Covariant gravitational dynamics in 3+1+1 dimensions

Classical and Quantum Gravity

Volumn 27, Issue 10, 2010, Pages

  Keresztes, Zoltn ^a   Gergely, Lszló Á ^a  

^a UNIVERSITY OF SZEGED   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951586509     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/10/105009     Document Type: Article

References (67)

1. Randall L and Sundrum R 1999 An alternative to compactification Phys. Rev. Lett. 83 4690 (arXiv:hep-th/9906064)
2. Maartens R 2004 Brane-world gravity Living Rev. Rel. 7 7 (arXiv:gr-qc/0312059)
3. Gergely L Á 2000 Generalized Friedmann branes Phys. Rev. D 68 124011 (arXiv:gr-qc/0308072)
4. Gergely L Á 2008 Friedmann branes with variable tension Phys. Rev. D 78 084006 (arXiv:0806.3857 [gr-qc]). The correspondence to the notations of this paper is
5. Mak M K and Harko T 2004 Can the galactic rotation curves be explained in brane world models? Phys. Rev. D 70 024010 (arXiv:gr-qc/0404104)
6. Harko T and Cheng K S 2006 Galactic metric, dark radiation, dark pressure and gravitational lensing in brane world models Astrophys. J. 636 8 (arXiv:gr-qc/0509576)
7. Boehmer C G and Harko T 2007 Galactic dark matter as a bulk effect on the brane Class. Quantum Grav. 24 3191 (arXiv:0705.2496)
8. Harko T and Cheng K S 2007 The virial theorem and the dynamics of clusters of galaxies in the brane world models Phys. Rev. D 76 044013 (arXiv:0707.1128)
9. Gergely L Á and Kovács Z 2005 Gravitational dynamics in s+1+1 dimensions Phys. Rev. D 72 064015 (arXiv:gr-qc/0507020). In the setup developed there the 5d spacetime is double-foliable; therefore, and hold in the notations of the present paper. The conversion of notations to the notations of the present paper is
10. Gergely L Á and Kovács Z 2008 Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory Phys. Rev. D 77 024003 (arXiv:0709.2131)
11. Maartens R 2000 Cosmological dynamics on the brane Phys. Rev. D 62 084023 (arXiv:hep-th/0004166). The correspondence to the notations of this paper is
12. Ehlers J 1961 Beiträge zur relativistischen Mechanik kontinuierlicher Medien Abh. Mainz Akad. Wiss. u. Litt. (Math. Nat. kl) 11 792
13. Ellis G F R 1971 General Relativity and Cosmology ed R K Sachs (New York: Academic)
14. Ellis G F R and van Elst H 1999 Cosmological models Theoretical and Observational Cosmology (NATO Adv. Study Inst. Ser. C. Math. Phys. Sci. vol 541) ed M Lachiéze-Rey (Dordrecht: Kluwer) pp 1-116 (arXiv:gr-qc/9812046)
15. Ellis G F R Cosmological models Modern Cosmology ed S Bonometto, V Gorini and U Moschella (London: Institute of Physics Publishing)
16. Clarkson C A and Barrett R K 2003 Covariant perturbations of Schwarzschild black holes Class. Quant. Grav. 20 3855-84 (arXiv:gr-qc/0209051v3)
17. Clarkson C 2007 A covariant approach for perturbations of rotationally symmetric spacetimes Phys. Rev. D 76 104034 (arXiv:0708.1398v1 [gr-qc])
18. Nzioki A M, Carloni S, Goswami R and Dunsby P K S 2009 A new framework for studying spherically symmetric static solutions in f(R) gravity arXiv:0908.3333 [gr-qc]
19. Hawking S W 1966 Perturbations of an expanding universe Astrophys. J. 145 544
20. Ellis G F R and Bruni M 1989 Covariant and gauge-invariant approach to cosmological density fluctuations Phys. Rev. D 40 1804
21. Ellis G F R, Hwang J and Bruni M 1989 Covariant and gauge-independent perfect-fluid Robertson-Walker perturbations Phys. Rev. D 40 1819
22. Ellis G F R, Bruni M and Hwang J 1989 Density-gradient-vorticity relation in perfect-fluid Robertson-Walker perturbations Phys. Rev. D 40 1819
23. Dunsby P, Bruni M and Ellis G F R 1992 Cosmological perturbations and the physical meaning of gauge-invariant variables Astrophys. J. 395 34
24. Challinor A and Lasenby A 1999 Cosmic microwave background anisotropies in the cold dark matter model: a covariant and gauge-invariant approach Astrophys. J. 513 1
25. Maartens R, Gebbie T and Ellis G F R 1999 Cosmic microwave background anisotropies: nonlinear dynamics Phys. Rev. D 59 083506 (arXiv:astro-ph/9808163)
26. Gebbie T and Ellis G F R 2000 1+3 covariant cosmic microwave background anisotropies I: algebraic relations for mode and multipole representations Ann. Phys. 282 285 (arXiv:astro-ph/9804316)
27. Gebbie T, Dunsby P and Ellis G F R 2000 1+3 covariant cosmic microwave background anisotropies II: the almost-Friedmann Lemaitre model Ann. Phys. 282 321
28. Mukohyama S 2000 Gauge-invariant gravitational perturbations of maximally symmetric spacetimes Phys. Rev. D 62 084015 (arXiv:hep-th/0004067)
29. Mukohyama S 2000 Perturbation of junction condition and doubly gauge-invariant variables Class. Quantum Grav. 17 4777 (arXiv:hep-th/0006146)
30. Koyama K and Soda J 2000 Evolution of cosmological perturbations in the brane world Phys. Rev. D 62 123502
31. Gordon C and Maartens R 2001 Density perturbations in the brane-world Phys. Rev. D 63 044022
32. Mukohyama S 2001 Integro-differential equation for brane-world cosmological perturbations Phys. Rev. D 64 064006 (arXiv:hep-th/0104185)
33. Mukohyama S 2002 Integro-differential equation for brane-world cosmological perturbations Phys. Rev. D 66 049902 (erratum)
34. Leong B, Dunsby P, Challinor A and Lasenby A 2002 (1+3) covariant dynamics of scalar perturbations in braneworlds Phys. Rev. D 65 104012 (arXiv:gr-qc/0111033)
35. Gumjudpai B, Maartens R and Gordon C 2003 Density perturbations in a brane-world universe with dark radiation Class. Quantum Grav. 20 3295 (arXiv:gr-qc/0304067)
36. Dunsby P K S, Goheer N, Bruni M and Coley A 2004 Are braneworlds born isotropic? Phys. Rev. D 69 101303 (arXiv:hep-th/0312174)
37. Goheer N, Dunsby P K S, Coley A and Bruni M 2004 Large-scale perturbations on the brane and the isotropy of the cosmological singularity Phys. Rev. D 70 123517 (arXiv:hep-th/0408092)
38. Koyama K, Langlois D, Maartens R and Wands D 2004 Scalar perturbations from brane-world inflation J. Cosmol. Astropart. Phys. JCAP11(2004)002 (arXiv:hep-th/0408222)
39. Deffayet C 2005 A note on the wellposedness of scalar brane world cosmological perturbations Phys. Rev. D 71 023520 (arXiv:hep-th/0409302)
40. Pal S 2006 Structure formation on the brane: a mimicry Phys. Rev. D 74 024005 (arXiv:gr-qc/0606085)
41. Pal S 2008 Brane cosmology, Weyl fluid, and density perturbations Phys. Rev. D 78 043517 (arXiv:0806.2505 [gr-qc])
42. Coley A 2008 Classification of the Weyl tensor in higher dimensions and applications Class. Quant. Grav. 25 033001 (arXiv:0710.1598)
43. Senovilla J M M 2000 General electric-magnetic decomposition of fields, positivity and Rainich-like conditions Proceedings of the Spanish Relativity Meeting (arXiv:gr-qc/0010095)
44. Dvali G, Gabadadze G and Porrati M 2000 4D gravity on a brane in 5D Minkowski space Phys. Lett. B 485 208 (arXiv:hep-th/0005016)
45. Deffayet C 2001 Cosmology on a brane in Minkowski bulk Phys. Lett. B 502 199 (arXiv:hep-th/0010186)
46. Deffayet C 2002 On brane world cosmological perturbations Phys. Rev. D 66 103504 (arXiv:hep-th/0205084)
47. Maeda K, Mizuno S and Torii T 2003 Effective gravitational equations on brane world with induced gravity Phys. Rev. D 68 024033 (arXiv:gr-qc/0303039)
48. Sahni V and Shtanov Y 2003 Brane-world models of dark energy J. Cosmol. Astropart. Phys. JCAP11(2003)014 (arXiv:astro-ph/0202346)
49. Gergely L Á and Maartens R 2005 Asymmetric brane-worlds with induced gravity Phys. Rev. D 71 024032 (arXiv:gr-qc/0411097)
50. Koyama K 2005 Are there ghosts in the self-accelerating brane universe? Phys. Rev. D 72 123511 (arXiv:hep-th/0503191)
51. Gorbunov D, Koyama K and Sibiryakov S 2006 More on ghosts in DGP model Phys. Rev. D 73 044016 (arXiv:hep-th/0512097)
52. Charmousis C, Gregory R, Kaloper N and Padilla A 2006 DGP spectroscopy J. High Energy Phys. JHEP10(2006)066 (arXiv:hep-th/0604086)
53. Izumi K, Koyama K and Tanaka T 2007 Unexorcized ghost in DGP brane world J. High Energy Phys. JHEP04(2007)053 (arXiv:hep-th/0610282)
54. Barrow J D, Maartens R and Tsagas C G 2007 Cosmology with inhomogeneous magnetic fields Phys. Rep. 449 131
55. Tsagas C G, Challinor A and Maartens R 2008 Relativistic cosmology and large-scale structure Phys. Rep. 465 61 (arXiv:0705.4397)
56. Israel W 1966 Singular hypersurfaces and thin shells in general relativity Nuovo Cimento B 44 B 4349
57. Israel W 1966 Singular hypersurfaces and thin shells in general relativity Nuovo Cimento B 48 B 2583 (errata)
58. Lanczos C 1922 Ein vereinfachendes koordinatensystem f ür Einsteinschen gravitationsgleichungen Phys. Zeils. 23 539
59. Lanczos C 1924 Flachenhafte verteilung der Materie in der EinsteinEinsteinschen gravitationstheorie Ann. Phys. (Lepzig) 74 518
60. Shiromizu T, Maeda K and Sasaki M 2000 The Einstein equations on the 3-brane world Phys. Rev. D 62 024012 (arXiv:gr-qc/9910076)
61. Campos A, Maartens R, Matravers D and Sopuerta C F 2003 Braneworld cosmological models with anisotropy Phys. Rev. D 68 103520 (arXiv:hep-th/ 0308158)
62. Fabbri A, Langlois D, Steer D A and Zegers R 2004 Brane cosmology with an anisotropic bulk J. High Energy Phys. JHEP09(2004)025 (arXiv:hep-th/0407262)
63. van Elst H and Ellis G F R 1996 The covariant approach to LRS perfect fluid space-time geometries Class. Quantum Grav. 13 1099 (arXiv:gr-qc/9510044)
64. Dadhich N, Maartens R, Papadopoulos P and Rezania V 2000 Black holes on the brane Phys. Lett. B 487 1 (arXiv:hep-th/0003061)
65. Aliev A N and Gümrükçüglu A E 2005 Charged rotating black holes on a 3-brane Phys. Rev. D 71 104027 (arXiv:hep-th/0502223)
66. Shibata M and Nakamura T 1995 Evolution of three-dimensional gravitational waves: harmonic slicing case Phys. Rev. D 52 5428
67. Baumgarte T W and Shapiro S L 1998 Numerical integration of Einstein's field equations Phys. Rev. D 59 024007