Maxwell equations and the optical geometry

Journal of Mathematical Physics

Volumn 39, Issue 6, 1998, Pages 3158-3166

  Sonego, Sebastiano ^a,b   Abramowicz, Marek A ^a,b,c  

^a UNIVERSITY OF UDINE   (Italy)

^b SISSA   (Italy)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032385123     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532245     Document Type: Article

References (29)

1. We adopt the following terminology. An observer is a future-directed, differentiable timelike curve. A reference frame is a congruence of observers, that can also be identified with the field of their four-velocities.
2. abcd, and work in units in which c=1.
3. R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
4. D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, 1980), pp. 343-344; H. Stephani, General Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1990), p. 174.
5. D. Kramer, H. Stephani, E. Herlt, and M. MacCallum, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, 1980), pp. 343-344; H. Stephani, General Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1990), p. 174.
6. S. A. Fulling, "Alternative vacuum states in static space-times with horizons," J. Phys. A 10, 917-951 (1977).
7. M. A. Abramowicz, B. Carter, and J. P. Lasota, "Optical reference geometry for stationary and static dynamics," Gen. Relativ. Gravit. 20, 1173-1183 (1988).
8. M. A. Abramowicz, "Centrifugal force: a few surprises." Mon. Not. R. Astron. Soc. 245, 733-746 (1990).
9. M. A. Abramowicz, "Inertial forces in general relativity," in The Renaissance of General Relativity and Cosmology, edited by G. Ellis, A. Lanza, and J. Miller (Cambridge University Press, Cambridge, 1993), pp. 40-58; M. A. Abramowicz, P. Nurowski, and N. Wex, "Covariant definition of inertial forces," Class. Quantum Grav. 10, L183-L186 (1993); S. Sonego and M. Massar, "Covariant definition of inertial forces: Newtonian limit and time-dependent gravitational fields," ibid. 13, 139-144 (1996).
10. M. A. Abramowicz, "Inertial forces in general relativity," in The Renaissance of General Relativity and Cosmology, edited by G. Ellis, A. Lanza, and J. Miller (Cambridge University Press, Cambridge, 1993), pp. 40-58; M. A. Abramowicz, P. Nurowski, and N. Wex, "Covariant definition of inertial forces," Class. Quantum Grav. 10, L183-L186 (1993); S. Sonego and M. Massar, "Covariant definition of inertial forces: Newtonian limit and time-dependent gravitational fields," ibid. 13, 139-144 (1996).
11. M. A. Abramowicz, "Inertial forces in general relativity," in The Renaissance of General Relativity and Cosmology, edited by G. Ellis, A. Lanza, and J. Miller (Cambridge University Press, Cambridge, 1993), pp. 40-58; M. A. Abramowicz, P. Nurowski, and N. Wex, "Covariant definition of inertial forces," Class. Quantum Grav. 10, L183-L186 (1993); S. Sonego and M. Massar, "Covariant definition of inertial forces: Newtonian limit and time-dependent gravitational fields," ibid. 13, 139-144 (1996).
12. S. Sonego (unpublished).
13. S. Sonego and M. Massar, "On the notions of gravitational and centrifugal force in static spherically symmetric space-times," Mon. Not. R. Astron, Soc. 281, 659-665 (1996).
14. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
15. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
16. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
17. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
18. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
19. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
20. M. A. Abramowicz and A. R. Prasanna, "Centrifugal-force reversal near a Schwarzschild black hole," Mon. Not. R. Astron. Soc. 245, 720-728 (1990); M. A. Abramowicz and J. C. Miller, "Ellipticity behavior of relativistic Maclaurin spheroids," ibid. 245, 729-732 (1990); M. A. Abramowicz and J. Bičák, "The interplay between relativistic gravitational, centrifugal and electric forces: A simple example," Gen. Relativ. Gravit. 23, 941-946 (1991) M. A. Abramowicz, J. C. Miller, and Z. Stuchlík, "Concept of radius of gyration in general realitivity," Phys. Rev. D 47, 1440-1447 (1993); S. Sonego and A. Lanza, "Relativistic perihelion advance as a centrifugal effect," Mon. Not. R. Astron. Soc. 279, L65-L66 (1996); M. A. Abramowicz, A. Lanza, J. C. Miller, and S. Sonego, "Curving Newtonian space," Gen. Relativ. Gravit. 29, 1585-1596 (1997); M. A. Abramowicz, N. Andersson, M. Bruni, P. Ghosh, and S. Sonego, "Gravitational waves from ultracompact stars: the optical geometry view of trapped modes," Class. Quantum Grav. 14, L189-L194 (1997)
21. R. D. Greene, E. L. Schucking, and C. V. Vishveshwara, "The rest frame in stationary space-times with axial symmetry," J. Math. Phys. 16, 153-162 (1975).
22. In spacetimes with a sufficiently high degree of symmetry, this definition turns out to be too weak, and one must supplement it with additional constraints (Ref. 9). However, these considerations do not affect the following discussion, and we shall therefore ignore them.
23. J. S. Dowker and G. Kennedy, "Finite temperature and boundary effects in static space-times," J. Phys. A 11, 895-920 (1978); G. W. Gibbons and M. J. Perry, "Black holes and thermal Green functions," Proc. R. Soc. London, Ser. A 358, 467-494 (1978); G. Kennedy, R. Critchley, and J. S. Dowker, "Finite temperature field theory with boundaries: Stress tensor and surface action renormalisation," Ann. Phys. (N.Y.) 125, 346-400 (1980).
24. J. S. Dowker and G. Kennedy, "Finite temperature and boundary effects in static space-times," J. Phys. A 11, 895-920 (1978); G. W. Gibbons and M. J. Perry, "Black holes and thermal Green functions," Proc. R. Soc. London, Ser. A 358, 467-494 (1978); G. Kennedy, R. Critchley, and J. S. Dowker, "Finite temperature field theory with boundaries: Stress tensor and surface action renormalisation," Ann. Phys. (N.Y.) 125, 346-400 (1980).
25. J. S. Dowker and G. Kennedy, "Finite temperature and boundary effects in static space-times," J. Phys. A 11, 895-920 (1978); G. W. Gibbons and M. J. Perry, "Black holes and thermal Green functions," Proc. R. Soc. London, Ser. A 358, 467-494 (1978); G. Kennedy, R. Critchley, and J. S. Dowker, "Finite temperature field theory with boundaries: Stress tensor and surface action renormalisation," Ann. Phys. (N.Y.) 125, 346-400 (1980).
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