUCAA, Pune

(iii) TIFR, Mumbai

(iv) HRI, Allahabad

(vii) Abant Izeet Baysal University, Bolu, Turkey

10. Conference Organized: (i) International (2) and National (4)

11. Participation in Conference/ Workshop/ Symposium:

(i) International (Abroad): 15

(ii) National/International (Inland) : 45

12. Lecture delivered

(i) Invited talks: 30

(ii) Guest lecture :20

(iii) Paper presentation National /International Conference: 30

(iv) Popular talks on Mathematics : (03)

13. Distinctions/Awards/Scholarship Received

1. Awarded Foreign Travel Grant from Council of Scientific and Industrial Research (CSIR), Govt. of

India Grant No. : 27/209/67/2002-ISTAD14

2. Awarded Foreign Travel Grant from Department of Science and Technology (DST), New Delhi,

India Grant No. SR/PF/106/2002-2003

3. Awarded Foreign Travel Grant from University Grant Commission (UGC), New Delhi, India Grant

No. Dev/Pa/309, 2002

4. Awarded Foreign Travel Grant from Council of Scientific and Industrial Research (CSIR), Govt. of

India Grant No. : 22/IA/PFA/61/2007, Dated 23/05/2007

5. Awarded Foreign Travel Grant from Department of Science and Technology (DST), New Delhi,

India Grant No. SR/PF/402/2007-2008, dated 31/05/2007.

6. Awarded Foreign Travel Grant from University Grant Commission (UGC), New Delhi, India Grant

No.Dev./SSS/580, dated 27/07/2007.

7. Awarded Foreign Travel Grant from Indian National Science Academy (INSA), Govt. of India Grant

No. : NBS/2007, dated 16/05/2007

8. Awarded Foreign Travel Grant from Indian National Science Academy (INSA), Govt. of India Grant

No. : SS/INSA/2012/773, dated 14/06/2012

9. Awarded Foreign Travel Grant from Council of Scientific and Industrial Research (CSIR), Govt. of

India Grant No. : PFA/1141/12-HRD, Dated 18/05/2012.

14. Associate:

Indian Institute of Mathematical Sciences (I I M Sc), Chennai, since 2006 to 2008

15. Academic Association with Indian Research Institute:-

1. Visited Center for theoretical Studies (CTS), I I T , Kharagpur, Nov. 12-20, 2000 to consult the

library and interaction with faculty

2. Visited Center for Theoretical Studies (CTS), I I T Kharagpur, Nov. 17 to 1st Dec., 2001

3. Visited Inter University Center for Astronomy and Astrophysics, (IUCAA) Pune, Feb. 15-28, 2002

4. Visited Inter University Center for Astronomy and Astrophysics, (IUCAA) Pune, during Nov. 7-17,

2002

5. Visited Harish Chandra Research Institute (HRI), Allahabad (INDIA), May 18-24 2003 for research

collaboration

6. Visited Harish Chandra Research Institute (HRI), Allahabad (INDIA), May 10 to June 2, 2004

7. Visited Harish Chandra Research Institute (HRI), Allahabad (INDIA), May 15 to June 15, 2005

8. Visited Indian Institute of Mathematical Sciences (IIMSc), Chennai, May 25 to June 12, 2006 under

Associateship programme

9. Visited Indian Institute of Mathematical Sciences (I I M Sc), Chennai, May 20 to June 5, 2007 under

Associateship programme for research interaction and library reference work.

10. Visited Indian Institute of Mathematical Sciences (I I M Sc), Chennai, May 18-28, 2008 under

Associateship programme for research interaction and library reference work

11. Visited Department of Mathematics, Jadhavpur University, Kolkata, Jan. 7-11, 2012 under Special

Assistance Programme (SAP) for research interaction and library reference work and discussion with

the faculties.

12. Visited Inter University Center for Astronomy and Astrophysics, (IUCAA) Pune, March 20-22, 2012

under Special Assistance Programme (SAP) for research interaction and library reference work and

discussion with the faculties.

13. Visited Tata Institute of Fundamental Research Center (TIFR), Mumbai, May 20-23, 2013 under

Special Assistance Programme (SAP) for research interaction and library reference work and

discussion with the faculties.

14. Visited Mumbai University, Mumbai,Jan. 1-4, 2015 under Special Assistance Programme (SAP) for

research interaction and library reference work and discussion with the faculties.

15. Visited Tata Institute of Fundamental Research Center (TIFR), Mumbai, Jan. 4-6, 2015 under

Special Assistance Programme (SAP) for research interaction and library reference work and

discussion with the faculties.

16. Visited Tata Institute of Fundamental Research Center (TIFR), Mumbai, May 20-23, 2013 under

Special Assistance Programme (SAP) for research interaction and library reference work and

discussion with the faculties.

17. Visited Inter University Center for Astronomy and Astrophysics, (IUCAA) Pune, Feb. 11-15, 2015,

under Special Assistance Programme (SAP) for research interaction and library reference work and

discussion with the faculties.

18. Visited Inter University Center for Astronomy and Astrophysics, TIFR CAM, Banglore Jan. 4-7,

2016, under Special Assistance Programme (SAP) for research interaction and library reference work

and discussion with the faculties.

16. Book written: (i) Advance Mechanics (For Post graduate student)

(ii) General Theory of Relativity

17. Member of Editorial Board: (i) Journal of Dynamical System and Geometric Theories,

published by Taylor and Francis

(ii) Open Astronomy Journal published from USA

(iii) CLIFFORD ANALYSIS, CLIFFORD ALGEBRAS AND

THEIR APPLICATIONS: CACAA - www.cliffordanalysis.com

18.Referee of the Journals: Classical Quantum Gravity (CQG)

Physical Review D (PRD)

International Journal of Modern Physics A and D (Singapore)

Astrophysics and Space Science, (Netherlands)}

Journal of Dynamical System and Geometric Theories

International Journal of Modern Physics Letter A (Singapore)

Chinees Physics letter ( IOP Journal)

International Journal of Theoretical Physics (IJTP) (London, UK)

Fizica B

13. Visited to the Country: USA, Russia, Francs, Turkey, Iran, Italy, Germany, UK.

14. Research Paper Published: (i) International Refereed Journal (50)

(ii) National Refereed Journal (09)

(iii) Conference Proceedings (3)

List of Publication:

International Refereed Journals

Year 2015

1. FRW viscous Cosmology with Inhomogeneous Equation of State and Future singulaity

By G S Khadekar, Deepti Raut and V G Miskin, Modern Phys. Lett. A, Vol. 30, No.29 pp. 1550144

(2015)

2. Bulk viscosity in Friedmann universe with a varying speed of light described by modified equation of

state

By G S Khadekar and Arti Raut: Int. J. Geometric Methods in Mod. Phys. Modern Phys. Vol. 12, pp.

1550126 (2015)

3. Inhomogeneous early viscous fluid universe: a concrete model for dark energy

By G S Khadekar: Int. J. Geometric Methods in Mod. Phys. Modern Phys. (in press)(2015)

4. Holography in (2+1)-dimensional cosmological model with generalized

equation of state, By G S Khadekar: International Journal of Theoretical Physics, (2015) (in press)

5.Casimir Effect Near the Future Singularity in Kaluza Klein Viscous Cosmology

By G S Khadekar, International Journal of Theoretical Physics, (2015) (in press)

6. Kaluza-Klein Type Cosmological Model with Dependent Cosmological Constant and Big Rip

Singularity, G S Khadekar with Rupalim Wanjari: Journal of Dynamical System and Geometric

Theories (JDSGT) (Publisher: Taylor & Francis), Vol.13, No.1, 43-50, (2015).

7. Noncommutative geometry Inspired Wormhole with Conformal Motion

By G S Khadekar, R Rahaman, Saibal Ray, P K F Kuhtting and I. Karar: International Journal of

Theoretical Physics, Vol. 54, p.699 (2015)

8. Higher dimensional inhomogeneous spherical symmetric models with linear equation of state and

varying cosmological term

By G S Khadekar and Rajani Shelote : Cliord Analysis, Cliord Algebra and their Applications, Vol. 4,

No. 2, pp. 131-140, (2015) (CSP - Cambridge, UK; I&S -Florida, USA.)

9. Flat Friedman-Robertson-Walker model in the varying speed of light theory

By G S Khadekar and V.G.Miskin: CliordAnalysis, Cliord Algebra and their Applications, Vol.

4, No. 2, pp. 151-159, (2015) (CSP - Cambridge, UK; I&S -Florida, USA.)

10. (2 + 1)-Dimensional viscous cosmological models with variable G and Lambda

By G S Khadekar and N V Gharad: Cliord Analysis, Cliord Algebra and their Applications, Vol.

4, No. 2, pp. 161-166, 2015 (CSP - Cambridge, UK; I&S - Florida, USA)

Year 2014

11. Isotropic and Anisotropic Charged Spheres Admitting One parameter

Group of Conformal Motions in Higher Dimensional Space:

By G S Khadekar, Saroj Khumbhare: Cliord Analysis, Cliord Algebra and their Applications, Vol.

3, No. 4, pp. 307-322, ( 2014) (CSP - Cambridge, UK; I&S -Florida, USA, (2014)

12. Big Rip Singularity in 5D Viscous Cosmology

By G S Khadekar, N V Gharad: Inte. The Open Astronomy Journal, Vol . 7, p 7-1, (2014).

13. Higher Dimensional Varying c Cosmological Model with M-dependent Cosmological Constant

By G S Khadekar, Rupali Wanjari: The African Review of Physics. Vol. 9, 299 (2014)

Year 2013

14. Implication of Time Varying Cosmological Constant on Kaluza-Klien Cosmological

Model:

By G S Khadekar, Namrata Jain, S S Bhoga: Inte. J. Theo. Phys. Vol. 52, 4416, (2013)

15. Kaluza-Klien Cosmological Model with String, SQM and Time varying $\Lambda$

By G S Khadekar, Namrata Jain, S S Bhoga: ARPN Jouranal of Sci. and Technology Vol.3, No.6, 647,

(2013)

Year 2012

16. Geometry of Quark and Strange Quark Matter in Higher Dimensional General Realtivity

By G S Khadekar, Rupali Wanjari: Inte. J. Theo. Phys. Vol. 51, 1408, (2012)

17. Higher Dimensional Cosmological Model with Quark and Strange Quark Matter

By G S Khadekar, Rajani Shelote: Inte. J. Theo. Phys. Vol. 51, 1442, (2012)

Year 2010

18. Kaluza-Klein Type Cosmological Model with Strange Quark Matter

By G S Khadekar, Cenap Ozel and H•unkar Kayhan: Adv. Studies Theor. Phys., Vol. 4, no. 3, 117 -

128, (2010)

Year 2009

19. Higher Dimensional CDM Universe: A Phenomenological Approach with many possibilities

By G S Khadekar, Vaishali Kamdi and Cenap Ozel: Inte. J. Theo. Phys. (IJTP) Vol.48, 373, (2009)

20. Domain Wall with Strange Quark Matter in Kaluza Klien Type Cosmological Model

By G S Khadekar, Rupali Wanjari: Inte. J. Theo. Phys. (IJTP) Vol.48, 2550, (2009)

21. Higher Dimensional Cosmological Model of the Universe with time dependent equation of state

G S Khadekar with Rajani Shelote: Journal of Dynamical System and Geometric Theories (JDSGT),

Vol.7, No.2, 125-135, (2009).

22. Cosmological Model of the Universe with Viscous Fluid in Kaluza-Klein Theory of Gravitaion

G S Khadekar with Bhavana Butey: Journal of Dynamical System and Geometric Theories (JDSGT),

(Publisher: Taylor & Francis), Vol.7, No.1, 91-99, (2009).

23. Cosmological Model of the Universe withViscous Fluid in Kaluza-Klein Theory of Gravitaion

G S Khadekar with Bhavana Butey: Journal of Dynamical System and Geometric Theories (JDSGT),

(Publisher: Taylor & Francis), Vol.7, No.1, 91-99, (2009).

Year 2008

24. Higher Dimensional Exact solutions for a charged Fluid Sphere in General Theory of Relativity

By G S Khadekar and P D Shobhane: Astrophysics and Space Sci. vol.315, p. 307-317( 2008)

25. Early viscous universe with variable cosmological and gravitational constants in higher

dimensional space time

By G S Khadekar, Gopal Kondawar, Vaishali Kamdi and Cenap Ozel: Inte. J. Theo. Phys. (IJTP) Vol.

47, 3057, (2008)

26. Higher dimensional unied description of early universe with Variable gravitational and

cosmological constants

By G S Khadekar, Gopal Kondawar, Vaishali Kamdi and Cenap Ozel: Inte. J. Theo. Phys. Vol. 47,

2444, (2008)

27. Early universe with variable cosmological constants in higher Dimensional space time

By G S Khadekar, Gopal Kondawar and Cenap Ozel: Inte. J. Theo. Phys. Vol.47, 1844, (2008)

28. Higher Dimensional Unified Description of Early Universe with Variable $G$ and $\Lambda$

G S Khadekar, B Sarada and Cenap Ozel: Inte. J. Theo. Phys. Vol. 47, 1542, (2008)

29. Kaluza-Klein Type Robertson Walker Cosmological Model With Dynamical Cosmological Term

$\Lambda$

By G S Khadekar, Vrushali Patki: Inte. J. Theo. Phys. Vol. 47, 1751, (2008)

30. Can Bianch Type-IICosmological Model with a Decay Law for Lambda term be Compatible with

Recent Observation?

By G S Khadekar and Pradhan Anirudha: Romanian Reports in Physics, Vol. 60, No. 1, P. 312, (2008)

Year 2007

31. Higher dimensional Starnge Quark Matter to the String Cloud with Electromagnetic Filed

Admitting One Parameter Group of Conrmal Motion

By Pradhan Anirudha , G S Khadekar, Mishra Mukesh Kumar and Saroj Kumbhare: Chin. Phys. Lett.

Vol. 24, No. 10, 1310 (2007)

32. String Cosmological Model with bulk viscosity in higher dimensional space time

G S Khadekar with Vrushali A. Patki and R Radha: Journal of Dynamical System and Geometric

Theories (JDSGT), (Publisher: Taylor & Francis), Vol.5, No.2, 117-123, (2007).

33. Anisotropic Spheres with Uniform energy density in Bimetric Theory of Relativity

By G S Khadekar and S D Tade: Astrophysics and Space Sci. Vol. 310, 41, (2007)

34. String Cosmological Models in Five Dimensional Bimetric Theory of Gravitation

By G S Khadekar and S D Tade: Astrophysics and Space Sci. Vol. 310, 47, (2007)

35. Five Dimensional Universe Model with Variable Cosmological Term Lambda and Big Bounce

By G S Khadekar and Vaishali Kamdi: Astrophysics and Space Sci. Vol. 310, 141, (2007)

36. Bianchi Type $VI_{1}$ Viscous fluid Cosmological Model in Wesson's Theory of Gravitation of

Gravitation

By G S Khadekar and G R Avachar: Turk J Phys. Vol. 31, 1, (2007)

37. Five dimensional cosmological Model with a time dependent equation of state in Wesson's theory of

gravitation

By G S Khadekar and G R Avachar: Astrophysics and Space Sci. Vol. 312, 311, (2007)

38. Cosmological Models with viscous fluid and Time dependent Equation of state in Wesson's Theory

By G S Khadekar and G R Avachar: Astrophysics and Space Sci. Vol. 310, 77, (2007)

Year 2006

39. Higher Dimensional Cosmological Implications of the Decay Law for $\Lambda$

term: Expressions for some observable quantities

By G S Khadekar, Anirudha Pradhan and Deepk Srivatsav: Astrophysics and Space Sci. Vol.305,415-

421, (2006)

40. Higher Dimensional Dust Cosmological Implications of the Decay Law for Lambda term:

Expressions for some observable quantities

By G S Khadekar, Anirudha Pradhan and M R Molaei: Inter.J.Mod.Phys.D (IJMPD) Vol.15, No.1, 95-

105, (2006).

41. On Top Spaces

By G S Khadekar, M R Molaei: Balkan Journal of Geometry and Its Applicatins Vol.11, No.1,

102-107, (2006).

42. Spherically symmetric static fluids in Rosen's bimetric theory of gravitation

G S Khadekar with G L Kondawar: Journal of Dynamical System and Geometric Theories (JDSGT),

(Publisher: Taylor & Francis), Vol.4, No.1, 95-102, (2006).

Year 2005

43. Exact Solutions for Charged Sphere in Rosen's Bimetric Theory of Gravitation

G S Khadekar: Journal of Dynamical System and Geometric Theories (JDSGT),(Publisher:

Taylor & Francis), Vol.3, No.1, 87-94, (2005).

44. String Dust Cosmological Model in Higher Dimensional Space-Time.

By G S Khadekar, Vrushali Patki and R.Radha: Inter.J.Mod.Phys.D (IJMPD) Vol.14, No 9, 1621-1634,

(2005)

Year 2004

45. Cosmological Solutions in Variable Rest Mass Theory of Gravitation.

By G S Khadekar Vrushali Patki and R.Radha: Fizika B Vol. 13, No.4,711-718, ( 2004)

46. Anisotropic fluid distribution in in Bimetric theory of Relativity

G S Khadekar with S P Kandalkar: Astrophysics and Space Sci.Vol. 293, p.415-422, (2004)

47. Mass Formulae for Spherically Symmetric Stellar Configurations in Five Dimension

G S Khadekar with K S Adhao and H R Ghate: Astrophysics Space Science Vol. 289 (1) p. 95- 101,

(2004).

Year 2003

48. Anisotropic fluid distribution in higher dimensional Rosen Theory of Gravitation

G S Khadekar with S P Kandalkar: Fizika B 12,257-266, (2003).

49. Bianchi Type -III Cosmological Model in Four and Five Dimensional Bimetric Theory of Relativity

G S Khadekar with K S Adhao and V G Mete, Astrophysics Space Sci. Vol. 295-, p.331-337, 2004

50. Higher Dimensional Exact Solution of Einstein's Field Equation For Massive Point Particle with

Scalar Point Charge

G S Khadekar with Megha Joshi, Aust. J. Phys. 51, 577-584, 1998.

National Refereed Journals

1. Cosmological Model with variable cosmological term in Kaluza-Klein theory

of gravitation

G S Khadekar with Shilpa Samdurkar: Indian Academy of Mathematics Vol.27, No2,p. 307-315, 2005

2. de-Sitter Type Cosmological Model in n-dimension Space-Time-Mass (STM)Theory

of gravitation

G S Khadekar with Vrushali Patki: Journal of Indian Academy of Mathematics Vol.27, No.1 p.123-

127, (2005)

3. String Cosmological Models in Higher dimensional Space Time

G S Khadekar with G R Avachar; Bull.Cal. Math. Sco.Vol.27, No.1 & 2 p.63-68, (2004)

4. Inhomogeneous Cosmological Model in (4+n) –dimensional Wesson's Theory of Gravitation

G S Khadekar with Shilpa Samdurkar: Bulletin of Pure and Applied Sciences (Vol.23E (No.1), p.105-

113, (2004)

5. Cosmological Model in ve dimensional Space Time Mass bimetric theory of Gravitation

G S Khadekar with Mohan Gaikwad: Indian Academy of Mathematics Vol.26, No2, p.407-410, (2004)

6. Exact solution of the field equations in higher dimensional bimetric theory of relativity

G S Khadekar with K S Adhav and H R Ghate: Journal of Indian Academy of Mathematics Vol.26,

No.1 p.167- 73, (2004)

7. Higher Dimensional Static Cosmological Model in Lyra Manifold

G S Khadekar, with Avinash Nagpure (gr-qc/0111096): Bulletin of Pure and Applied Sciences Vol.23E

(No.1)p.49-52, (2004)

Article published in book

1. Higher Dimensional Cosmological Model of the Universe with Variable Equation of state parameter

in the presence of $G$ and $\Lambda$-I

By G S Khadekar, Vaishali Kamdi and Vitthal Miskin

Aspect of Todays Cosmology, Edited by Antonio Alfonso-Faus, published by In Tech, page no. 173

(2011)

Article published in Conference Proceedings:

1. The Behavior of the Strange Quark Matter for FRW Model with Time Varying Constant

By G S Khadekar, Arti Ghogre: Theoretical Physics and Its Applications, Edited by T F Ka-

malov, published by Moscow State Open University, Russia, Page No. 92-102, (2013)

2. Higher Dimensional Cosmological Model of the Universe with Variable Equation of state parameter

in the presence of G and Lambda trem

By G S Khadekar, Vaishali Kamdi and Vitthal Miskin

AIP Conference Proceedings, Edited by C. Ozel and A. Kilicman, published by American Institute of

Physics, Page No. 578-589 (2010)

3. FRW Cosmological Model of the Universe with Strange Quark Matter and Varying G; c, and

Lambda

By G S Khadekar and Arti Ghogre: Proceedings of International Conference on Recent Advances in

Mathematics (ICRAM 2014)

Edited by K. C. Deshmukh, G S Khadekar, R V Saraykar, S H Ghate, M S Borkar and G D Kedar

and, published by Department of Mathematics Rashtrasant Tukadoji Maharaj Nagpur University,

Nagpur, Vol. 2 Page No. 238-249 (2014).