Investigation of the DKP Equation for A Two-Dimensional Black Hole

Year 2021, Volume: 11 Issue: 1, 147 - 156, 30.06.2021

Evrim Ersin Kangal , Ali Havare

https://doi.org/10.37094/adyujsci.892038

Abstract

In the present study, we firstly investigated the spatial properties of event horizon of a two- dimensional black hole. Then we solve Duffin-Kemmer-Petiau (DKP) equation for such a black hole metric depending on the signs of spatial variable. After obtaining the exact solutions, we determine thermal parameters related to this metric. Finally, the harmonic oscillation behavior of the system is evaluated.

Keywords

DKP equation, Black hole, Thermal parameters, Harmonic oscillation

References

• [1] Koyama, K., Gravity beyond general relativity, International Journal of Modern Physics D, 27 (15), 1848001, 2018.
• [2] Gupta, S.N., Gravitation and electromagnetism, Physical Review, 96(6), 1683–1685, 1954.
• [3] Boulware, D.G., Deser, S., Classical general relativity derived from quantum gravity, Annals of Physics, 89(1), 193–240, 1975.
• [4] Hawking, S.W., Black holes in general relativity, Communications in Mathematical Physics, 25(2), 152–166, 1972.
• [5] Hawking, S.W., Black holes and thermodynamics, Physical Review D, 13(2), 191–197, 1976.
• [6] Teitleboim, C., Gravitation and Hamiltonian structure in two spacetime dimensions, Physics Letters B, 126(2), 41–45, 1983.
• [7] Jackiw, R., Lower Dimensional Gravity, Nuclear Physics B, 252, 343–356, 1985.
• [8] Mann, R.B., Shiekh, A., Tarasov, L., Classical and quantum properties of tow-dimensional black holes, Nuclear Physics B, 341(1),134-154, 1989.
• [9] Duffin, R.J., On the characteristic matrices of covariant systems, Physical Review, 54, 1114, 1938.
• [10] Kemmer, N., The particle aspect of meson theory, Proceeding of the Royal Society A, 173, 91-116, 1939.
• [11] Petiau, G., PhD thesis, Academie Royale de Belgique, Classe des Sciences, Memoires, Collection 8, 1936.
• [12] Lunardi, J.T., A note on the Duffin-Kemmer-Petiau equation in (1+1) space-time dimensions, Journal of Mathematical Physics, 58, 123501-123505, 2017.
• [13] Lunardi, J.T., Pimentel, B.M., Teixeiri, R.G., Valverde, J.S., Remarks on Duffin–Kemmer–Petiau theory and gauge invariance, Physics Letter A, 268(3), 165-173, 2000.
• [14] Sogut, K., Havare, A., Transmission resonances in the Duffin–Kemmer–Petiau equation in (1+1) dimensions for an asymmetric cusp potential, Physica Scripta, 82(4), 045013, 2010.
• [15] Parker, L., Toms, D.J., Quantum Field Theory in curved spacetime, Cambridge University Press, 2009.
• [16] Merad, M., DKP equation with smooth potential and position-dependent mass, International Journal of Theoretical Physics, 46, 2105-2118, 2007.
• [17] Cheraitia, B.B., Boudjedaa, T., Solution of DKP equation in Woods–Saxon potential, Physics Letter A, 338(2), 97-107, 2005.
• [18] Yasuk, F., Berkdemir, A., Onem, C., Exact Solutions of the Duffin–Kemmer–Petiau Equation for the Deformed Hulthen Potential, Physica Scripta, 71(4), 340-343, 2005.
• [19] Unal, N., Duffin–Kemmer–Petiau equation, Proca equation and Maxwells equation in (1+1) D, Concepts of Physics, 2, 273, 2005.
• [20] Unal, N., Path integral quantization of a spinning particle, Foundations of Physics, 28, 755-762, 1998.
• [21] Unal, N., A simple model of the classical Zitterbewegung: Photon wave function, Foundations of Physics, 27, 731-746, 1997.
• [22] Abramowitz, M., Stegun, I.A., Handbook of mathematical functions, National Bureau of Standards Applied Mathematics, 55, 1964.
• [23] Boumali, A., One-dimensional thermal properties of the Kemmer oscillator, Physica Scripta, 76(6), 669–673, 2007.
• [24] Pacheco, M.H., Landim, R.R., Almeida, C.A.S., One-dimensional Dirac oscillator in a thermal bath, Physics Letters A, 311, 93–96, 2003.
• [25] Wolfram Research Company, Mathematica 9.0, 2012.