Skip to main content

Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-Branes

  • Conference paper
  • First Online:
Mathematical and Quantum Aspects of Relativity and Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 537))

Abstract

Multidimensional model describing the cosmological evolution and/ or spherically symmetric configuration with (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p- brane ansatz is adopted, n “internal” spaces are Ricci-flat, one space M 0 has a non- zero curvature, and all p-branes do not “live” in M 0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V.N. Melnikov, Multidimensional Classical and Quantum Cosmology and Gravitation. Exact Solutions and Variations of Constants. CBPF-NF-051/93, Rio de Janeiro, 1993; V.N. Melnikov. In: Cosmology and Gravitation, ed. M. Novello (Editions Frontieres, Singapore, 1994) p. 147.

    Google Scholar 

  2. V.N. Melnikov, Multidimensional Cosmology and Gravitation, CBPF-MO-002/95, Rio de Janeiro, 1995, 210 p. V.N. Melnikov. In Cosmology and Gravitation.II ed. M. Novello (Editions Frontieres, Singapore, 1996) p. 465.

    Google Scholar 

  3. K.P. Staniukovich and V.N. Melnikov, Hydrodynamics, Fields and Constants in the Theory of Gravitation, (Energoatomizdat, Moscow, 1983), (in Russian).

    Google Scholar 

  4. C. Hull and P. Townsend, Unity of Superstring Dualities, Nucl. Phys. B 438, 109 (1995). P. Horava and E. Witten, Nucl. Phys. B 460, 506 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  5. C.M. Hull, String dynamics at strong coupling, Nucl. Phys. B 468, 113 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  6. J.M. Schwarz, Lectures on Superstring and M-Theory Dualities, hepth/9607201

    Google Scholar 

  7. M.J. Duff, M-theory (the Theory Formerly Known as Strings), hepth/9608117.

    Google Scholar 

  8. C. Vafa, Evidence for F-Theory, hep-th/9602022; Nucl. Phys. B 469, 403 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  9. H. Nicolai, On M-theory, hep-th/9801090.

    Google Scholar 

  10. V.N. Melnikov, Int. J. Theor.Phys. 33, N7, 1569 (1994).

    Article  Google Scholar 

  11. V. de Sabbata, V.N. Melnikov and P.I. Pronin, Prog. Theor. Phys. 88, 623 (1992).

    Article  ADS  Google Scholar 

  12. V.N. Melnikov. In: Gravitational Measurements, Fundamental Metrology and Constants. Eds. V. de Sabbata and V.N. Melnikov (Kluwer Academic Publ.) Dordtrecht, 1988, p.283.

    Google Scholar 

  13. A.J. Sanders and G.T. Gillies, Rivista Nuovo Cim. 19, N2, 1 (1996).

    Article  Google Scholar 

  14. A.J. Sanders and G.T. Gillies, Grav. and Cosm. 3, N4(12), 285 (1997).

    MATH  ADS  Google Scholar 

  15. A.J. Sanders and W.E. Deeds. Phys. Rev. D 46, 480 (1992).

    ADS  Google Scholar 

  16. G.T. Gillies, Rep. Progr. Phys. 60, 151 (1997).

    Article  ADS  Google Scholar 

  17. V. Achilli et al., Nuovo Cim. B 12, 775 (1997).

    Google Scholar 

  18. T. Kaluza, Sitzungsber. Preuss. Akad. Wiss. Berlin Phys. Math., K1 33, 966 (1921).

    Google Scholar 

  19. O. Klein, Z. Phys. 37, 895 (1926).

    Article  ADS  Google Scholar 

  20. V. De Sabbata and E. Schmutzer, Unified Field Theories in more than Four Dimensions, (World Scientific, Singapore, 1982).

    Google Scholar 

  21. H. C. Lee, An Introduction to Kaluza-Klein Theories, (World Scientific, Singapore, 1984).

    Google Scholar 

  22. Yu.S. Vladimirov Physical Space-Time Dimension and Unification of Interactions (University Press, Moscow, 1987) (in Russian).

    Google Scholar 

  23. P.S. Wesson and J. Ponce de Leon, Gen. Rel. Gravit. 26, 555 (1994).

    Article  ADS  Google Scholar 

  24. P. Jordan, Erweiterung der projektiven Relativitatstheorie, Ann. der Phys. 219 (1947).

    Google Scholar 

  25. C. Brans and R.H. Dicke, Phys. Rev. D 124, 925 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  26. E. Cremmer, B. Julia, and J. Scherk, Phys. Lett. B76 409 (1978).

    ADS  Google Scholar 

  27. A. Salam and E. Sezgin, eds., Supergravities in Diverse Dimensions, reprints in 2 vols., (World Scientific, Singapore, 1989).

    Google Scholar 

  28. M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory (Cambridge University Press., Cambridge, 1987).

    MATH  Google Scholar 

  29. V.A. Belinskii and I.M. Khalatnikov, ZhETF, 63, 1121 (1972).

    ADS  Google Scholar 

  30. P. Forgacs and Z. Horvath, Gen. Rel. Grav. 11, 205 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  31. A. Chodos and S. Detweyler, Phys. Rev. D 21, 2167 (1980).

    ADS  Google Scholar 

  32. P.G.O. Freund, Nucl. Phys. B 209, 146 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  33. R. Abbot, S. Barr and S. Ellis, Phys. Rev. D 30, 720 (1984).

    ADS  Google Scholar 

  34. V.A. Rubakov and M.E. Shaposhnikov, Phys. Lett. B 125 136 (1983).

    ADS  Google Scholar 

  35. D. Sahdev, Phys. Lett. B 137, 155 (1984).

    ADS  Google Scholar 

  36. E. Kolb, D. Linkley and D. Seckel, Phys. Rev. D 30 1205 (1984).

    ADS  Google Scholar 

  37. S. Ranjbar-Daemi, A. Salam and J. Strathdee, Phys. Lett. B 135, 388 (1984).

    ADS  Google Scholar 

  38. D. Lorentz-Petzold, Phys. Lett. B 148 43 (1984).

    ADS  Google Scholar 

  39. R. Bergamini and C.A. Orzalesi, Phys. Lett. B 135, 38 (1984).

    ADS  Google Scholar 

  40. M. Gleiser, S. Rajpoot and J.G. Taylor, Ann. Phys. (NY) 160, 299 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  41. U. Bleyer and D.-E. Liebscher, in Proc. III Sem. Quantum Gravity ed. M.A. Markov, V.A. Berezin and V.P. Frolov (Singapore, World Scientific, 1985) p. 662.

    Google Scholar 

  42. U. Bleyer and D.-E. Liebscher, Gen. Rel. Gravit. 17, 989 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  43. M. Demianski, Z. Golda, M. Heller and M. Szydlowski, Class. Quantum Grav. 3, 1190 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  44. D.L. Wiltshire, Phys. Rev. D 36, 1634 (1987).

    ADS  MathSciNet  Google Scholar 

  45. U. Bleyer and D.-E. Liebscher, Annalen d. Physik (Lpz) 44 81 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  46. G.W. Gibbons and K. Maeda, Nucl. Phys. B 298, 741 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  47. Y.-S. Wu and Z. Wang, Phys. Rev. Lett. 57 1978 (1986).

    Article  ADS  Google Scholar 

  48. G.W. Gibbons and D.L. Wiltshire, Nucl. Phys. B 287, 717 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  49. V.D. Ivashchuk and V.N. Melnikov, Nuovo Cimento B 102, 131 (1988).

    ADS  MathSciNet  Google Scholar 

  50. K.A. Bronnikov, V.D. Ivashchuk and V.N. Melnikov, Nuovo Cimento B 102, 209 (1988).

    ADS  Google Scholar 

  51. V.D. Ivashchuk and V.N. Melnikov, Phys. Lett. A 135, 465 (1989).

    ADS  MathSciNet  Google Scholar 

  52. V.D. Ivashchuk, V.N. Melnikov and A.I. Zhuk, Nuovo Cimento B 104, 575 (1989).

    ADS  MathSciNet  Google Scholar 

  53. V.A. Berezin, G. Domenech, M.L. Levinas, C.O. Lousto and N.D. Umerez, Gen. Relativ. Grav. 21, 1177 (1989).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  54. V.D. Ivashchuk and V.N. Melnikov, Chinese Phys. Lett. 7, 97 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  55. M. Demiansky and A. Polnarev, Phys. Rev. D 41, 3003 (1990).

    ADS  Google Scholar 

  56. S.B. Fadeev, V.D. Ivashchuk and V.N. Melnikov in Gravitation and Modern Cosmology (Plenum, N.-Y., 1991) p. 37.

    Google Scholar 

  57. U. Bleyer, D.-E. Liebscher and A.G. Polnarev, Class. Quant. Grav. 8, 477 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  58. V.D. Ivashchuk, Phys. Lett. A 170, 16 (1992).

    ADS  MathSciNet  Google Scholar 

  59. A. Zhuk, Class. Quant. Grav. 9, 202 (1992).

    Article  MathSciNet  Google Scholar 

  60. A. Zhuk, Phys. Rev. D 45, 1192 (1992).

    ADS  MathSciNet  Google Scholar 

  61. A. Zhuk, Sov. Journ. Nucl. Phys. 55, 149 (1992).

    MathSciNet  Google Scholar 

  62. A.I. Zhuk, Sov. Journ. Nucl. Phys. 56, 223 (1993).

    MathSciNet  Google Scholar 

  63. C.W. Misner, In: Magic without Magic: John Archibald Wheeler, ed. J.R. Klauder, Freeman, San Francisko, 1972.

    Google Scholar 

  64. J.J. Halliwell, Phys. Rev. D 38, 2468 (1988).

    ADS  MathSciNet  Google Scholar 

  65. S.W. Hawking and D.N. Page, Phys. Rev. D 42, 2655 (1990).

    ADS  MathSciNet  Google Scholar 

  66. H. Liu, P.S. Wesson and J. Ponce de Leon, J. Math. Phys. 34, 4070 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  67. V.R. Gavrilov, Hadronic J. 16, 469 (1993).

    MATH  ADS  Google Scholar 

  68. V.D. Ivashchuk and V.N. Melnikov, Teor. Mat. Fiz. 98, 312 (1994) (in Russian).

    MathSciNet  Google Scholar 

  69. V.D. Ivashchuk and V.N. Melnikov, Multidimensional cosmology with m-component perfect fluid, gr-qc/ 9403063; Int. J. Mod. Phys. D 3, 795 (1994).

    ADS  Google Scholar 

  70. V.R. Gavrilov, V.D. Ivashchuk and V.N. Melnikov, Integrable pseudoeuclidean Toda-like systems in multidimensional cosmology with multicomponent perfect fluid, J. Math. Phys 36, 5829 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  71. U. Bleyer and A. Zhuk, On multidimensional cosmological models with static internal spaces, Class. and Quantum Grav. 12, 89 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  72. U. Bleyer and A. Zhuk, Multidimensional integrable cosmological models with negative external curvature, Grav. and Cosmol., 2106 (1995).

    ADS  Google Scholar 

  73. U. Bleyer and A. Zhuk, Multidimensional integrable cosmological models with positive external space curvature, Grav. and Cosmol. 1, 37 (1995).

    MATH  ADS  Google Scholar 

  74. U. Bleyer and A. Zhuk, Kasner-like, inflationary and steady-state solutions in multidimensional cosmology, Astron. Nachrichten 317, 161 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  75. A.I. Zhuk, Sov. Journ. Nucl. Phys. 58, No 11 (1995).

    Google Scholar 

  76. J.D. Barrowand J. Stein-Schabes, Phys. Rev. D 32, 1595 (1985).

    ADS  Google Scholar 

  77. J. Demaret, M. Henneaux and P. Spindel, Phys. Lett. B 164 27 (1985).

    ADS  MathSciNet  Google Scholar 

  78. M. Szydlowski and G. Pajdosz, Class. Quant. Grav. 6 (1989), 1391.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  79. V.D. Ivashchuk, A.A. Kirillov and V.N. Melnikov, Izv. Vuzov (Fizika), 37, No 11 (1994) 107 (in Russian).

    MathSciNet  Google Scholar 

  80. V.D. Ivashchuk, A.A. Kirillov and V.N. Melnikov, Pis’ma ZhETF 60 No 4 (1994), 225 (in Russian).

    ADS  Google Scholar 

  81. V.D. Ivashchuk and V.N. Melnikov, Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity, Class. Quantum Grav. 12, 809 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  82. A.A. Kirillov and V.N. Melnikov, Dynamics Inhomogeneouties of Metric in the Vicinity of a Singularity in Multidimensional Cosmology, Phys. Rev. D 52, 723 (1995). A.A. Kirillov and V.N. Melnikov, On Properties of Metrics Inhomogeneouties in the Vicinity of a Singularity in K-K Cosmological Models, Astron. Astrophys. Trans., 10, 101 (1996).

    ADS  MathSciNet  Google Scholar 

  83. M. Rainer, Grav. and Cosmol. 1, 81 (1995).

    ADS  Google Scholar 

  84. M. Gasperini and G. Veneziano, Phys. Rev. D 50, 2519 (1994).

    ADS  Google Scholar 

  85. M. Gasperini and G. Veneziano, Mod. Phys. Lett. A 8, 701 (1993).

    MathSciNet  Google Scholar 

  86. C. Angelantonj, L. Amendola, M. Litterio and F. Occhionero, String cosmology and inflation, Phys. Rev. D 51, 1607 (1995).

    ADS  Google Scholar 

  87. D. Kramer, Acta Physica Polonica 2, F. 6, 807 (1969).

    Google Scholar 

  88. A.I. Legkii, in Probl. of Grav. Theory and Elem. Particles (Atomizdat, Moscow) 10, 149 (1979) (in Russian).

    MathSciNet  Google Scholar 

  89. D.J. Gross and M.J. Perry, Nucl. Phys. B 226, 29 (1993).

    ADS  MathSciNet  Google Scholar 

  90. F.R. Tangherlini, Nuovo Cimento 27, 636 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  91. K.A. Bronnikov, V.D. Ivashchuk in Abstr. VIII Soviet Grav. Conf (Erevan, EGU, 1988) p. 156.

    Google Scholar 

  92. S.B. Fadeev, V.D. Ivashchuk and V.N. Melnikov, Phys. Lett. A 161, 98 (1991).

    ADS  MathSciNet  Google Scholar 

  93. S.B. Fadeev, V.D. Ivashchuk and V.N. Melnikov, Chinese Phys. Lett. 8, 439 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  94. K.A. Bronnikov and V.N. Melnikov, Annals of Physics (N.Y.) 239, 40 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  95. U. Bleyer and V.D. Ivashchuk, Phys. Lett. B 332, 292 (1994).

    ADS  MathSciNet  Google Scholar 

  96. V.D. Ivashchuk and V.N. Melnikov, Class. Quantum Grav., 11, 1793 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  97. V.D. Ivashchuk and V.N. Melnikov, Grav. and Cosmol. 1, No 3, 204 (1995).

    MATH  ADS  Google Scholar 

  98. V.D. Ivashchuk and V.N. Melnikov, Extremal Dilatonic Black Holes in Stringlike Model with Cosmological Term, Phys. Lett. B 384, 58 (1996).

    ADS  MathSciNet  Google Scholar 

  99. V.A. Rubakov, Phys. Lett., B 214, 503 (1988).

    ADS  MathSciNet  Google Scholar 

  100. S. Giddings and A. Strominger, Nucl. Phys. B 321, 481 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  101. A.A. Kirillov, Pis’ma ZhETF 55, 541 (1992).

    ADS  MathSciNet  Google Scholar 

  102. E.I. Guendelman and A.B. Kaganovich, Phys. Lett. B 301, 15 (1993).

    ADS  Google Scholar 

  103. T. Horigushi, Mod. Phys. Lett. A 8, 777 (1993).

    ADS  Google Scholar 

  104. U. Bleyer, V.D. Ivashchuk, V.N. Melnikov and A.I. Zhuk, Multidimensional classical and quantum wormholes in models with cosmological constant. grqc/9405020; Nucl. Phys. B 429 117 (1994).

    MathSciNet  Google Scholar 

  105. V.R. Gavrilov, U. Kasper, V.N. Melnikov and M. Rainer, Toda Chains with Type A m Lie Algebra for Multidimensional m-component Perfect Fluid Cosmology, Preprint Math-97/ Univ. Potsdam, 1997.

    Google Scholar 

  106. V.R. Gavrilov, V.D. Ivashchuk, and V.N. Melnikov, Class. Quant. Grav. 13, 3039 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  107. V.R. Gavrilov and V.N. Melnikov, Theor. Math. Phys 114, N3, 454 (1998).

    Article  MathSciNet  Google Scholar 

  108. V.R. Gavrilov, V.N. Melnikov and R. Triay, Exact Solutions in Multidimensional Cosmology with Shear and Bulk Viscosity, Class. Quant. Grav. 14, 2203 (1997). V.R. Gavrilov, V.N. Melnikov and M. Novello, Exact Solutions in Multidimensional Cosmology with Bulk Viscosity, Grav. and Cosmol. 1, No 2, 149 (1995). V.R. Gavrilov, V.N. Melnikov and M. Novello, Bulk Viscosity and Entropy Production in Multidimensional Integrable Cosmology Grav. and Cosmol. 2, No 4(8), 325 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  109. M. Rainer and A. Zhuk, Phys. Rev., D 54 6186 (1996).

    ADS  MathSciNet  Google Scholar 

  110. V.D. Ivashchuk and V.N. Melnikov, Multidimensional Gravity with Einstein Internal spaces, hep-th/9612054; Grav. and Cosmol. 2, No 3(7), 177 (1996).

    Google Scholar 

  111. K.A. Bronnikov and J.C. Fabris, Grav. and Cosmol. 2, No 4(8), (1996).

    Google Scholar 

  112. M.J. Duff, R.R. Khuri and J.X. Lu, Phys. Rep. 259, 213 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  113. K.S. Stelle, Lectures on Supergravity p-Branes, hep-th/9701088. hepth/9608117.

    Google Scholar 

  114. G.W. Gibbons, G.T. Horowitz and P.K. Townsend, Class. Quant. Grav. 12, 297 (1995); hep-th/9410073.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  115. A. Dabholkar, G. Gibbons, J.A. Harvey, and F. Ruiz Ruiz, Nucl. Phys. B 340, 33 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  116. C.G. Callan, J.A. Harvey and A. Strominger, Nucl. Phys. 359 (1991) 611; Nucl. Phys. B 367, 60 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  117. M.J. Duff and K.S. Stelle, Phys. Lett. B 253, 113 (1991).

    ADS  MathSciNet  Google Scholar 

  118. G.T. Horowitz and A. Strominger, Nucl. Phys. B 360, 197 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  119. R. Güven, Phys. Lett. B 276, 49 (1992); Phys. Lett. B 212, 277 (1988).

    ADS  Google Scholar 

  120. R. Kallosh, A. Linde, T. Ortin, A. Peet and A. van Proeyen, Phys. Rev. D 46, 5278 (1992).

    ADS  Google Scholar 

  121. H. Lü, C.N. Pope, E. Sezgin and K. Stelle, Nucl. Phys. B 456, 669 (1995).

    Article  ADS  Google Scholar 

  122. A. Strominger, Phys. Lett. B 383, 44 (1996); hep-th/9512059.

    ADS  MathSciNet  Google Scholar 

  123. P.K. Townsend, Phys. Lett. B 373, 68 (1996); hep-th/9512062.

    ADS  MathSciNet  Google Scholar 

  124. A.A. Tseytlin, Nucl. Phys. B 487, 141 (1997); hep-th/9609212.

    Article  ADS  MathSciNet  Google Scholar 

  125. A.A. Tseytlin, Mod. Phys. Lett. A11, 689 (1996); hep-th/9601177.

    ADS  MathSciNet  Google Scholar 

  126. G. Papadopoulos and P.K. Townsend, Phys. Lett. B 380, 273 (1996).

    ADS  MathSciNet  Google Scholar 

  127. A.A. Tseytlin, Harmonic Superpositions of M-branes, hep-th/9604035; Nucl. Phys. B 475, 149 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  128. J.P. Gauntlett, D.A. Kastor, and J. Traschen, Overlapping Branes in M-Theory, hep-th/9604179; Nucl. Phys. B 478, 544 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  129. N. Khvengia, Z. Khvengia, H. Lü, C.N. Pope, Intersecting M-Branes and Bound States, hep-th/9605082.

    Google Scholar 

  130. H. Lü, C.N. Pope, and K.W. Xu, Liouville and Toda Solitons in M-Theory, hep-th/9604058.

    Google Scholar 

  131. M. Cvetic and A. Tseytlin, Nucl. Phys. B 478, 181 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  132. I.R. Klebanov and A.A. Tseytlin, Intersecting M-branes as Four-Dimensional Black Holes, Preprint PUPT-1616, Imperial/TP/95-96/41, hep-th/9604166; Nucl. Phys. B 475, 164 (1996).

    Google Scholar 

  133. N. Ohta and T. Shimizu, Non-extreme Black Holes from Intersecting M-branes, hep-th/9701095.

    Google Scholar 

  134. H. Lü, C.N. Pope, and K.S. Stelle, Vertical Versus Diagonal Reduction for p-Branes, hep-th/9605082.

    Google Scholar 

  135. E. Bergshoeff, R. Kallosh and T. Ortin, Stationary Axion/Dilaton Solutions and Supersymmetry, hep-th/9605059; Nucl. Phys. B 478, 156 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  136. G. Clément and D.V. Gal’tsov, Stationary BPS solutions to dilaton-axion gravity Preprint GCR-96/07/02 DTP-MSU/96-11, hep-th/9607043.

    Google Scholar 

  137. A. Volovich, Three-block p-branes in various dimensions, hep-th/9608095.

    Google Scholar 

  138. I.Ya. Aref’eva and A.I. Volovich, Composite p-branes in Diverse Dimensions, Preprint SMI-19-96, hep-th/9611026; Class. Quantum Grav. 14(11), 2990 (1997).

    MathSciNet  Google Scholar 

  139. I.Ya. Aref’eva, K. Viswanathan, A.I. Volovich and I.V. Volovich, p-Brane Solutions in Diverse Dimensions, hep-th/9701092.

    Google Scholar 

  140. N. Khvengia, Z. Khvengia, H. Lănd C.N. Pope, Toward Field Theory of F-Theory, hep-th/9703012.

    Google Scholar 

  141. V.D. Ivashchuk and V.N. Melnikov, Intersecting p-Brane Solutions in Multidimensional Gravity and M-Theory, hep-th/9612089; Grav. and Cosmol. 2, No 4, 297 (1996).

    MATH  Google Scholar 

  142. V.D. Ivashchuk and V.N. Melnikov, Phys. Lett. B 403, 23 (1997).

    ADS  MathSciNet  Google Scholar 

  143. V.D. Ivashchuk and V.N. Melnikov, Sigma-Model for Generalized Composite p-branes, hep-th/9705036; Class. and Quant. Grav. 14, 11, 3001 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  144. V.D. Ivashchuk, M. Rainer and V.N. Melnikov, Multidimensional Sigma-Models with Composite Electric p-branes, gr-qc/9705005; Gravit. and Cosm. 4, No1(13) (1998).

    Google Scholar 

  145. I.Ya. Aref’eva and O.A. Rytchkov, Incidence Matrix Description of Intersecting p-brane Solutions, hep-th/9612236.

    Google Scholar 

  146. R. Argurio, F. Englert and L. Hourant, Intersection Rules for p-branes, hepth/9701042.

    Google Scholar 

  147. I.Ya. Aref’eva M.G. Ivanov and O.A. Rytchkov, Properties of Intersecting p-branes in Various Dimensions, hep-th/9702077.

    Google Scholar 

  148. I.Ya. Aref’eva, M.G. Ivanov and I.V. Volovich, Non-Extremal Intersecting p-Branes in Various Dimensions, hep-th/9702079; Phys. Lett. B 406, 44 (1997).

    ADS  MathSciNet  Google Scholar 

  149. N. Ohta, Intersection Rules for Non-extreme p-branes, hep-th/9702164.

    Google Scholar 

  150. K.A. Bronnikov, V.D. Ivashchuk and V.N. Melnikov, The Reissner-Nordström Problem for Intersecting Electric and Magnetic p-Branes, gr-qc/9710054; Grav. and Cosmol. 3, No 3(11), 203 (1997).

    MATH  ADS  Google Scholar 

  151. K.A. Bronnikov, U. Kasper and M. Rainer, Intersecting Electric and Magnetic p-Branes: Spherically Symmetric Solutions, gr-qc/9708058.

    Google Scholar 

  152. K.A. Bronnikov, M.A. Grebeniuk, V.D. Ivashchuk and V.N. Melnikov, Integrable Multidimensional Cosmology for Intersecting p-branes, Grav. and Cosmol. 3, No 2(10), 105 (1997).

    MATH  ADS  Google Scholar 

  153. M.A. Grebeniuk, V.D. Ivashchuk and V.N. Melnikov, Integrable Multidimensional Quantum Cosmology for Intersecting p-Branes, Grav. and Cosmol. 3, No 3(11), 243 (1997), gr-qc/9708031.

    MATH  ADS  Google Scholar 

  154. H. Lü, J. Maharana, S. Mukherji and C.N. Pope, Cosmological Solutions, p-branes and the Wheeler De Witt Equation, hep-th/9707182.

    Google Scholar 

  155. H. Lü, S. Mukherji, C.N. Pope and K.-W. Xu, Cosmological Solutions in String Theories, hep-th/9610107.

    Google Scholar 

  156. S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).

    Google Scholar 

  157. V.D. Ivashchuk and V.N. Melnikov, Multidimensional Ouantum Cosmology with Intersecting p-branes, Hadronic J. 21, 319 (1998).

    MATH  MathSciNet  ADS  Google Scholar 

  158. M.A. Grebeniuk, V.D. Ivashchuk and V.N. Melnikov, Multidimensional Cosmology for Intersecting p-branes with Static Internal Spaces, Grav. and Cosm., 4, No 2(14) (1998).

    Google Scholar 

  159. S.D. Majumdar, Phys. Rev. 72, 930 (1947); A. Papapetrou, Proc. R. Irish Acad. A51, 191 (1947).

    Article  Google Scholar 

  160. N.M. Bocharova, K.A. Bronnikov and V.N. Melnikov, Vestnik MGU (Moscow Univ.), 6, 706 (1970)(in Russian)-first MP-type solution with conformal scalar field; K.A. Bronnikov, Acta Phys. Polonica, B4, 251 (1973); K.A. Bronnikov and V.N. Melnikov, in Problems of Theory of Gravitation and Elementary Particles, 5, 80 (1974) (in Russian)-first MP-type solution with conformal scalar and electromagnetic fields.

    Google Scholar 

  161. M. SzydRlowski, Acta Cosmologica 18, 85 (1992).

    ADS  Google Scholar 

  162. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2752 (1977).

    ADS  MathSciNet  Google Scholar 

  163. V.D. Ivashchuk and V.N. Melnikov, Int. J. Mod. Phys. D 4, 167 (1995).

    ADS  MathSciNet  Google Scholar 

  164. V.D. Ivashchuk and V.N. Melnikov, On Singular Solutions in Multidimensional Gravity, hep-th/9612089; Grav. and Cosmol. 1, No 3, 204 (1996).

    ADS  Google Scholar 

  165. V.D. Ivashchuk and V.N. Melnikov, Multidimensional Classical and Quantum Cosmology with Intersecting p-branes, hep-th/9708157; J. Math. Phys., 39, 2866 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  166. K.A. Bronnikov, Block-orthogonal Brane systems, Black Holes and Wormholes, hep-th/9710207; Grav. and Cosmol. 4, No 2(14), (1998).

    Google Scholar 

  167. V.D. Ivashchuk and V.N. Melnikov, Mudjumdar-Papapetrou Type Solutions in Sigma-model and Intersecting p-branes, hep-th/9702121; Class. Quantum Grav. 16, 849 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  168. V.D. Ivashchuk, Composite p-branes on Product of Einstein spaces, Phys. Lett. B 434, 28 (1998).

    ADS  MathSciNet  Google Scholar 

  169. T. Damour, “Gravitation, Experiment and Cosmology”, gr-qc/9606079.

    Google Scholar 

  170. R.D. Reasenberg et. al., Astrophys. J. 234, L219 (1979).

    Article  ADS  Google Scholar 

  171. J.O. Dickey et al., Science 265, 482 (1994).

    Article  ADS  Google Scholar 

  172. K. Nordtvedt, Phys. Rev. 169, 1017 (1968).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ivashchuk, V., Melnikov, V. (2000). Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-Branes. In: Cotsakis, S., Gibbons, G.W. (eds) Mathematical and Quantum Aspects of Relativity and Cosmology. Lecture Notes in Physics, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46671-1_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-46671-1_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66865-7

  • Online ISBN: 978-3-540-46671-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics