Entropy of 4D extremal black holes

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volumn 378, Issue 1-4, 1996, Pages 78-86

  Johnson, Clifford V ^c   Khuri, Ramzi R ^a,b   Myers, Robert C ^b  

^a CERN   (Switzerland)

^b MCGILL UNIVERSITY   (Canada)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002008053     PISSN: 03702693     EISSN: None     Source Type: Journal    
DOI: 10.1016/0370-2693(96)00383-8     Document Type: Article

References (65)

1. A. Strominger and C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, hep-th/9601029.
2. F. Larsen and F. Wilczek, Internal Structure of Black Holes, hep-th/9511064.
3. M. Cvetič and A.A. Tseytlin, Solitonic Strings and BPS Saturated Dyonic Black Holes, hep-th/9512031.
4. C.G. Callan Jr. and J.M. Maldacena, D-Brane Approach to Black Hole Quantum Mechanics, hep-th/9602043.
5. G. Horowitz and A. Strominger, Counting States of Near-Extremal Black Holes, hep-th/9602051.
6. J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-Branes and Spinning Black Holes, hep-th/9602065; J.C. Breckenridge, R.C. Myers, A.W. Peet, A. Strominger and C. Vafa, in preparation.
7. J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-Branes and Spinning Black Holes, hep-th/9602065; J.C. Breckenridge, R.C. Myers, A.W. Peet, A. Strominger and C. Vafa, in preparation.
8. P.K. Townsend, P-brane Democracy, hep-th/9507048.
9. C.V. Johnson, N. Kaloper, R.R. Khuri and R.C. Myers, Is String Theory a Theory of Strings?, Phys. Lett. B 368 (1996) 71, hep-th/9509070.
10. J. Polchinski, Dirichlet Branes and Ramond-Ramond Charges in String Theory, Phys. Rev. Lett. 75 (1995) 4724, hep-th/9510017.
11. J. Dai, R.G. Leigh and J. Polchinski, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
12. J. Dai, R.G. Leigh and J. Polchinski, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
13. J. Dai, R.G. Leigh and J. Polchinski, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
14. J. Dai, R.G. Leigh and J. Polchinski, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
15. J. Polchinski, S. Chaudhuri and C.V. Johnson, Notes on D-Branes, hep-th/9602052.
16. R. Kallosh, A. Linde, T. Ortin, A. Peet and A. Van Proeyen, Phys. Rev. D 46 (1992) 5278, hep-th/9205027.
17. M.J. Duff, R.R. Khuri, R. Minasian and J. Rahmfeld, New Black Hole, String and Membrane Solutions of the Four-Dimensional Heterotic String, Nucl. Phys. B 418 (1994) 195.
18. M.J. Duff and J. Rahmfeld, Massive String States as Extreme Black Holes, Phys. Lett. B 345 (1995) 441.
19. M. Cvetič and D. Youm, Four-Dimensional Supersymmetric Dyonic Black Holes in Eleven-Dimensional Supergravity, Nucl. Phys. B 453 (1995) 259; Dyonic BPS Saturated Black Holes of Heterotic String on a Six Torus, hep-th/9509070; M. Cvetič and A.A. Tseytlin, General Class of BPS Saturated Dyonic Black Holes as Exact Superstring Solutions, hep-th/9510097.
20. M. Cvetič and D. Youm, Four-Dimensional Supersymmetric Dyonic Black Holes in Eleven-Dimensional Supergravity, Nucl. Phys. B 453 (1995) 259; Dyonic BPS Saturated Black Holes of Heterotic String on a Six Torus, hep-th/9509070; M. Cvetič and A.A. Tseytlin, General Class of BPS Saturated Dyonic Black Holes as Exact Superstring Solutions, hep-th/9510097.
21. M. Cvetič and D. Youm, Four-Dimensional Supersymmetric Dyonic Black Holes in Eleven-Dimensional Supergravity, Nucl. Phys. B 453 (1995) 259; Dyonic BPS Saturated Black Holes of Heterotic String on a Six Torus, hep-th/9509070; M. Cvetič and A.A. Tseytlin, General Class of BPS Saturated Dyonic Black Holes as Exact Superstring Solutions, hep-th/9510097.
22. M. Cvetič and D. Youm, All the Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus, hep-th/9512127; Singular BPS Saturated States and Enhanced Symmetries of Four-Dimensional N = 4 Supersymmetric String Vacua, Phys. Lett. B 359 (1995) 87.
23. M. Cvetič and D. Youm, All the Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus, hep-th/9512127; Singular BPS Saturated States and Enhanced Symmetries of Four-Dimensional N = 4 Supersymmetric String Vacua, Phys. Lett. B 359 (1995) 87.
24. H. Lu and C.N. Pope, P-brane Solitons in Maximal Supergravities, hep-th/9512012; Multi Scalar p-brane Solitons, hep-th/9512153; An Approach to the Classification of p-brane Solitons, hep-th/9601089.
25. H. Lu and C.N. Pope, P-brane Solitons in Maximal Supergravities, hep-th/9512012; Multi Scalar p-brane Solitons, hep-th/9512153; An Approach to the Classification of p-brane Solitons, hep-th/9601089.
26. H. Lu and C.N. Pope, P-brane Solitons in Maximal Supergravities, hep-th/9512012; Multi Scalar p-brane Solitons, hep-th/9512153; An Approach to the Classification of p-brane Solitons, hep-th/9601089.
27. R.R. Khuri and T. Ortín, Supersymmetric Black Holes in N = 8 Supergravity, hep-th/9512177; A Non-Supersymmetric Dyonic Extreme Reissner-Nordström Black Hole, hep-th/9512178.
28. R.R. Khuri and T. Ortín, Supersymmetric Black Holes in N = 8 Supergravity, hep-th/9512177; A Non-Supersymmetric Dyonic Extreme Reissner-Nordström Black Hole, hep-th/9512178.
29. D.J. Gross and M.J. Perry, Nucl. Phys. B 226 (1983) 29; R.D. Sorkin, Phys. Rev. Lett. 51 (1983) 87.
30. D.J. Gross and M.J. Perry, Nucl. Phys. B 226 (1983) 29; R.D. Sorkin, Phys. Rev. Lett. 51 (1983) 87.
31. G.W. Gibbons, Nucl. Phys. B 207 (1982) 337; Nucl. Phys. B 298, (1988) 741.
32. G.W. Gibbons, Nucl. Phys. B 207 (1982) 337; Nucl. Phys. B 298, (1988) 741.
33. M.J. Duff and C.N. Pope, Nucl. Phys. B 255 (1985) 355.
34. I. Bakas, Space-Time Interpretations of S Duality and Supersymmetry Violations of T Duality, Phys. Lett. B 343 (1995) 103; E. Bergshoeff, R. Kallosh and T. Ortín, Duality Versus Supersymmetry and Compactification, Phys. Rev. D 51 (1995) 3009; I. Bakas and K. Sfetsos, T Duality and World-Sheet Supersymmetry, Phys. Lett. B 349 (1995) 448; S.F. Hassan, T-duality And Non-Local Supersymmetry, hep-th/9504148; E. Alvarez, L. Alvarez-Gaume and I. Bakas, T Duality and Space-Time Supersymmetry, hep-th/9510028.
35. I. Bakas, Space-Time Interpretations of S Duality and Supersymmetry Violations of T Duality, Phys. Lett. B 343 (1995) 103; E. Bergshoeff, R. Kallosh and T. Ortín, Duality Versus Supersymmetry and Compactification, Phys. Rev. D 51 (1995) 3009; I. Bakas and K. Sfetsos, T Duality and World-Sheet Supersymmetry, Phys. Lett. B 349 (1995) 448; S.F. Hassan, T-duality And Non-Local Supersymmetry, hep-th/9504148; E. Alvarez, L. Alvarez-Gaume and I. Bakas, T Duality and Space-Time Supersymmetry, hep-th/9510028.
36. I. Bakas, Space-Time Interpretations of S Duality and Supersymmetry Violations of T Duality, Phys. Lett. B 343 (1995) 103; E. Bergshoeff, R. Kallosh and T. Ortín, Duality Versus Supersymmetry and Compactification, Phys. Rev. D 51 (1995) 3009; I. Bakas and K. Sfetsos, T Duality and World-Sheet Supersymmetry, Phys. Lett. B 349 (1995) 448; S.F. Hassan, T-duality And Non-Local Supersymmetry, hep-th/9504148; E. Alvarez, L. Alvarez-Gaume and I. Bakas, T Duality and Space-Time Supersymmetry, hep-th/9510028.
37. I. Bakas, Space-Time Interpretations of S Duality and Supersymmetry Violations of T Duality, Phys. Lett. B 343 (1995) 103; E. Bergshoeff, R. Kallosh and T. Ortín, Duality Versus Supersymmetry and Compactification, Phys. Rev. D 51 (1995) 3009; I. Bakas and K. Sfetsos, T Duality and World-Sheet Supersymmetry, Phys. Lett. B 349 (1995) 448; S.F. Hassan, T-duality And Non-Local Supersymmetry, hep-th/9504148; E. Alvarez, L. Alvarez-Gaume and I. Bakas, T Duality and Space-Time Supersymmetry, hep-th/9510028.
38. I. Bakas, Space-Time Interpretations of S Duality and Supersymmetry Violations of T Duality, Phys. Lett. B 343 (1995) 103; E. Bergshoeff, R. Kallosh and T. Ortín, Duality Versus Supersymmetry and Compactification, Phys. Rev. D 51 (1995) 3009; I. Bakas and K. Sfetsos, T Duality and World-Sheet Supersymmetry, Phys. Lett. B 349 (1995) 448; S.F. Hassan, T-duality And Non-Local Supersymmetry, hep-th/9504148; E. Alvarez, L. Alvarez-Gaume and I. Bakas, T Duality and Space-Time Supersymmetry, hep-th/9510028.
39. E. Bergshoeff, C.M. Hull and T. Ortín, Nucl. Phys. B 451 (1995) 547, hep-th/9504081; K. Behrndt, E. Bergshoeff, B. Janssen, Type II Duality symmetries in Six Dimensions, hep-th/9512152.
40. E. Bergshoeff, C.M. Hull and T. Ortín, Nucl. Phys. B 451 (1995) 547, hep-th/9504081; K. Behrndt, E. Bergshoeff, B. Janssen, Type II Duality symmetries in Six Dimensions, hep-th/9512152.
41. A.H. Taub, Ann. Math. 53 (1951) 472; E. Newmann, L. Tamburino and T. Unti, J. Math. Phys. 4 (1963) 915.
42. A.H. Taub, Ann. Math. 53 (1951) 472; E. Newmann, L. Tamburino and T. Unti, J. Math. Phys. 4 (1963) 915.
43. C.W. Misner, J. Math. Phys. 4 (1963) 924.
44. J. Rahmfeld, Extremal Black Holes as Bound States, hep-th/9512089.
45. D. Garfinkle, G.T. Horowitz and A. Strominger, Phys. Rev. D 43 (1991) 3140; D 45 (1992) 3888 (E).
46. D. Garfinkle, G.T. Horowitz and A. Strominger, Phys. Rev. D 43 (1991) 3140; D 45 (1992) 3888 (E).
47. R.R. Khuri, Phys. Lett. B 259 (1991) 261; Nucl. Phys. B 387 (1992) 315, hep-th/9205081.
48. R.R. Khuri, Phys. Lett. B 259 (1991) 261; Nucl. Phys. B 387 (1992) 315, hep-th/9205081.
49. J. Bekenstein, Phys. Rev. D 7 (1973) 2333; D 9 (1974) 3292; S.W. Hawking, Comm. Math. Phys. 43 (1975) 199; Phys. Rev. D 13 (1976) 191.
50. J. Bekenstein, Phys. Rev. D 7 (1973) 2333; D 9 (1974) 3292; S.W. Hawking, Comm. Math. Phys. 43 (1975) 199; Phys. Rev. D 13 (1976) 191.
51. J. Bekenstein, Phys. Rev. D 7 (1973) 2333; D 9 (1974) 3292; S.W. Hawking, Comm. Math. Phys. 43 (1975) 199; Phys. Rev. D 13 (1976) 191.
52. J. Bekenstein, Phys. Rev. D 7 (1973) 2333; D 9 (1974) 3292; S.W. Hawking, Comm. Math. Phys. 43 (1975) 199; Phys. Rev. D 13 (1976) 191.
53. G. Horowitz, A. Strominger and J. Maldacena, to appear.
54. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
55. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
56. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
57. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
58. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
59. E. Witten, Bound States of Strings and P-Branes, hep-th/9510135; M. Li, Boundary States of D-Branes and Dy-Strings, hep-th/9510161; M. Douglas, Branes Within Branes, hep-th/9512077; C. Vafa, Gas of D-Branes and Hagedorn Density of BPS States, hep-th/9511088; M. Bershadsky, C. Vafa and V. Sadov, D-Strings on D-Manifolds, hep-th/9510225; A. Sen, U-Duality and Intersecting D-Branes, hep-th/9511026.
60. C. Vafa, Instantons on D-Branes, hep-th/9512078.
61. S. Ferrara and R. Kallosh, Supersymmetry and Attractors, hep-th/9602136; J. Polchinski, unpublished.
62. S. Ferrara and R. Kallosh, Supersymmetry and Attractors, hep-th/9602136; J. Polchinski, unpublished.
63. R. Kallosh and B. Kol, E(7) Symmetric Area of the Black Hole Horizon, hep-th/9602014.
64. C.M. Hull and P.K. Townsend, Unity of Superstring Dualities, Nucl. Phys. B 438 (1995) 109, hep-th/9410167.
65. E. Witten, String Theory Dynamics in Various Dimensions, Nucl. Phys. B 443 (1995) 85, hep-th/9503124.