Conformally Flat Space-Time with Dust Matter in f(R) Gravity

Yıl 2019, , 59 - 65, 01.04.2019

Doğukan Taşer

https://doi.org/10.19113/sdufenbed.442768

Öz

In this
study, conformally flat space-times filled with dust matter is investigated in framework
of f(R) gravitation theory. Exact
solutions and field equations of conformally flat space-time in the presence of
dust matter are obtained without using any restrictive method and approximation.
It is shown that conformally flat space-times in framework of f(R) gravitation theory permit to dust
matter with constant energy density. f(R)
function which characterise dynamic structure of theory is obtained from
solutions of field equations for constructed model. Obtained f(R) function for constructed model and
viable f(R) functions, which are used
to express various conditions and situations in theory, are compared. Change of
the metric potential with respect to radial coordinate is examined by the help
of graphic and limiting cases of the solutions are investigated. Finally, obtained
results are discussed in the terms of physical and geometric aspects.    

Anahtar Kelimeler

f(R) gravitation theory, Dust matter, Conformal space-time

f(R) Gravitasyon Teorisinde Toz Bulutlu Konformal Düz Uzay-Zamanlar

Öz

Bu
çalışmada, toz bulutu bulunan konformal düz uzay-zamanlar f(R) gravitasyon teorisi çerçevesinde incelenmiştir. Toz bulutu varlığında
konformal düz uzay-zamanların alan denklemleri ve tam çözümleri herhangi bir yaklaşım
ve kısıtlayıcı metot kullanılmadan elde edilmiştir. f(R) gravitasyon teorisi çerçevesinde konformal düz uzay-zamanların
sabit enerji yoğunluklu toz bulutu varlığına izin verdiği gösterilmiştir.  Teorinin dinamik yapısını karakterize eden f(R) fonksiyonu oluşturulan model için
alan denklemlerinin çözümlerinden elde edilmiştir. Oluşturulan model için elde
edilen f(R) fonksiyonu ile teoride
farklı koşul ve durumları ifade etmek için kullanılan uygulanabilir f(R) fonksiyonları karşılaştırılmıştır.
Metrik potansiyelin radyal koordinata göre değişimi grafik yardımıyla
irdelenmiş ve çözümlerin sınır durumları incelenmiştir. Son olarak, elde edilen
sonuçlar fiziksel ve geometrik açıdan irdelenerek tartışılmıştır.    

Anahtar Kelimeler

f(R) Gravitasyon Teorisi, Toz Madde, Konformal uzay-zaman

Kaynakça

• [1] Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R. A., Nugent, P., Castro, P. G., Deustua, S., Fabbro, S., Goobar, A., Groom, D. E., Hook, I. M., Kim, A. G., Kim, M. Y., Lee, J. C., Nunes, N. J., Pain, R., Pennypacker, C. R., Quimby, R., Lidman, C., Ellis, R. S., Irwin, M., McMahon, R. G., Ruiz-Lapuente, P., Walton, N., Schaefer, B., Boyle, B. J., Filippenko, A. V., Matheson, T., Fruchter, A. S., Panagia, N., Newberg, H. J. M., Couch, W. J. 1999. Measurements of Ω and Λ from 42 High-Redshift Supernovae. Astrophysical Journal, 517(1999), 565.
• [2] Riess, A. G., Filippenko, A. V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P. M., Gilliland, R. L., Hogan, C. J., Jha, S., Kirshner, R. P., Leibundgut, B., Phillips, M. M., Reiss, D., Schmidt, B. P., Schommer, R. A., Smith, R. C., Spyromilio, J., Stubbs, C., Suntzeff, N. B., Tonry, J. 1998. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116(1998), 1009.
• [3] Astier, P., Guy, J., Regnault, N., Pain, R., Aubourg, E., Balam, D., Basa, S., Carlberg, R. G., Fabbro, S., Fouchez, D., Hook, I. M., Howell, D. A., Lafoux, H., Neill, J. D., Palanque-Delabrouille, N., Perrett, K., Pritchet, C. J., Rich, J., Sullivan, M., Taillet, R., Aldering, G., Antilogus, P., Arsenijevic, V., Balland, C., Baumont, S., Bronder, J., Courtois, H., Ellis, R. S., Filiol, M., Gon¸calves, A. C., Goobar, A., Guide, D., Hardin, D., Lusset, V., Lidman, C., McMahon, R., Mouchet, M., Mourao, A., Perlmutter, S., Ripoche, P., Tao, C., Walton, N. 2006. The Supernova Legacy Survey: measurement of Ω_m , Ω_Λ and w from the first year data set. Astronomy & Astrophysics, 447(2006), 31-48.
• [4] Spergel, D. N., Verde, L., Peiris, H. V., Komatsu, E., Nolta, M. R., Bennett, C. L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Page, L., Tucker, G. S., Weiland, J. L., Wollack, E., Wright, E. L. 2003. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. The Astrophysical Journal Supplement Series, 148(2003), 175.
• [5] Bennett, C. L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Page, L., Spergel, D. N., Tucker, G. S., Wollack, E., Wright, E. L., Barnes, C., Greason, M. R., Hill, R. S., Komatsu, E., Nolta, M. R., Odegard, N., Peiris, H. V., Verde, L., Weiland, J. L. 2003. First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results. The Astrophysical Journal Supplement Series, 148(2003), 1.
• [6] Allen, S. W., Schmidt, R. W., Ebeling, H., Fabian, A. C., & van Speybroeck, L. 2004. Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters. Monthly Notices of the Royal Astronomical Society, 353(2004), 457.
• [7] Tegmark, M., Strauss, M. A., Blanton, M. R., Abazajian, K., Dodelson, S., Sandvik, H., Wang, X., Weinberg, D. H., Zehavi, I., Bahcall, N. A., Hoyle, F., Schlegel, D., Scoccimarro, R., Vogeley, M. S., Berlind, A., Budavari, T., Connolly, A., Eisenstein, D. J., Finkbeiner, D., Frieman, J. A., Gunn, J. E., Hui, L., Jain, B., Johnston, D., Kent, S., Lin, H., Nakajima, R., Nichol, R. C., Ostriker, J. P., Pope, A., Scranton, R., Seljak, U., Sheth, R. K., Stebbins, A., Szalay, A. S., Szapudi, I., Xu, Y., Annis, J., Brinkmann, J., Burles, S., Castander, F. J., Csabai, I., Loveday, J., Doi, M., Fukugita, M., Gillespie, B., Hennessy, G., Hogg, D. W., Ivezić, Ž., Knapp, G. R., Lamb, D. Q., Lee, B. C., Lupton, R. H., McKay, T. A., Kunszt, P., Munn, J. A., O'Connell, L., Peoples, J., Pier, J. R., Richmond, M., Rockosi, C., Schneider, D. P., Stoughton, C., Tucker, D. L., vanden Berk, D. E., Yanny, B., York, D. G. 2004. Cosmological parameters from SDSS and WMAP. Physical Review D, 69(2004), 103501.
• [8] Shamir, M. F., Jhangeer, A., Bhatti, A. A. 2012. Conserved Quantities in 𝑓(𝑅) Gravity via Noether Symmetry. Chinese Physics Letters, 29(2012), 080402.
• [9] Mohammadi, A. K., Malekjani M., Monshizadeh, M. 2012. Reconstruction Of Modified Gravity With Ghost Dark Energy Models. Modern Physics Letters A, 27(2012), 1250100.
• [10] Martin, J. 2008. Quintessence: A Mini-Review. Modern Physics Letters A, 23(2008), 1252.
• [11] Nojiri, S., Odintsov, S.D., Sami, M. 2006. Dark energy cosmology from higher-order, string-inspired gravity, and its reconstruction. Physical Review D, 74(2006), 046004.
• [12] Padmanabhan, T., Chaudhury, T.R. 2002. Can the clustered dark matter and the smooth dark energy arise from the same scalar field?. Physical Review D, 66(2002), 081301.
• [13] Chiba, T., Okabe, T., Yamaguchi, M. 2000. Kinetically driven quintessence. Physical Review D, 62(2000), 023511.
• [14] Bento, M. C., Bertolami, O., Sen, A.A. 2002. Generalized Chaplgin gas, accelerated expansion, and dark-energy-matter unification. Physical Review D, 66(2002), 043507.
• [15] Mishra, B., Tripathy, S. K., Tarai, S., 2018. Cosmological models with a hybrid scale factor in an extended gravity theory. Modern Physics Letter A, 33(2008), 1850052.
• [16] Buchdahl, H. A. 1970. Non-linear Lagrangians and cosmological theory. Monthly Notices of the Royal Astronomical Society, 150(1970), 1.
• [17] Bengochea, G. R., Ferraro, R. 2009. Dark torsion as the cosmic speed-up. Physical Review D, 79(2009), 124019.
• [18] Harko, T., Lobo, F. S. N., Nojiri, S., Odintsov, S. D. 2011. f(R,T) gravity. Physical Review D, 84(2011), 024020.
• [19] Bamba, K., Odintsov S. D., Sebastiani, L., Zerbini, S. 2010. Finite-time future singularities in modified Gauss-Bonnet and F(R,G) gravity and singularity avoidance. The European Physical Journal C, 67 (2010), 295.
• [20] Nojiri, S., Odintsov, S. D. 2007. Introduction to Modified Gravity and Gravitational Alternative for Dark Energy. International Journal of Geometric Methods in Modern Physics. 4(2007), 115.
• [21] Nojiri, S., Odintsov, S. D. 2008. Dark energy, inflation and dark matter from modified F(R) gravity. https://arxiv.org/pdf/0807.0685.pdf. (Erişim tarihi : 05.07.2008).
• [22] Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S. 2004. Is cosmic speed-up due to new gravitational physics?. Physical Review D, 70(2004), 043528.
• [23] Rebouças, M. J., Santos, J. 2009. Gödel-Type Universes in f(R) Gravity. Physical Review D, 80(2009)(6): 063009.
• [24] Sharif, H., Shamir, M. F. 2009. Exact Solutions of Bianchi I and V Spacetimes in f(R) Theory of Gravity. Classical and Quantum Gravity, 26(2009), 235020.
• [25] Pradhan, A., Pandey, O. P. 2002. Conformally Flat Spherically Symmetric Cosmological Models-Revisited. Spacetime and Substance, 4(2002), 169-173.
• [26] Reddy, D. R. K. 1979. Spherically symmetric static conformally flat solutions in Brans-Dicke and Sen-Dunn theories of gravitation. Journal of Mathematical Physics, 20(1979), 23.
• [27] Reddy, D. R. K., Avadhanulu, M. B., Venkateswarlu, R. 1988. A Static Conformally-Flat Vacuum Model in Self-Creation Cosmology. Astrophysics and Space Science, 141(1988), 181-184.
• [28] Yadav, R. B. S., Prasad, U. 1993. Non-static conformally flat spherically symmetric perfect fluid distributionin Einstein-Cartan theory. Astrophysics and Space Science, 203(1993), 37-42.
• [29] Khadekar, G. S., Nagpure, A. R. 2001. Higher Dimensional Static Cosmological Model in Lyra Manifold. https://arxiv.org/pdf/gr-qc/0111096 .pdf (Erişim tarihi : 28.11.2001).
• [30] Abebe, G., Govinder K. S., Maharaj S. D. 2013. Lie symmetries for a conformally flat radiating star. International Journal of Theoretical Physics, 52(2013): 3244-3254.
• [31] Sharif, M., Kausar, H. R. 2011. Dust Static Spherically Symmetric Solution in f(R) Gravity. Journal of the Physical Society of Japan, 80(2011), 044004.
• [32] Shamir, M. F., Raza, Z. 2014. Dust Static Cylindrically Symmetric Solutions in f(R) Gravity. Communications in Theoretical Physics, 62(2014), 348-352.
• [33] Shamir, M. F., Ahmad, Z., Raza, Z. 2015. Gravitational Dust Collapse in f(R) Gravity. International Journal of Theoretical Physics, 54(2015), 1450-1460.
• [34] Lobo, F. S. N., Oliveira, M. A. 2009. Wormhole geometries in f(R) modified theories of gravity. Physical Review D, 80(2009), 104012.
• [35] Gron, O., Johannesen, S. 2011. A solution of the Einstein-Maxwell equations describing conformally flat spacetime outside a charged domain wall. https://arxiv.org/pdf/1104.1 383. pdf. (Erişim tarihi : 07.04.2011).
• [36] Nojiri, S., Odintsov, S. D. 2004. Modified gravity with lnR terms and cosmic acceleration. General Relativity and Gravitation, 36(2004), 1765-1780.
• [37] Capozziello, S., Cardone, V.F., Francaviglia, M. 2006. f(R) theories of gravity in Palatini approach matched with observations. General Relativity and Gravitation, 38(2006), 711-734.