Holographic gravity and the surface term in the Einstein-Hilbert action

Brazilian Journal of Physics

Volumn 35, Issue 2 A, 2005, Pages 362-372

  Padmanabhan, T ^a  

^a INTER UNIVERSITY CENTRE FOR ASTRONOMY AND ASTROPHYSICS   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22544485375     PISSN: 01039733     EISSN: None     Source Type: Journal    
DOI: 10.1590/S0103-97332005000200023     Document Type: Conference Paper

References (69)

1. A.D. Sakharov, Sov. Phys. Dokl. 12, 1040 (1968);
2. T. Padmanabhan, Int. Jour. Mod. Phys. D (2004) (in press)[grqc/04080511;
3. M.B. Cantcheff,hep-th/0408151; J. Makela and A. Peltola, Phys. Rev. D 69, 124008 (2004);
4. for a discussion of condensed matter analogues, see: G. E. Volovik, The universe in a helium droplet (Oxford University Press, UK, 2003).
5. T. Padmanabhan Gravity and the Thermodynamics of Horizons, Phys. Rep. (in press) [gr-qc/0311036].
6. For reviews, see: B. S. Dewitt, Phys. Rep. 19, 295 (1975);
7. L. Sriramkumar and T. Padmanabhan, Int. J. Mod. Phys. D 11, 1 (2002), [gr-qc-9903054];
8. R. Brout et al., Phys. Rep. 260, 329 (1995);
9. D. W. Sciama et al., Adv. Phys. 30, 327 (1981);
10. T. Padmanabhan, Mod. Phys. Lett. A 17, 923 (2002), [gr-qc/0202078].
11. A non-representative sample of papers related to our discussion are: G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977);
12. K. Srinivasan and T. Padmanabhan, Phys. Rev. D 60, 024007 (1999), [gr-qc-9812028];
13. M. Visser, Phys. Rev. D 48, 5697 (1993);
14. T. Padmanabhan, Phys. Lett. B 173, 43 (1986);
15. Phys. Rev. Lett. 81, 4297 (1998), [hep-th-9801015];
16. Phys. Rev. D 59, 124012 (1999), [hep-th-9801138];
17. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).
18. M. Francaviglia and M. Raiteri, Class. Quant. Grav.21, 3459 (2004);
19. H. Culetu, hep-th/0409079; D.V. Fursaev, gr-qc/0404038; D.Marolf et al., Phys. Rev. D 69, 064006 (2004);
20. A.J.M. Medved et al., Phys. Rev. D 70, 024009 (2004).
21. T. Padmanabhan, Mod. Phys. Lett. A 17, 1147 (2002), [hep-th/0205278];
22. Astroph. Sp. Sci. 285, 407 (2003), [grqc/0209088];
23. Gen. Rel. Grav. 35, 2097 (2003);
24. Gen. Rel. Grav. 34, 2029 (2002), [gr-qc/0205090].
25. G. Date, Class. Quant. Grav. 18, 5219 (2001);
26. A. Ashtekar and B. Krishnan, Phys. Rev. D 68, 104030 (2003).
27. The Greek indices vary over 1-3 and Latin indices go over 0-3. Except for this, we use the conventions of ref.[20].
28. J. D. Brown, Phys. Rev. D 52, 7011 (1995).
29. S. A. Fulling, Phys. Rev. D 7, 2850 (1973);
30. P. C. W. Davies, J. Phys. A 8, 609 (1975);
31. D. G. Boulware, Phys. Rev. D 11, 1404 (1975);
32. W. Troost and H. van Dam, Nucl. Phys. B 152, 442 (1979);
33. E. Keski-Vakkuri and P. Kraus, Nucl. Phys. B 491, 249 (1997);
34. M. K. Parikh and F. Wilczek, Phys. Rev. Lett. 85, 5042 (2000);
35. S. Shankaranarayanan, et al., Mod. Phys. Lett. A 16, 571 (2001), [gr-qc-0007022];
36. Class. Quant. Grav. 19, 2671 (2002), [gr-qc/0010042].;
37. T. Padmanabhan, Mod. Phys. Letts. A 19, 2637 (2004), [gr-qc/0405072];
38. A. J. M. Medved, Phys. Rev. D 66, 124009 (2002);
39. J. S. Dowker, Class. Quant. Grav. 11, L55 (1994);
40. W. Israel, Phys. Lett. A 57, 107 (1976);
41. J. Callan, Curtis G. and F. Wilczek, Phys. Lett. B 333, 55 (1994).
42. T. Padmanabhan and A. Patel, Role of horizons in semiclassical gravity: Entropy and the area spectrum, [gr-qc/0309053] (2003)
43. S. M. Christensen and M. J. Duff, Nucl. Phys. B 146, 11 (1978).
44. T. Padmanabhan, Mod. Phys. Letts. A 18, 2903 (2003), [hepth/0302068].
45. K. Srinivasan et al. Phys. Rev. D 56, 6692 (1997);
46. K. Srinivasan et al., Int. J. Mod. Phys. D 6, 607 (1997);
47. M. Visser, Int. J. Mod. Phys. D 12, 649 (2003).
48. T. Padmanabhan, Phys. Rep. 188, 285 (1990);
49. R. Nityananda and T. Padmanabhan, MNRAS, 271, 976 (1994), [gr-qc-9304022]; D. Lynden-Bell, [cond-mat-9812172].
50. a) for any scalar Q. Simple manipulation with Q = R gives the result. Similarly, the variation of Eq.(12) can be obtained by using Q=T. This approach will be discussed, in detail, in a separate publication.
51. Thus entropy can be expressed as a surface term or as volume integral; this result has been stressed by J.D. Bjorken and applied in the context of QCD, etc., see J.D. Bjorken, astroph/0404233.
52. T. Padmanabhan, Class. Quant. Grav. 19, 5387 (2002), [grqc/0204019].
53. J. R. Ellis, Phil. Trans. Roy. Soc. Lond. A 361, 2607 (2003);
54. T. Padmanabhan, astro-ph/0411044; T. Padmanabhan and T. R. Choudhury, Phys. Rev. D 66,081301 (2002), [hep-th/0205055];
55. J.S. Bagla et al., Phys. Rev. D 67, 063504 (2003), [astroph/0212198];
56. H.K. Jassal et al., MNRAS Letters (in press), [astro-ph/0404378].
57. As far as I know, this relation was first discussed in an unpublished work by D. Lynden-Bell and I in 1994 and is given as an exercise in my book Cosmology and astrophysics - through problems (Cambridge University Press, 1996), p. 170, p. 325. Later I exploited it to obtain gravity in Ref. [5]. It is surprising such a relation went unnoticed for nearly eight decades!
58. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation (Freeman and Co., 1973), p. 422.
59. 1/2r̂, this is called Painleve-Gullstrand coordinates, which have been (re)discovered several times.
60. L.D. Landau and E.M. Lifshitz, Classical Theory of Fields (Pergamon, 1975).
61. T. Padmanabhan, Class. Quant. Grav. 21, 4485 (2004), [gr-qc/0308070].
62. T. Padmanabhan, From gravitons to gravity: Myths and reality, [gr-qc/0409089] (2004).
63. L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, 1975).
64. M. Green, J. Schwarz, and E. Witten, Superstring Theory, vol. 1,2 (Cambridge University Press, 1988).
65. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989);
66. T. Padmanabhan, Phys. Rep. 380, 235 (2003), [hep-th/0212290];
67. J.J. Van der Bij et.al, Physica A 116, 307 (1982);
68. W. Buchmuller and N. Dragon, Phys. Lett. B 207, 292 (1988); and references cited therein.
69. T. Padmanabhan, Class. Quan. Grav. 19, L167 (2002), [gr-qc/0204020]; hep-th/0406060.