Modified dispersion relations and black hole physics

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 73, Issue 8, 2006, Pages

  Ling, Yi ^a,b   Hu, Bo ^a   Li, Xiang ^a,b  

^a NANCHANG UNIVERSITY   (China)

^b CCAST WORLD LABORATORY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645559610     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.73.087702     Document Type: Article

References (47)

1. D.J. Gross and P.F. Mende, Nucl. Phys. NUPBBO 0550-3213 B303, 407 (1988). 10.1016/0550-3213(88)90390-2
2. M. Maggiore, Phys. Lett. B 304, 65 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)91401-8
3. C. Rovelli and L. Smolin, Nucl. Phys. NUPBBO 0550-3213 B442, 593 (1995); 10.1016/0550-3213(95)00150-Q
4. C. Rovelli L. Smolin Nucl. Phys. NUPBBO 0550-3213 B456, 753(E) (1995); 10.1016/0550-3213(95)00550-5
5. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity CQGRDG 0264-9381 14, A55 (1997); 10.1088/0264-9381/14/1A/006
6. A. Ashtekar J. Lewandowski Adv. Theor. Math. Phys. 1, 388 (1998); 1095-0761
7. J. Brunnemann and T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 23, 1289 (2006). 10.1088/0264-9381/23/4/014
8. G. Amelino-Camelia, Phys. Lett. B 510, 255 (2001); PYLBAJ 0370-2693 10.1016/S0370-2693(01)00506-8
9. G. Amelino-Camelia Int. J. Mod. Phys. D 11, 35 (2002); IMPDEO 0218-2718 10.1142/S0218271802001330
10. G. Amelino-Camelia, J. Kowalski-Glikman, G. Mandanici, and A. Procaccini, Int. J. Mod. Phys. A 20, 6007 (2005); IMPAEF 0217-751X 10.1142/ S0217751X05028569
11. T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 66, 081302 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.66.081302
12. G. Amelino-Camelia, gr-qc/0309054.
13. J. Magueijo and L. Smolin, Phys. Rev. Lett. 88, 190403 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.88.190403
14. J. Magueijo L. Smolin Phys. Rev. D 67, 044017 (2003). PRVDAQ 0556-2821 10.1103/PhysRevD.67.044017
15. R. Gambini and J. Pullin, Phys. Rev. D 59, 124021 (1999); PRVDAQ 0556-2821 10.1103/PhysRevD.59.124021
16. J. Alfaro, H.A. Morales-Tecotl, and L.F. Urrutia, Phys. Rev. D 65, 103509 (2002); PRVDAQ 0556-2821 10.1103/PhysRevD.65.103509
17. L. Smolin, hep-th/0209079;
18. H. Sahlmann and T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 23, 909 (2006). 10.1088/0264-9381/23/3/020
19. L. Smolin, hep-th/0501091.
20. W.G. Unruh, Phys. Rev. D 51, 2827 (1995). PRVDAQ 0556-2821 10.1103/PhysRevD.51.2827
21. D. Colladay and V.A. Kostelecky, Phys. Rev. D 58, 116002 (1998). PRVDAQ 0556-2821 10.1103/PhysRevD.58.116002
22. S.R. Coleman and S.L. Glashow, Phys. Rev. D 59, 116008 (1999). PRVDAQ 0556-2821 10.1103/PhysRevD.59.116008
23. G. Amelino-Camelia and T. Piran, Phys. Rev. D 64, 036005 (2001); PRVDAQ 0556-2821 10.1103/PhysRevD.64.036005
24. R.C. Myers and M. Pospelov, Phys. Rev. Lett. 90, 211601 (2003); PRLTAO 0031-9007 10.1103/PhysRevLett.90.211601
25. T.A. Jacobson, S. Liberati, D. Mattingly, and F.W. Stecker, Phys. Rev. Lett. 93, 021101 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.93.021101
26. S. Corley and T. Jacobson, Phys. Rev. D 59, 124011 (1999); PRVDAQ 0556-2821 10.1103/PhysRevD.59.124011
27. S. Hossenfelder, Phys. Lett. B 575, 85 (2003); PYLBAJ 0370-2693 10.1016/j.physletb.2003.09.040
28. S. Hossenfelder, Classical Quantum Gravity CQGRDG 0264-9381 23, 1815 (2006). 10.1088/0264-9381/23/5/N01
29. B.Z. Foster, Phys. Rev. D 73, 024005 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.024005
30. J.W. Moffat, Int. J. Mod. Phys. D 2, 351 (1993); IMPDEO 0218-2718 10.1142/S0218271893000246
31. A. Albrecht and J. Magueijo, Phys. Rev. D 59, 043516 (1999). PRVDAQ 0556-2821 10.1103/PhysRevD.59.043516
32. R.J. Adler, P. Chen, and D.I. Santiago, Gen. Relativ. Gravit. GRGVA8 0001-7701 33, 2101 (2001); 10.1023/A:1015281430411
33. P. Chen and R.J. Adler, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 124, 103 (2003). 10.1016/S0920-5632(03)02088-7
34. R.J. Adler and T.K. Das, Phys. Rev. D 14, 2474 (1976); PRVDAQ 0556-2821 10.1103/PhysRevD.14.2474
35. R.S. Hanni and R. Ruffini, in Black Holes, edited by, C. DeWitt, and, B.S. DeWitt, (Gordon Breach, New York, 1973).
36. We assume that the modified dispersion relation will not change this relation which is consistent with the result in, where the impact of doubly special relativity on gravity is investigated. also see for recent work on the thermodynamics of modified black holes from gravity's rainbow.
37. We make this assumption based on the belief that the thermodynamical laws of black holes can still be captured even in the quantum theory of gravity. This belief has been supported by recent work in isolated horizon programs as well as the stretched horizon program, where the first law of black hole thermodynamics can still be established in a quasilocal fashion. In the context of DSR, which may be viewed as the semiclassical effect of quantum gravity, we assume the modification of dispersion relations of particle would not change this picture. However, before proceeding, we cautiously point out that this exact form of the first law may not be generally true but receives a small modification, or even fails for instance in the Einstein-Aether theory as investigated in.
38. The factor -1/2 in the logarithmic term happens to be the same as the one appearing in where this factor is rigorously fixed in the context of loop quantum gravity. However, we stress that, at the semiclassical level as discussed in our paper, this factor cannot be fixed uniquely, but depends on the value of η which has been set as a unit in our paper. A straightforward calculation shows that in general the factor would be -η/2. If we insist that the minimum area in our paper is the same as that in loop quantum gravity as we suggested in above reference, then the factor turns out to be -3πγ/4, rather than -1/2. Reversely, if we insist on setting the factor exactly to be -1/2, namely η=1, then from this approach we have an Immirzi parameter γ 0.37, different from the result in. This discrepancy can be understood as this specific MDR we proposed is only a coarse grained model at the semiclassical limit of quantum gravity.
39. G. Amelino-Camelia, M. Arzano, and A. Procaccini, Phys. Rev. D 70, 107501 (2004); PRVDAQ 0556-2821 10.1103/PhysRevD.70.107501
40. G. Amelino-Camelia, M. Arzano, Y. Ling, and G. Mandanici, Classical Quantum Gravity CQGRDG 0264-9381 23, 2585 (2006); 10.1088/0264-9381/23/7/022
41. A.J.M. Medved and E.C. Vagenas, Phys. Rev. D 70, 124021 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.124021
42. J.H. MacGibbon, Nature (London) NATUAS 0028-0836 329, 308 (1987); 10.1038/329308a0
43. J.D. Barrow, E.J. Copeland, and A.R. Liddle, Phys. Rev. D 46, 645 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.46.645
44. B.J. Carr, J.H. Gilbert, and J.E. Lidsey, Phys. Rev. D 50, 4853 (1994). PRVDAQ 0556-2821 10.1103/PhysRevD.50.4853
45. J. Magueijo and L. Smolin, Classical Quantum Gravity CQGRDG 0264-9381 21, 1725 (2004). 10.1088/0264-9381/21/7/001
46. Y. Ling, X. Li, and H. Zhang, gr-qc/0512084.
47. K.A. Meissner, Classical Quantum Gravity CQGRDG 0264-9381 21, 5245 (2004). 10.1088/0264-9381/21/22/015