Semra GÜRTAŞ DOĞAN

EFFECTS OF GRAVITY’S RAINBOW ON A RELATIVISTIC SPIN-1 OSCILLATOR

We consider a relativistic spin-1 particle with non-minimal coupling in the context of gravity’s rainbow in the three dimensional background spacetime spanned by static cosmic string. In this context, we acquire an exact solution of the associated spin-1 equation in the modified three dimensional static cosmic string-spanned background spacetime. This relativistic wave equation includes a reducible spinor and this allows us to acquire a non-perturbative expression including the modification functions in the energy domain. In the low energy limit, our results agree well with current literature and provide a basis to discuss the fundamental features of the relativistic spin-1 oscillator. Afterwards, we try to discuss the effects of gravity rainbow functions on the considered spin-1 oscillator in three different scenarios for the modification functions.

Keywords:

Gravity rainbow, Spin-1 oscillator, Planck energy, Doubly special relativity, Cosmic string Topological defect,

PDF

___

[1] Barut, A. O. (1990). Excited states of zitterbewegung. Physics Letters B, 237, 436–439.
[2] Unal, N. (1997). A simple model of the classical zitterbewegung: photon wave function. Foundations of Physics, 27, 731–746.
[3] Unal, N. (1998). Path Integral Quantization of a Spinning Particle. Foundations of Physics, 28, 755–762.
[4] Sucu, Y., Unal, N. (2005). Vector bosons in the expanding universe, The European Physical Journal C, 44, 287–291.
[5] Sucu, Y., Tekincay, C. (2019). Photon in the Earth-ionosphere cavity: Schumann resonances. Astrophysics and Space Science, 364, 1–7.
[6] Guvendi, A., Zare, S. and Hassanabadi, H. (2021). Vector boson oscillator in the spiral dislocation spacetime, European Physical Journal A, 57, 1–6..
[7] Dogan, S.G. (2022). Landau Quantization for Relativistic Vector Bosons in a Gödel-Type Geometric Background. Few-Body Systems, 63, 1–10.
[8] Hosseinpour, M., Hassanabadi, H., Kriz, J., Hassanabadi, S., Lutfuoğlu, B.C. (2021). Interaction of the generalized DKP equation with a non-minimal coupling under the cosmic rainbow gravity. International Journal of Geometric Methods in Modern Physics, 18, 2150224.
[9] Zare, S., Hassanabadi, H., Guvendi, A., Chung, W.S. (2022). On the interaction of a Cornell-type nonminimal coupling with the scalar field under the background of topological defects. International Journal of Modern Physics A, 37, 2250033.
[10] Guvendi, A. and Hassanabadi, H. (2021). Relativistic Vector Bosons with non-minimal coupling in the spinning cosmic string spacetime. Few-Body Systems, 62, 1–8.
[11] Gecim, G., Sucu, Y. (2017). Massive vector bosons tunnelled from the (2+1)-dimensional Blackholes. The European Physical Journal Plus, 132, 1–8.
[12] Gecim, G., Sucu, Y. (2018). The GUP effect on tunneling of massive vector bosons from the 2+1 dimensional blackhole, Advances in High Energy Physics, 2018.
[13] Carvalho, J., Furtado, C., Moraes, F. (2011). Dirac oscillator interacting with a topological Defect. Physical Review A, 84, 032109.
[14] Ahmed, F. (2019). The Klein-Gordon oscillator in (1+2)-dimensions Gurses space-time Backgrounds. Annals of Physics, 404, 1–9.
[15] Guvendi, A. (2021). Dynamics of a composite system in a point source-induced spacetime. International Journal of modern Physics A, 36, 2150144.
[16] Guvendi, A., Hassanabadi, H. (2021). Noninertial effects on a composite system. International Journal of Modern Physics A, 36, 2150253.
[17] Marques, G. A., Bezerra, V. B. (2002). Hydrogen atom in the gravitational fields of topological Defects. Physical Review D, 66, 105011.
[18] Guvendi, A., Sahin, R., Sucu, Y. (2021). Binding energy and decaytime of exciton in dielectric medium. The European Physical Journal B, 94, 1–7.
[19] Guvendi, A., Sucu, Y. (2020). An interacting fermion-antifermion pair in the spacetime background generated by static cosmic string. Physics Letters B, 811, 135960.
[20] Moshinsky, M., Szczepaniak, A. (1989). The Dirac oscillator. Journal of Physics A: Mathematical and General, 22, L817.
[21] Bruce, S., Minning, P. (1993). The Klein Gordon oscillator. Il Nuovo Cimento A, (1965-1970), 106, 711–713.
[22] Nedjadi, Y., Barrett, R.C. (1994). The Duffin-Kemmer-Petiau oscillator. Journal of Physics A: Mathematical and General, 27, 4301.
[23] Guvendi, A. (2021). Effects of Rotating Frame on a Vector Boson Oscillator. Sakarya University Journal of Science, 25, 834–840.
[24] Dogan, S.G. (2021). Two-Dimensional Vector Boson Oscillator. Sakarya University Journal of Science, 25, 1210–1217.
[25] Bentez, J., y Romero, R.P.M., Nuez-Yepez, H.N., Salas- Brito, A.L. (1990). Solution and hidden supersymmetry of a Dirac oscillator. Physical Review Letters, 64, 1643 6.
[26] Guvendi, A. (2021). Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction. The European Physical Journal C, 81, 1–7.
[27] Mandal, B. P., Verma, S. (2010). Path integral solution of noncentral potential. Physics Letters A 374, 1021– 1023.
[28] Bakke, K. (2013). Rotating effects on the Dirac oscillator in the cosmic string spacetime. General Relativity and Gravitation, 45, 1847– 1859
[29] Vitoria, R.L., Bakke, K. (2016). Relativistic quantum effects of confining potentials on the Klein Gordon oscillator. The European Physical Journal Plus, 131, 1–8.
[30] Soares, A.R., Vitoria, R.L.L., Aounallah, H. (2021). On the Klein–Gordon oscillator in topological charged Ellis–Bronnikov-type wormhole spacetime. The European Physical Journal Plus, 136, 1–8.
[31] Zare, S., Hassanabadi, H., de Montigny, M. (2020). Non-inertial effects on a generalized DKP oscillator in a cosmic string space-time. General Relativity and Gravitation, 52, 1–20.
[32] Guvendi, A., Boumali, A. (2021). Superstatistical properties of a fermion-antifermion pair interacting via Dirac oscillator coupling in one-dimension. The European Physical Journal Plus, 136, 1–18.
[33] Zare, S., Hassanabadi H., Guvendi, A. (2022). Relativistic Landau quantization for a composite system in the spiral dislocation spacetime, The European Physical Journal Plus, 137, 1–8.
[34] Guvendi, A., Dogan, S. G. (2022). Effect of internal magnetic flux on a relativistic spin-1 Oscillator in the spinning point source-generated spacetime, arXiv preprint arXiv:2206.09898.
[35] Franco-Villafane, J.A., Sadurni, E., Barkhofen, S., Kuhl, U., Mortessagne, F., Seligman, T.H. (2013). First Experimental Realization of the Dirac Oscillator, Physical Review Letters, 111, 170405.
[36] Vilenkin, A. (1985). Cosmic strings and domain walls. Physics Reports, 121, 263–315.
[37] Deser, S., Jackiw, R., Hooft, G. (1984). Three-dimensional Einstein gravity: dynamics of flat Space. Annals of Physics, 152, 220–235.
[38] Clement, G. (1990). Rotating string sources in three-dimensional gravity. Annals of Physics, 201, 241–257.
[39] Gott, J.R., Alpert, M. (1984). General relativity in a (2+1)-dimensional space-time. General Relativity and Gravitation, 16, 243–247.
[40] Dogan, S.G., Sucu, Y. (2019). Quasinormal modes of dirac field in 2+1 dimensional gravitational wave background. Physics Letters B, 797, 134839
[41] Yeşiltaş, Ö. (2015). Su (1,1) solutions for the relativistic quantum particle in cosmic string Spacetime. The European Physical Journal Plus ,130, 7, 128.
[42] Bakke, K., Furtado, C. (2020). Bound states for neutral particles in a rotating frame in the cosmic string spacetime, Physical Review D, 82, 084025.
[43] Huang, Z. (2020). Quantum entanglement of nontrivial spacetime topology. The European Physical Journal C, 8:2, 1–8.
[44] Guvendi, A. (2022). Influence of spinning topological defect on the landau levels of relativistic spin-0 particles. Journal of Scientific Reports-A, 050, 245– 253.
[45] Magueijo, J., Smolin, L. (2003). Generalized Lorentz invariance with an invariant energy scale. Physical Review D, 67, 044017.
[46] Magueijo, J., Smolin, L. (2004). Gravity’s Rainbow. Classical and Quantum Gravity, 21, 1725.
[47] Amelino Camelia, G. (2013). Quantum Spacetime Phenomenology. Living Reviews in Relativity, 16, 1–137..
[48] Bakke, K., Mota, H. (2018). Dirac ocillator in the cosmic string spacetime in the context of gravity's rainbow. The European Physical Journal Plus, 133, 1–9.
[49] de Montigny, M., Pinfold, J., Zare, S., Hassanabadi, H. (2022). Klein–Gordon oscillator in a global monopole space–time with rainbow gravity. The European Physical Journal Plus, 137, 1–17.
[50] Amelino-Camelia, G. (2002). Relativity in spacetimes with short-distance structure governed by an observer-independent (planckian) length scale. International Journal of Modern Physics D, 11, 35–59.
[51] Magueijo, J., Smolin, L. (2002). Lorentz Invariance with an Invariant Energy Scale. Physical Review Letters, 88, 190403.
[52] Galan, P., Marugan, G.A.M. (2004). Quantum time uncertainty in a gravity's rainbow formalism. Physical Review D, 70, 124003.
[53] Jacob, U., Mercati, F., Amelino-Camelia, G., Piran, T. (2010). Modifications to Lorentz invariant dispersion in relatively boosted frames. Physical Review D, 82, 084021.
[54] Amelino-Camelia, G., Ellis, J., Mavromatos, N.E., Nanopoulos, D.V., Sarkar, S. (1998). Tests of quantum gravity from observations of γ-ray bursts. Nature, 393, 763–765.
[55] Hendi, S.H., Panah, B.E., Panahiyan, S. (2017). Topological charged black holes in massive gravity's rainbow and their thermodynamical analysis through various approaches, Physics Letters B, 769, 191–201.
[56] Bezerra, V.B., Mota, H.F., Muniz, C.R. (2017). Casimir effect in the rainbow Einstein's universe. Europhysics Letters, 120, 10005.
[57] Bezerra, V.B., Christiansen, H.R., Cunha, M.S., Muniz, C.R. (2017). Exact solutions and phenomenological constraints from massive scalars in a gravity’s rainbow spacetime, Physical Review D, 96, 024018.
[58] Garattini, R. and Lobo, F. S. N. (2012). Self-sustained wormholes in modified dispersion relations. Physical Review D, 85, 024043.
[59] Garattini, R. and Lobo, F. S. N. (2018). Gravity's Rainbow and traversable wormholes. In Fourteenth Marcel Grossmann Meeting - MG14, 1448–1453.
[60] Bezerra, V.B., Mota, H.F., Muniz, C.R. (2017). Casimir effect in the rainbow Einstein's universe. Europhysics Letters, 120, 10005.
[61] Sogut, K., Salti, M., Aydogdu, O. (2021). Quantum dynamics of photon in rainbow gravity. Annals of Physics, 431, 168556.
[62] Dogan, S.G. (2022). Landau Quantization for Relativistic Vector Bosons in a Gödel-Type Geometric Background. Few-Body Systems, 63, 1–10.
[63] Hendi, S. H. Momennia, M., Panah, B. E., Panahiyan, S. (2017). Nonsingular universe in massive gravity's rainbow. Physics of the Dark Universe, 16, 26–33.
[64] Awad, A., Ali, A. F., Majumder, B. (2013). Nonsingular rainbow universes. Journal of Cosmology and Astroparticle Physics, 2013, 052.
[65] Bezerra, V.B., Christiansen, H.R., Cunha, M.S., Muniz, C.R. (2017). Exact solutions and phenomenological constraints from massive scalars in a gravity’s rainbow spacetime. Physical Review D, 96, 024018.