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A SECOND COUNTER-EXAMPLE FOR SHEAR-FREE PERFECT FLUID CONJECTURE IN F(R,T) GRAVITY

Year 2016, Volume: 18 Issue: 54, 317 - 332, 01.09.2016

Abstract

In this study, to find the second counter-example for shear-free perfect fluid conjecture in modified gravitation theories and to investigate whether similar solutions are valid for all Bianchi type metrics in f(R,T) gravity; spatially homogeneous and anisotropic, shear-free, rotating and expanding Bianchi type-II and V models have been considered in context of f(R,T) theory of gravity. An exact solution has been obtained, functional form of f(R,T) function has been reconstructed for Bianchi type-II model and it has been shown that the matter-energy content of such a universe is stiff fluid. It has also been shown that Bianchi type-V model filled with a shear-free perfect fluid cannot rotate and expand simultaneously

References

  • Gödel K. Rotating Universes in General Relativity Theory, Proceedings of the International Congress of Mathematicians, cilt.1, 1950, s.175-181; (yeniden basım: General Relativity and Gravitation, cilt.32, 2000, s.1419).
  • Ellis, GFR. Dynamics of Pressure-Free Matter in General Relativity, Journal of Mathematical Physics, Cilt.8, 1967, s.1171-1180.
  • Schücking E. Homogene Scherungsfreie Weltmodelle in der Relativistischen Kosmologie, Naturwiss, cilt.19, 1957, s.507.
  • Banerji S. Homogeneous Cosmological Models without Shear, Progress of Theoretical Physics, cilt.39, 1968, s.365-371.
  • Treciokas R, Ellis GFR. The Shear Dynamics, Communications in Mathematical Physics, cilt.23, 1971, s.1-17.
  • King AR, ELLIS GFR. Tilted Homogeneous Cosmological Models, Communications in Mathematical Physics, 1973, cilt.31, s.209-220.
  • White AJ. Collins CB., A Class of Shear-free Perfect Fluids in General Relativity I,
  • Journal of Mathematical Physics, cilt.25, 1984, s.332-337.
  • Collins CB. Shear‐free Perfect Fluids with Zero Magnetic Weyl Tensor, Journal of Mathematical Physics, cilt.25, 1984, 995-1000.
  • Carminati J. Shear-free perfect fluids in general relativity. I. Petrov type N Weyl tensor, Journal of Mathematical Physics, cilt.28, 1987, s.1848-1853.
  • Carminati J. Type N, Shear-free, Perfect Fluid Space-times with a Barotropic Equation of State, General Relativity and Gravitation, cilt.20, 1988, s.1239-1248.
  • Carminati J. Shear-free Perfect Fluids in General Relativity. II. Aligned, Petrov Type III Space-times, Journal of Mathematical Physics, cilt.31, 1990, 2434-2440.
  • Senovilla JMM, Sopuerta CF, Szekeres P. Theorems on Shear-free Perfect Fluids with Their Newtonian Analogues, General Relativity and Gravitation, cilt.30, 1998, s.389- 411.
  • Sopuerta CF. Covariant Study of a Conjecture on Shear-free Barotropic Perfect Fluids, Classical and Quantum Gravity, cilt.15, 1998, s.1043-1062.
  • Van den Bergh N. The Shear-free Perfect Fluid Conjecture, Classical and Quantum Gravity, cilt.16, 1999, s.1-13.
  • Van den Bergh N, Carminati J, Karimian HR. Shearfree Perfect Fluids with Solenoidal Magnetic Curvature and a Gamma-law Equation of State, Classical and Quantum Gravity, cilt.24, 2007, s.3735-3744.
  • Carminati J. Karimian HR, Van den Bergh N, Vu KT. Shear-free Perfect Fluids with a Solenoidal Magnetic Curvature, Classical and Quantum Gravity, cilt.26, 2009, 195002.
  • Herrera L, Di Prisco A, Ospino J. On the Stability of the Shear-free Condition, General Relativity and Gravitation, cilt.42, 2010, s.1585-1599.
  • Herrera L, Di Prisco A, Ospino J. Shear-free Axially Symmetric Dissipative Fluids, Physical Review D, cilt.89, 2014, s.127502.
  • Slobodeanu R. Shear-free Perfect Fluids with Linear Equation of State, Classical and Quantum Gravity, cilt.31, 2014, s.125012.
  • Van den Bergh N, Slobodeanu R. Shear-free Perfect Fluids with a Barotropic Equation of State in General Relativity: the Present Status, arXiv, [http://arxiv.org/abs/1510.05798], 2015, Erişim Tarihi: 25.10.2015.
  • Narlikar JV. Newtonian Universes with Shear and Rotation, Monthly Notices of the Royal Astronomical Society cilt.126, 1963, s.203.
  • Heckmann O, Schücking E. Handbuch der Physik LIII (ed) Flügge S. Berlin: Springer, 1959, s.489.
  • Sofuoğlu D, Mutuş H. Investigations of f(R)-Gravity Counterparts of the General Relativistic Shear-free Conjecture by Illustrative Examples, General Relativity and Gravitation, cilt.46, 2014, s.1-25.
  • Sofuoğlu D. Rotating and Expanding Bianchi Type-IX Model in f(R,T) Theory of Gravity, Astrophysics and Space Science, cilt.361, 2016, s.1-7.
  • Harko T, Lobo FSN, Nojiri S, Odintsov SD. f(R,T) Gravity, Physical Review D, cilt.84, 2011, s.024020.
  • Ellis GFR, Van Elst H. Cosmological Models (Cargese Lectures 1998), arXiv, [http://arxiv.org/abs/gr-qc/9812046], 1998, Erişim Tarihi: 17.11.2004.
  • Van Elst H, Uggla C. General Relativistic 1+3 Orthonormal Frame Approach, Classical and Quantum Gravity, cilt.14, 1997, s.2673-2695.
  • MacCallum MAH. “Anisotropic and Inhomogeneous Relativistic Cosmologies” in: General Relativity An Einstein Centenary Survey, (Ed.) Hawking SW, Israel W., Cambridge: Cambridge University Press, 1979, s.179-236 (Tablo 11.2, s.194).

F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK

Year 2016, Volume: 18 Issue: 54, 317 - 332, 01.09.2016

Abstract

Bu çalışmada, değiştirilmiş gravitasyon teorilerinde makaslamasız mükemmel akışkan iddiasına ikinci bir karşıt-örnek bulmak ve benzer çözümlerin f(R,T) gravitede tüm Bianchi tip metrikler için geçerli olup olmadığını incelemek amacıyla, f(R,T) gravitasyon teorisi çerçevesinde, uzayca homojen, eşyönsüz, makaslamasız, dönen ve genişleyen Bianchi tip-II ve V modelleri göz önüne alınmıştır. Bianchi tip-II modeli için kesin bir çözüm elde edilmiş, f(R,T) fonksiyonunun fonksiyonel formu inşa edilmiş ve böyle bir evrenin madde-enerji içeriğinin katı akışkan olduğu gösterilmiştir. Makaslamasız bir mükemmel akışkanla dolu Bianchi tip-V modelinin ise, aynı anda hem dönme ve hem de genişlemeye sahip olamayacağı gösterilmiştir

References

  • Gödel K. Rotating Universes in General Relativity Theory, Proceedings of the International Congress of Mathematicians, cilt.1, 1950, s.175-181; (yeniden basım: General Relativity and Gravitation, cilt.32, 2000, s.1419).
  • Ellis, GFR. Dynamics of Pressure-Free Matter in General Relativity, Journal of Mathematical Physics, Cilt.8, 1967, s.1171-1180.
  • Schücking E. Homogene Scherungsfreie Weltmodelle in der Relativistischen Kosmologie, Naturwiss, cilt.19, 1957, s.507.
  • Banerji S. Homogeneous Cosmological Models without Shear, Progress of Theoretical Physics, cilt.39, 1968, s.365-371.
  • Treciokas R, Ellis GFR. The Shear Dynamics, Communications in Mathematical Physics, cilt.23, 1971, s.1-17.
  • King AR, ELLIS GFR. Tilted Homogeneous Cosmological Models, Communications in Mathematical Physics, 1973, cilt.31, s.209-220.
  • White AJ. Collins CB., A Class of Shear-free Perfect Fluids in General Relativity I,
  • Journal of Mathematical Physics, cilt.25, 1984, s.332-337.
  • Collins CB. Shear‐free Perfect Fluids with Zero Magnetic Weyl Tensor, Journal of Mathematical Physics, cilt.25, 1984, 995-1000.
  • Carminati J. Shear-free perfect fluids in general relativity. I. Petrov type N Weyl tensor, Journal of Mathematical Physics, cilt.28, 1987, s.1848-1853.
  • Carminati J. Type N, Shear-free, Perfect Fluid Space-times with a Barotropic Equation of State, General Relativity and Gravitation, cilt.20, 1988, s.1239-1248.
  • Carminati J. Shear-free Perfect Fluids in General Relativity. II. Aligned, Petrov Type III Space-times, Journal of Mathematical Physics, cilt.31, 1990, 2434-2440.
  • Senovilla JMM, Sopuerta CF, Szekeres P. Theorems on Shear-free Perfect Fluids with Their Newtonian Analogues, General Relativity and Gravitation, cilt.30, 1998, s.389- 411.
  • Sopuerta CF. Covariant Study of a Conjecture on Shear-free Barotropic Perfect Fluids, Classical and Quantum Gravity, cilt.15, 1998, s.1043-1062.
  • Van den Bergh N. The Shear-free Perfect Fluid Conjecture, Classical and Quantum Gravity, cilt.16, 1999, s.1-13.
  • Van den Bergh N, Carminati J, Karimian HR. Shearfree Perfect Fluids with Solenoidal Magnetic Curvature and a Gamma-law Equation of State, Classical and Quantum Gravity, cilt.24, 2007, s.3735-3744.
  • Carminati J. Karimian HR, Van den Bergh N, Vu KT. Shear-free Perfect Fluids with a Solenoidal Magnetic Curvature, Classical and Quantum Gravity, cilt.26, 2009, 195002.
  • Herrera L, Di Prisco A, Ospino J. On the Stability of the Shear-free Condition, General Relativity and Gravitation, cilt.42, 2010, s.1585-1599.
  • Herrera L, Di Prisco A, Ospino J. Shear-free Axially Symmetric Dissipative Fluids, Physical Review D, cilt.89, 2014, s.127502.
  • Slobodeanu R. Shear-free Perfect Fluids with Linear Equation of State, Classical and Quantum Gravity, cilt.31, 2014, s.125012.
  • Van den Bergh N, Slobodeanu R. Shear-free Perfect Fluids with a Barotropic Equation of State in General Relativity: the Present Status, arXiv, [http://arxiv.org/abs/1510.05798], 2015, Erişim Tarihi: 25.10.2015.
  • Narlikar JV. Newtonian Universes with Shear and Rotation, Monthly Notices of the Royal Astronomical Society cilt.126, 1963, s.203.
  • Heckmann O, Schücking E. Handbuch der Physik LIII (ed) Flügge S. Berlin: Springer, 1959, s.489.
  • Sofuoğlu D, Mutuş H. Investigations of f(R)-Gravity Counterparts of the General Relativistic Shear-free Conjecture by Illustrative Examples, General Relativity and Gravitation, cilt.46, 2014, s.1-25.
  • Sofuoğlu D. Rotating and Expanding Bianchi Type-IX Model in f(R,T) Theory of Gravity, Astrophysics and Space Science, cilt.361, 2016, s.1-7.
  • Harko T, Lobo FSN, Nojiri S, Odintsov SD. f(R,T) Gravity, Physical Review D, cilt.84, 2011, s.024020.
  • Ellis GFR, Van Elst H. Cosmological Models (Cargese Lectures 1998), arXiv, [http://arxiv.org/abs/gr-qc/9812046], 1998, Erişim Tarihi: 17.11.2004.
  • Van Elst H, Uggla C. General Relativistic 1+3 Orthonormal Frame Approach, Classical and Quantum Gravity, cilt.14, 1997, s.2673-2695.
  • MacCallum MAH. “Anisotropic and Inhomogeneous Relativistic Cosmologies” in: General Relativity An Einstein Centenary Survey, (Ed.) Hawking SW, Israel W., Cambridge: Cambridge University Press, 1979, s.179-236 (Tablo 11.2, s.194).
There are 29 citations in total.

Details

Other ID JA75KP65ZS
Journal Section Research Article
Authors

Değer Sofuoğlu This is me

Publication Date September 1, 2016
Published in Issue Year 2016 Volume: 18 Issue: 54

Cite

APA Sofuoğlu, D. (2016). F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 18(54), 317-332.
AMA Sofuoğlu D. F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK. DEUFMD. September 2016;18(54):317-332.
Chicago Sofuoğlu, Değer. “F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 18, no. 54 (September 2016): 317-32.
EndNote Sofuoğlu D (September 1, 2016) F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 18 54 317–332.
IEEE D. Sofuoğlu, “F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK”, DEUFMD, vol. 18, no. 54, pp. 317–332, 2016.
ISNAD Sofuoğlu, Değer. “F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 18/54 (September 2016), 317-332.
JAMA Sofuoğlu D. F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK. DEUFMD. 2016;18:317–332.
MLA Sofuoğlu, Değer. “F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, vol. 18, no. 54, 2016, pp. 317-32.
Vancouver Sofuoğlu D. F(R,T) GRAVİTEDE MAKASLAMASIZ MÜKEMMEL AKIŞKAN İDDİASINA İKİNCİ BİR KARŞIT ÖRNEK. DEUFMD. 2016;18(54):317-32.

Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.