Abstract
This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy–momentum squared gravity. This newly developed proposal resolves the singularity of big bang and yields feasible cosmological results in the early times. We consider the particular model of this theory to establish symmetry generators and corresponding conserved quantities. For constant and variable red-shift functions, we examine the presence of viable traversable wormhole solutions for both dust and non-dust matter distributions and analyze the stable state of these solutions. We investigate the graphical interpretation of null and weak energy bounds for normal and effective energy–momentum tensors to examine the presence of physically viable wormhole geometry. It is found that realistic traversable and stable wormhole solutions are obtained for a particular model of this gravity.
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References
A.D. Felice, S.R. Tsujikawa, Living Rev. Relativ. 13, 3 (2010)
S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)
Bamba, et al., Astrophys. Space Sci. 342, 155 (2012)
T. Harko et al., Phys. Rev. D 84, 024020 (2011)
Z. Haghani et al., Phys. Rev. D 88, 044023 (2013)
P.H.R.S. Moraes, J.R.L. Santos, Eur. Phys. J. C 76, 60 (2016)
N. Katirci, M. Kavuk, Eur. Phys. J. Plus 129, 163 (2014)
C.Y. Chen, P. Chen, Phys. Rev. D 101, 064021 (2020)
S. Bhattacharjee, P.K. Sahoo, Eur. Phys. J. Plus 135, 86 (2020)
A.H. Barbar, A.M. Awad, M.T. AlFiky, Phys. Rev. D 101, 044058 (2020)
M. Sharif, M.Z. Gul, Phys. Scr. 96, 025002 (2020)
C.V.R. Board, J.D. Barrow, Phys. Rev. D 96, 123517 (2017)
N. Nari, M. Roshan, Phys. Rev. D 98, 024031 (2018)
P.H.R.S. Moraes, P.K. Sahoo, Phys. Rev. D 97, 024007 (2018)
S. Bahamonde, M. Marciu, P. Rudra, Phys. Rev. D 100, 083511 (2019)
M. Sharif, M.Z. Gul, Int. J. Mod. Phys. A 36, 2150004 (2021)
M. Sharif, M.Z. Gul, Chin. J. Phys. 71, 365 (2021)
Demianski, et al., Phys. Rev. D 46, 1391 (1992)
S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 24, 2153 (2007)
S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 25, 085004 (2008)
S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 27, 165008 (2010)
M.F. Shamir, A. Jhangeer, A.A. Bhatti, Chin. Phys. Lett. 29, 080402 (2012)
Y. Kucukakca, U. Camci, I. Semiz, Gen. Relativ. Gravit. 44, 1893 (2012)
M. Sharif, S. Waheed, Can. J. Phys. 88, 833 (2010)
M. Sharif, S. Waheed, Phys. Scr. 83, 015014 (2011)
M. Sharif, S. Waheed, J. Cosmol. Astropart. Phys. 2, 043 (2013)
M. Sharif, I. Nawazish, J. Exp. Theor. Phys. 120, 49 (2014)
M. Sharif, I. Shafique, Phys. Rev. D 90, 084033 (2014)
M. Sharif, H.I. Fatima, J. Exp. Theor. Phys. 122, 104 (2016)
M. Sharif, M.Z. Gul, Eur. Phys. J. Plus 133, 345 (2018)
M. Sharif, M.Z. Gul, Int. J. Mod. Phys. D 28, 1950054 (2019)
M. Sharif, M.Z. Gul, Chin. J. Phys. 57, 329 (2019)
P.E. Kashargin, S.V. Sushkov, Gravit. Cosmol. 14, 80 (2008)
E.F. Eiroa, C. Simeone, Phys. Rev. D 82, 084039 (2010)
S. Bahamonde et al., Phys. Rev. D 94, 044041 (2016)
M. Sharif, I. Fatima, Gen. Relativ. Gravit. 48, 148 (2016)
M. Sharif, I. Fatima, Gen. Relativ. Gravit. 400, 37 (2019)
M. Sharif, I. Fatima, Astrophys. Space Sci. 361, 127 (2016)
S.H. Mazharimousavi, M. Halilsoy, Mod. Phys. Lett. A 31, 1650203 (2016)
S. Bahamonde et al., Phys. Rev. D 94, 084042 (2016)
M. Sharif, I. Nawazish, Ann. Phys. 389, 283 (2018)
M. Zubair, S. Waheed, Y. Ahmed, Eur. Phys. J. C 76, 444 (2016)
M. Morris, A. Thorne, Am. J. Phys. 56, 395 (1988)
G.F.R. Ellis, R. Maartens, M.A.H. MacCallum, Relativistic Cosmology (Cambridge University Press, Cambridge, 2012)
S. Carroll, Spacetime and Geomety, An Introduction to General Relativity (Addison Wesley, Boston, 2004)
J. Santos et al., Phys. Rev. D 76, 083513 (2007)
S. Capozziello, M. De Laurentis, S.D. Odintsov, Eur. Phys. J. C 72, 1434 (2012)
S. Basilakos et al., Phys. Rev. D 88, 103526 (2013)
A. Paliathanasis et al., Phys. Rev. D 89, 063532 (2014)
A. Paliathanasis, M. Tsamparlis, S. Basilakos, Phys. Rev. D 84, 123514 (2011)
S. Basilakos, M. Tsamparlis, A. Paliathanasis, Phys. Rev. D 83, 103512 (2011)
M. Roshan, M. Shojai, Phys. Rev. D 94, 044002 (2016)
S. Kar, D. Sahdev, Phys. Rev. D 52, 2030 (1995)
F.S.N. Lobo, M.A. Oliveira, Phys. Rev. D 80, 104012 (2009)
M.F. Shamir, M. Ahmad, Int. J. Geom. Methods Mod. Phys. 15, 1850070 (2018)
M. Sharif, I. Nawazish, S. Hussain, Eur. Phys. J. C 80, 783 (2021)
S. Capozziello, O. Luongo, L. Mauro, Eur. Phys. J. Plus 136, 167 (2021)
V. De Falco et al., Eur. Phys. J. C 81, 157 (2021)
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Sharif, M., Zeeshan Gul, M. Viable wormhole solutions in energy–momentum squared gravity. Eur. Phys. J. Plus 136, 503 (2021). https://doi.org/10.1140/epjp/s13360-021-01512-x
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DOI: https://doi.org/10.1140/epjp/s13360-021-01512-x