اصلاح قانون گرانش نیوتن در فرمول‌بندی ورلایند از نقطه نظر ساختار ریز گسترش یافته

مهدی پور, سید حمید

doi:10.22055/jrmbs.2021.17276

اصلاح قانون گرانش نیوتن در فرمول‌بندی ورلایند از نقطه نظر ساختار ریز گسترش یافته

نوع مقاله : مقاله پژوهشی کامل

نویسنده

سید حمید مهدی پور

گروه فیزیک، دانشکده علوم پایه، دانشگاه آزاد اسلامی واحد لاهیجان، لاهیجان، ایران

10.22055/jrmbs.2021.17276

چکیده

در این مقاله، می خواهیم خواص کوچک-مقیاس فضا-زمان را از دیدگاه اثرات ساختار ریز گسترش یافته مورد تحلیل قرار دهیم. در این راستا، تمامی ساختارهای نقطه ای به دلیل حضور اثر گستردگی ساختار ریز، با توزیع های لکه ای جایگزین و اصلاح می شوند. ما به بررسی اثری می پردازیم که چنین اصلاحی از جرم و بار نقطه ای روی ترمودینامیک یک سیاهچاله آنتی-دوسیته باردار می گذارد. به عنوان یک پیامد مهم در فواصل بسیار کوتاه نشان می دهیم که نیروی آنتروپیایی چنین سیاهچاله ای به ازای قدری پسمانده خنثی، به مقدار صفر سقوط می کند و به هیچ وجه واگرا نمی شود. همچنین، بهره گیری از توزیع های لکه ای بجای ساختارهای نقطه ای باعث اصلاح انرژی سیاهچاله می گردد. اثرات چنین اصلاحاتی روی هندسه بزرگ-مقیاس نیز به کمک اصول هولوگرافی و همبخشی انرژی موضعی مورد مطالعه قرار می گیرند. از اینرو، به تصحیحات نیروی آنتروپیایی در این نظریه تغییر شکل یافته دست پیدا می کنیم، و این به نوبه خود منجر به اصلاح قانون گرانش نیوتن در فرمولبندی ورلایند خواهد شد.

کلیدواژه‌ها

موضوعات

گرانش و کیهانشناسی

عنوان مقاله [English]

Modified Newton's gravity law in Verlinde formalism based on an extended microstructure

نویسنده [English]

Sayed Hamid Mehdipour

Department of Physics, College of Basic Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

چکیده [English]

This paper analyses the effects of an extended microstructure in the microscopic discretion of spacetime. In this setup, all point structures get replaced by smeared distributions owing to this extended microstructure. We investigate the effect that such a modification of point mass and charge has on the thermodynamics of a charged anti-de Sitter black hole. In addition, the modification of point structures by smeared distributions modifies the energy of the black hole. The effects of such a deformation in the macroscopic geometry are studied by using the local equipartition of energy and the holographic principle. Thus, it is possible to obtain the corrections to the entropic force from such a deformation of the theory. This will in turn modify the Newton's gravity law in the Verlinde formalism.

کلیدواژه‌ها [English]

Entropic Gravity
Black Hole Thermodynamics
Extended Structure
Holographic Screens
Cosmological Constant

مراجع

[1] J.M. Bardeen, B. Carter, S.W. Hawking, The four laws of black hole mechanics, Communications in Mathematical Physics 31 (1973) 161-170. https://doi.org/10.1007/BF01645742

[2] J.D. Bekenstein, Black Holes and Entropy, Physical Review D 7 (1973) 2333-2346. https://doi.org/10.1142/9789811203961_0023

[3] S.W. Hawking, Particle creation by black holes, Communications in Mathematical Physics 43 (1975) 199-220. https://doi.org/10.1007/BF02345020

[4] T. Jacobson, Thermodynamics of Spacetime: The Einstein Equation of State, Physical Review Letters 75 (1995) 1260. https://doi.org/10.1103/PhysRevLett.75.1260

[5] R. Bousso, The holographic principle, Reviews of Modern Physics 74 (2002) 825. https://doi.org/10.1103/RevModPhys.74.825

[6] G.T. Hooft, Dimensional Reduction in Quantum Gravity, gr-qc/9310026. https://arxiv.org/pdf/gr-qc/9310026

[7] T. Padmanabhan, Equipartition of energy in the horizon degrees of freedom and the emergence of gravity, Modern Physics Letters A 25 (2010) 1129-1136. https://doi.org/10.1142/S021773231003313X

[8] E.P. Verlinde, On the origin of gravity and the laws of Newton, Journal of High Energy Physics 1104 (2011) 029. https://doi.org/10.1007/JHEP04(2011)029

[9] S. Soroushfar, B. Pourhassan, Thermodynamic geometry of a charged AdS black hole ‎with corrected entropy, Journal of Research on Many-body Systems 11 3 (2021) 74-89.‏ https://dx.doi.org/10.22055/jrmbs.2021.17029

[10] S.H. Hendi, R. Ramezani-Arani and E. Rahimi, Thermal stability of d-dimensional Lifshitz like topological black holes in special class of F(R) gravity, Journal of Research on Many-body Systems 10 2 (2020) 149-162.‏ https://dx.doi.org/10.22055/jrmbs.2020.15569

[11] M. Isi, J. Mureika, P. Nicolini, Self-completeness and the generalized uncertainty principle, Journal of High Energy Physics 1311 (2013) 139. https://doi.org/10.1007/JHEP11(2013)139

[12] B.J. Carr, J. Mureika, P. Nicolini, Sub-Planckian black holes and the Generalized Uncertainty Principle, Journal of High Energy Physics 1507 (2015) 052. https://doi.org/10.1007/JHEP07(2015)052

[13] N.V. Krasnikov, Nonlocal gauge theories, Theoretical and Mathematical Physics 73 (1988) 1184-1190. https://inis.iaea.org/search/search.aspx?orig_q=RN:20070208

[14] L. Modesto, J.W. Moffat, P. Nicolini, Black holes in an ultraviolet complete quantum gravity, Physics Letters B 695 (2011) 397-400. https://doi.org/10.1016/j.physletb.2010.11.046

[15] A. Sheykhi, Entropic corrections to Friedmann equations, Physical Review D 81 (2010) 104011. https://doi.org/10.1103/PhysRevD.81.104011

[16] A. Sheykhi, S.H. Hendi, Power-law entropic corrections to Newton’s law and Friedmann equations, Physical Review D 84 (2011) 044023. https://doi.org/10.1103/PhysRevD.84.044023

[17] S.H. Hendi, A. Sheykhi, Entropic Corrections to Coulomb’s Law, International Journal of Theoretical Physics 51 (2011) 1125-1136. https://doi.org/10.1103/PhysRevD.84.044023

[18] S.H. Hendi, A. Sheykhi, Entropic corrections to Einstein equations, Physical Review D 83 (2011) 084012. https://doi.org/10.1103/PhysRevD.83.084012

[19] M. Maggiore, A generalized uncertainty principle in quantum gravity, Physics Letters B 304 (1993) 65-69. https://doi.org/10.1016/0370-2693(93)91401-8

[20] D. Amati, M. Ciafaloni, G. Veneziano, Can spacetime be probed below the string size?, Physics Letters B 216 (1989) 41-47. https://doi.org/10.1016/0370-2693(89)91366-X

[21] M. Faizal, A.F. Ali, A. Nassar, AdS/CFT correspondence beyond its supergravity approximation, International Journal of Modern Physics A 30 (2015) 1550183. https://doi.org/10.1142/S0217751X15501833

[22] C. Rovelli, L. Smolin, Discreteness of area and volume in quantum gravity, Nuclear Physics B 442 (1995) 593-619. https://doi.org/10.1016/0550-3213(95)00150-Q

[23] H. Weyl, The Theory of Groups and Quantum Mechanics, Dover, New York, (1931). https://www.amazon.com/Theory-Groups-Quantum-Mechanics/dp/1614275807

[24] E.P. Wigner, On the Quantum Correction For Thermodynamic Equilibrium, Physical Review 40 (1932) 749. https://doi.org/10.1103/PhysRev.40.749

[25] J.E. Moyal, Quantum mechanics as a statistical theory, Mathematical Proceedings of the Cambridge Philosophical Society 45 (1949) 99-124. https://doi.org/10.1017/S0305004100000487

[26] A. Smailagic, E. Spallucci, Feynman path integral on the non-commutative plane, Journal of Physics A: Mathematical and General 36 (2003) L467. https://doi.org/10.1088/0305-4470/36/33/101

[27] P. Nicolini, A. Smailagic, E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Physics Letters B 632 (2006) 547-551. https://doi.org/10.1016/j.physletb.2005.11.004

[28] X. Calmet, A. Kobakhidze, Noncommutative general relativity, Physical Review D 72 (2005) 045010. https://doi.org/10.1103/PhysRevD.72.045010

[29] R.B. Mann, P. Nicolini, Cosmological production of noncommutative black holes, Physical Review D 84 (2011) 064014. https://doi.org/10.1103/PhysRevD.84.064014

[30] A.H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Physical Review D 23 (1981) 347. https://doi.org/10.1103/PhysRevD.23.347

[31] S. Perlmutter et al., Discovery of a supernova explosion at half the age of the Universe, Nature 391 (1998) 51-54. https://doi.org/10.1038/34124

[32] P. Nicolini, Noncommutative Black Holes, The Final Appeal to Quantum Gravity: A Review, International Journal of Modern Physics A 24 (2009) 1229-1308. https://doi.org/10.1142/S0217751X09043353

[33] S. Ansoldi, P. Nicolini, A. Smailagic and E. Spallucci, Non-commutative geometry inspired charged black holes, Physics Letters B 645 (2007) 261-266. https://doi.org/10.1016/j.physletb.2006.12.020

[34] P. Nicolini, G. Torrieri, The Hawking-Page crossover in noncommutative anti-deSitter space, Journal of High Energy Physics 08 (2011) 097. https://doi.org/10.1007/JHEP08(2011)097

[35] K. Nozari, S.H. Mehdipour, Parikh-Wilczek tunneling from noncommutative higher dimensional black holes, Journal of High Energy Physics 03 (2009) 061. https://doi.org/10.1088/1126-6708/2009/03/061

[36] S.H. Mehdipour, Thermodynamical features of Verlinde’s approach for a non-commutative Schwarzschild-anti-deSitter black hole in a broad range of scales, The European Physical Journal Plus 129 (2014) 197. https://doi.org/10.1140/epjp/i2014-14197-8

[37] S.H. Mehdipour, Some aspects of entropic gravity in the presence of a noncommutative Schwarzschild-deSitter black hole, Astrophysics and Space Science 345 (2013) 339-344. https://doi.org/10.1007/s10509-013-1413-6

[38] P. Nicolini, Entropic force, noncommutative gravity, and ungravity, Physical Review D 82 (2010) 044030. https://doi.org/10.1103/PhysRevD.82.044030

[39] I. Hinchliffe, N. Kersting, Y.L. Ma, Review of the Phenomenology of Noncommutative Geometry, International Journal of Modern Physics A 19 (2004) 179-204. https://doi.org/10.1142/S0217751X04017094

[40] I. Antoniadis, A possible new dimension at a few TeV, Physics Letters B 246 (1990) 377-384. https://doi.org/10.1016/0370-2693(90)90617-F

[41] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, G. Dvali, New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV, Physics Letters B 436 (1998) 257-263. https://doi.org/10.1016/S0370-2693(98)00860-0

[42] M. Chaichian, M.M. Sheikh-Jabbari and A. Tureanu, Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED, Physical Review Letters 86 (2001) 2716-2719. https://doi.org/10.1103/PhysRevLett.86.2716

[43] A. Joseph, Particle Phenomenology on Noncommutative Spacetime, Physical Review D 79 (2009) 096004. https://doi.org/10.1103/PhysRevD.79.096004

[44] E. Akofor, A.P. Balachandran, A. Joseph, L. Pekowsky, B.A. Qureshi, Constraints from CMB on Spacetime Noncommutativity and Causality Violation, Physical Review D 79 (2009) 063004. https://doi.org/10.1103/PhysRevD.79.063004

[45] E. Chang-Young, M. Eune, K. Kimm, D. Lee, Schwarzschild-de Sitter black hole from entropic viewpoint, Modern Physics Letters A 26 (2011) 1975-1983. https://doi.org/10.1142/S0217732311036450

[46] R. Bousso, S.W. Hawking, Pair creation of black holes during inflation, Physical Review D 54 (1996) 6312. https://doi.org/10.1103/PhysRevD.54.6312

[47] G.W. Gibbons, S.W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Physical Review D 15 (1977) 2738. https://doi.org/10.1103/PhysRevD.15.2738

[48] R.A. Matzner, N. Zamorano, V.D. Sandberg, Instability of the Cauchy horizon of Reissner-Nordstrӧm black holes, Physical Review D 19 (1979) 2821. https://doi.org/10.1103/PhysRevD.19.2821

[49] D. Batic, P. Nicolini, Fuzziness at the horizon, Physics Letters B 692 (2010) 32-35. https://doi.org/10.1016/j.physletb.2010.07.007

[50] E. Brown, R. Mann, Instability of the noncommutative geometry inspired black hole, Physics Letters B 694 (2011) 440-445. https://doi.org/10.1016/j.physletb.2010.10.014

[51] S.H. Mehdipour, Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas, The European Physical Journal Plus 127 (2012) 80. https://doi.org/10.1140/epjp/i2012-12080-4