بارهای پایسته سیاهچاله های سه بعدی در نظریه گرانش جرمدار جدید گسترش یافته از رهیافت والد

مهدویان یکتا, داوود

doi:10.22055/jrmbs.2021.17017

بارهای پایسته سیاهچاله های سه بعدی در نظریه گرانش جرمدار جدید گسترش یافته از رهیافت والد

نوع مقاله : مقاله پژوهشی کامل

نویسنده

داوود مهدویان یکتا

گروه فیزیک، دانشکده علوم پایه، دانشگاه حکیم سبزواری، سبزوار، ایران

10.22055/jrmbs.2021.17017

چکیده

یک مدل اسباب بازی از تعمیم گرانش 3 بعدی در حضور تصحیحات خمشی مرتبة بالاتر را بررسی خواهیم کرد که به گرانش جرمدار جدید گسترش یافته ENMG موسوم می باشد. با استفاده از رهیافت والد در فرمالیسم فضای فاز هموردا، بارهای پایستة سیاهچاله های چرخان در نظریة ENMG را محاسبه می کنیم. در واقع عبارت های دقیقی را برای جرم و اندازه حرکت زاویه ای سیاهچاله های چرخان بانادوس-توتلبویم-زانلی BTZ و آنتی دوسیته تابدار (WAdS3) بدست خواهیم آورد. نشان می دهیم نه تنها این کمیت های فیزیکی فرمول اسمار برای جرم سیاهچاله بلکه قانون اول ترمودینامیک سیاهچاله ها را نیز به طور کامل برآورده می‌کنند.

کلیدواژه‌ها

موضوعات

گرانش و کیهانشناسی

عنوان مقاله [English]

Conserved charges of 3D black holes in ENMG theory from Wald formalism

نویسنده [English]

ِDavood Mahdavian Yekta

Department of Physics, Faculty of Science, Hakim Sabzevari University, Sabzevar, Iran

چکیده [English]

We will consider a toy model of generalization of three-dimensional (3D) gravity in the presence of higher curvature corrections known as extended new massive gravity (ENMG). By employing the Wald approach in the context of covariant phase space formalism, we compute the conserved charges of 3D rotating black holes in ENMG. In fact, we will obtain exact expressions for the mass and angular momentum of two kinds of rotating black holes the so called Banados-Teitelboim-Zanelli (BTZ) and warped anti-de Sitter (WAdS3) black holes. We show that these physical quantities not only satisfy the Smarr-like formula for the mass of a black hole but also fulfill the first law of black holes thermodynamics.

کلیدواژه‌ها [English]

Extended new massive gravity
Black holes
Conserved charges
Wald formalism

مراجع

[1] A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik Ser 4 49 (1916) 769-822. https://doi.org/10.1002/andp.19163540702

[2] L.B. Szabados, Quasi-local energy-momentum and angular momentum in general relativity, Living reviews in relativity 12.1 (2009) 1-163. http://doi.org/10.12942/lrr-2004-4

[3] A. Komar, Covariant conservation laws in general relativity, Physical Review 113 (1959) 934–936. https://doi.org/10.1103/PhysRev.113.934

[4] R.L. Arnowitt, S. Deser, C.W. Misner, Dynamical Structure and Definition of Energy in General Relativity, Physical Review 116 (1959) 1322-1330. https://doi.org/10.1103/PhysRev.116.1322

[5] R.L. Arnowitt, S. Deser, C.W. Misner, Canonical variables for general relativity, Physical Review 117 (1960) 1595–1602. https://doi.org/10.1103/PhysRev.117.1595

[6] H. Bondi, M.G.J. van der Burg, A.W.K. Metzner, Gravitational waves in general relativity 7 Waves from axisymmetric isolated systems, Proceedings of The Royal Society London A 269 (1962) 21–52. https://doi.org/10.1098/rspa.1962.0161

[7] R. Sachs, Asymptotic symmetries in gravitational theory, Physical Review 128 (1962) 2851–2864. https://doi.org/10.1103/PhysRev.128.2851

[8] L.F. Abbott, S. Deser, Stability of gravity with a cosmological constant, Nuclear Physics B 195 (1982) 76. https://doi.org/10.1016/0550-3213(82)90049-9

[9] A. Ashtekar, A. Magnon, Asymptotically anti-de Sitter space-times, Classical and Quantum Gravity 1 (1984) L39–L44. https://doi.org/10.1088/0264-9381/1/4/002

[10] S. Deser, B. Tekin, Gravitational energy in quadratic curvature gravities, Physical Review Letters 89 (2002) 101101. https://doi.org/10.1103/PhysRevLett.89.101101

[11] A. Ashtekar, L. Bombelli, R. Koul, Phase space formulation of general relativity without a 3+1 splittin, Lecture Notes in Physics 278 (1987) 356–359. https://doi.org/10.1007/3-540-17894-5-378

[12] G. Barnich, F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charge, Nuclear Physics B 633 (2002) 3–82.

[13] J. Lee, R.M. Wald, Local symmetries and constraints, Journal of Mathematical Physics 31 (1990) 725–743. https://doi.org/10.1063/1.528801

[14] R.M. Wald, Black hole entropy is the Noether charge, Physical Review D 48 (1993) 3427-3431. https://doi.org/10.1103/PhysRevD.48.R3427

[15] V. Iyer, R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Physical Review D 50 (1994) 846-864. https://doi.org/10.1103/PhysRevD.50.846

[16] J.D. Brown, J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Physical Review D 47 (1993) 1407–1419. https://doi.org/10.1103/PhysRevD.47.1407

[17] H. Leutwyler, A 2+1 Dimensional Model For The Quantum Theory Of Gravity, Nuovo Cimento A 42 (1966) 159-178. https://doi.org/10.1007/BF02856201

[18] S. Carlip, Conformal Field Theory, (2+1) dimensional Gravity, and the BTZ Black hole, Classical and Quantum Gravity 22 (2005) 85-124. https://doi.org/10.1088/0264-9381/22/12/R01

[19] E. witten, 2+1 dimensional gravity as an exactly solvable system, Nuclear Physics B 311 (1988) 46-78. https://doi.org/10.1016/0550-3213(88)90143-5

[20] S. Deser, R. Jackiw, S. Templeton, Three-Dimensional Massive Gauge Theories, Physical Review Letters 48 (1982) 975. https://doi.org/10.1103/PhysRevLett.48.975

[21] S. Deser, R. Jackiw, S. Templeton, Topologically massive gauge theories, Annals of Physics 140 (1982) 372. https://doi.org/10.1006/aphy.2000.6013

[22] E.A. Bergshoeff, O. Hohm, P.K. Townsend, Massive Gravity in Three Dimensions, Physical Review Letters 102 (2009) 201301. https://doi.org/10.1103/PhysRevLett.102.201301

[23] E.A. Bergshoeff, O. Hohm, P.K. Townsend, More on Massive 3D Gravity, Physical Review D 79 (2009) 124042. https://doi.org/10.1103/PhysRevD.79.124042

[24] M. Fierz, W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proceedings of The Royal Society London A 173 (1939) 211. https://doi.org/10.1098/rspa.1939.0140

[25] A. Sinha, on the new massive gravity and AdS/CFT, Journal of High Energy Physics 06 (2010) 061. https://doi.org/10.1007/JHEP06(2010)061

[26] I. Gullu, T.C. Sisman, B. Tekin, Born-Infeld extension of new massive gravity, Classical and Quantum Gravity 27 (2010) 162001. https://doi.org/10.1088/0264-9381/27/16/162001

[27] J.M. Bardeen, B. Carter, S.W. Hawking, the four laws of black hole mechanics, Communications in mathematical physics 31 (1973) 161-170. http://doi.org/10.1007/BF01645742

[28] M. Banados, C. Teitelboim, J. Zanelli, Black hole in three-dimensional spacetime, Physical Review Letters 69 (1992) 1849. https://doi.org/10.1103/PhysRevLett.69.1849

[29] K. Sfetsos, K. Skenderis, Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black hole, Nuclear Physics B 517 (1998) 179-204. https://doi.org/10.1016/S0550-3213(98)00023-6

[30] R. Emparan, G.T. Horowitz, R.C. Myers, Exact description of black holes on branes II: comparison with BTZ black holes and black strings, Journal of High Energy Physics 01 (2000) 021. https://doi.org/10.1088/1126-6708/2000/01/021

[31] K.A. Moussa, G. Clement, C. Leygnac, The black holes of topologically massive gravity, Classical and Quantum Gravity 20 (2003) L277. https://doi.org/10.1088/0264-9381/20/24/L01

[32] S. Detournay, D. Israel, J.M. Lapan, M. Romo, String theory on Warped AdS3 and Virasoro Resonances, Journal of High Energy Physics 01 (2011) 030. https://doi.org/10.1007/JHEP01(2011)030

[33] G. Clement, Particle-like solutions to topologically massive gravity, Classical and Quantum Gravity 11 (1994) L115. https://doi.org/10.1088/0264-9381/11/9/001

[34] G. Clement, Black hole mass and angular momentum in 2+1 gravity, Physical Review D 68 (2003) 024032. https://doi.org/10.1103/PhysRevD.68.024032

[35] S. Nam, J.D. Park, S.H. Yi, AdS Black Hole Solutions in the Extended New Massive Gravity, Journal of High Energy Physics 07 (2010) 058. https://doi.org/10.1007/JHEP07(2010)058[36] A. Ghodsi, D.M. Yekta, On asymptotically AdS-like solutions of three dimensional massive gravity, Journal of High Energy Physics 06 (2012) 131. https://doi.org/10.1007/JHEP06(2012)13

[37] S. Nam, J.D. Park, Mass and angular momentum of black holes in 3D gravity theories with first order formalism, European Physical Journal C 78 (2018) 535. https://doi.org/10.1140/epjc/s10052-018-6016-5

[38] S. Nam, J.D. Park, Warped AdS₃ black hole in minimal massive gravity with first order formalism, Physical Review D 98 (2018) 124034. https://doi.org/10.1103/PhysRevD.98.124034

[39] J.M. Maldacena, the large N limit of superconformal field theories and supergravity, International Journal of Theoretical Physics 38 (1999) 1113. https://doi.org/10.1023/A:1026654312961

[40] D. Lovelock, The Einstein tensor and its generalizations, Journal of Mathematical Physics 12 (1971) 498–501. https://doi.org/10.1063/1.1665613

[41] H. Afshar, E.A. Bergshoeff, W. Merbis, Extended massive gravity in three dimensions, Journal of High Energy Physics 08 (2014) 115. https://doi.org/10.1007/JHEP08(2014)115

[42] S. Carlip, The (2+1)-dimensional black hole, Classical and Quantum Gravity 12 (1995) 2853-2879. https://doi.org/10.1088/0264-9381/12/12/005

[43] L. Smarr, Mass formula for Kerr black holes, Physical Review Letters 30 (1973) 71. https://doi.org/10.1103/PhysRevLett.30.71

[44] D. Anninos, W. Li, M. Padi, W. Song, A. Strominger, Warped AdS₃ Black holes, Journal of High Energy Physics 03 (2009) 130. https://doi.org/10.1088/1126-6708/2009/03/130

[45] S. Detournay, T. Hartman, D. Hofman, Warped conformal field theory, Physical Review D 86 (2012) 124018. https://doi.org/10.1016/j.nuclphysb.2015.05.01

[46] M. Cvetic, G.W. Gibbons, C.N. Pope, Universal Area Product Formulas for Rotating and Charged Black Holes in Four and Higher Dimensions, Physical Review Letters 106 (2011) 121301. https://doi.org/10.1103/PhysRevLett.106.121301

[47] B. Chen, Z. Xue, J.J. Zhang, Note on thermodynamics method of black hole/CFT correspondence, Journal of High Energy Physics 03 (2013) 102. https://doi.org/10.1007/JHEP03(2013)102