Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes

Classical and Quantum Gravity

Volumn 19, Issue 21, 2002, Pages 5387-5408

  Padmanabhan, T ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036417749     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/19/21/306     Document Type: Article

References (48)

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2. For a review of early results, see the articles in DeWitt C and DeWitt B S (eds) 1973 Black Holes (New York: Gordon and Breach) Carter B 1987 Gravitation in Astrophysics, Cargese 1986 ed B Carter and J B Hartle (New York: Plenum) For a more recent discussion, see Bekenstein J 1994 Do we understand black hole entropy Preprint gr-qc/9409015
3. For a review of early results, see the articles in DeWitt C and DeWitt B S (eds) 1973 Black Holes (New York: Gordon and Breach) Carter B 1987 Gravitation in Astrophysics, Cargese 1986 ed B Carter and J B Hartle (New York: Plenum) For a more recent discussion, see Bekenstein J 1994 Do we understand black hole entropy Preprint gr-qc/9409015
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5. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
6. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
7. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
8. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
9. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
10. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
11. Bekenstein J D 1973 Phys. Rev. D 7 2333 Hawking S W 1975 Commun. Math. Phys. 43 199 Gerlach U H 1976 Phys. Rev. D 15 1479 t'Hooft G 1985 Nucl. Phys. B 256 727 York J 1985 Phys. Rev. D 15 2929 Zurek W H and Thorne K S 1985 Phys. Rev. Lett. 54 2171 Bombelli L et al 1986 Phys. Rev. D 34 73 For a recent review, see Sorkin R D 1997 Preprint gr-qc/9705006
12. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
13. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
14. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
15. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
16. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
17. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
18. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
19. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
20. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
21. Hay ward G and Wong K 1992 Phys. Rev. D 46 620 Hayward G and Wong K 1993 Phys. Rev. D 47 4778 Hayward G 1993 Phys. Rev. D 47 3275 Brill D and Hayward G 1994 Phys. Rev. D 50 4914 Martinez E A 1994 Phys. Rev. D 50 4920 Hayward G 1995 Phys. Rev. D 52 2001 Frolov V and Martinez E A 1996 Class. Quantum Grav. 13 481 Booth I S and Mann R B 1999 Phys. Rev. D 60 124004 Booth I S and Creighton J 2000 Phys. Rev. D 62 067503 Epp R J 2000 Phys. Rev. D 62 124018
22. Padmanabhan T 2002 Mod. Phys. Lett. A 17 923 (Preprint gr-qc/0202078) This view has also been expressed in the literature before, see for example, Jacobsen T 1999 Preprint gr-qc/9908031
23. Padmanabhan T 2002 Mod. Phys. Lett. A 17 923 (Preprint gr-qc/0202078) This view has also been expressed in the literature before, see for example, Jacobsen T 1999 Preprint gr-qc/9908031
24. Padmanabhan T 2002 Mod. Phys. Lett. A17 1147 (Preprint hep-th/0205278)
25. Lin Feng-Li and Soo Chopin 1999 Class. Quantum Grav. 16 551
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33. Padmanabhan T 2002 The holography of gravity encoded in a relation between entropy, horizon area and action for gravity Preprint gr-qc/0205090 Padmanabhan T 2002 Second prize essay in the Gravity Research Foundation Essay Contest Gen. Rel. Grav. at press
34. Padmanabhan T 2002 The holography of gravity encoded in a relation between entropy, horizon area and action for gravity Preprint gr-qc/0205090 Padmanabhan T 2002 Second prize essay in the Gravity Research Foundation Essay Contest Gen. Rel. Grav. at press
35. Gibbons G W and Hawking S W 1977 Phys. Rev. D 15 2738
36. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
37. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
38. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
39. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
40. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
41. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
42. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
43. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
44. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
45. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
46. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
47. Brown J D, Lau S R and York J W Preprint gr-qc/0010024 Banados M, Teitelboim C and Zanelli J 1994 Phys. Rev. Lett. 72 957 Ashworth M C and Hayward S A 2000 Phys. Rev. D 62 064024 Iyer V and Wald R M 1995 Phys. Rev. D 52 4430 Brown J D and York J W 1993 Phys. Rev. D 47 1420 Brown J D and York J W 1993 Phys. Rev. D 47 1407 Lau S R 1993 Class. Quantum Grav. 10 2379 Brown J D, Creighton J and Mann R 1994 Phys. Rev. D 50 6394 Hawking S W and Horowitz G T 1996 Class. Quantum Grav. 13 1487 Hawking S W and Hunter C J 1996 Class. Quantum Grav. 13 2735 Brown J D, Lau S R and York J W 1997 Phys. Rev. D 55 1977 Brown J D, Lau S R and York J W 1999 Phys. Rev. D 59 064028
48. Gibbons G W and Hawking S W 1977 Phys. Rev. D 15 2738