Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole
This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.
[1] J. A. Kong, Electromagnetic Wave Theory, 2nd Ed. New York: Wiley,
1990.
[2] K. Murawski, Analytical and Numerical Methods for wave propagation
in fluid media, World Scientific Publishing Co. Pte. Ltd., Vol. 7, series
A, 2002.
[3] P.A.M. Dirac,General Theory of Relativity, second edition, Princeton
University Press, 1996.
[4] Geroch and Robert, General Relativity from A to B, University of Chicago
Press, Chicago, 1981.
[5] Thorne, Kip S.; Misner, Charles and Wheeler, John (1973), Gravitation
, W. H. Freeman and Company, ISBN 0-7167-0344-0.
[6] Wald, Robert M. (1992), Space, Time, and Gravity: The Theory of the
Big Bang and Black Holes, University of Chicago Press, ISBN 0-226-
87029-4.
[7] D. Finkelstein (1958), Past-Future Asymmetry of the Gravitational Field
of a Point Particle, Phys. Rev. 110: 965-967.
[8] Lewis G. F. and Kwan, J. No Way Back: Maximizing Survival Time
Below the Schwarzschild Event Horizon, Publications of the Astronomical
Society of Australia 24 (2): 46-52(2007).
[9] R. P. Kerr, Gravitational field of a spinning mass as an example of
algebraically special metrics , Phys. Rev. Lett. 11, 237 (1963).
[10] Carr B.J. , Primordial Black Holes: Do They Exist and Are They Useful?,
Proceedings of "Inflating Horizon of Particle Astrophysics and Cosmology",
Universal Academy Press Inc and Yamada Science Foundation,
http://arxiv.org/abs/astro-ph/0511743 2005.
[11] McClintock, Jeffrey E.; Shafee, Rebecca; Narayan, Ramesh; Remillard,
Ronald A.; Davis, Shane W. and Li, Li-Xin (2006), The Spin of the Near-
Extreme Kerr Black Hole GRS 1915+105 , Astrophys.J. 652: 518-539,
¡http://arxiv.org/abs/astro-ph/0606076¿.
[12] Page, Ron N. , Hawking Radiation and Black Hole Thermodynamics,
New.J.Phys. 7(203), (2005).
[13] Bloom, J.S., Kulkarni, S. R., Djorgovski, S. G., The Observed Offset
Distribution of Gamma-Ray Bursts from Their Host Galaxies: A Robust
Clue to the Nature of the Progenitors, Astronomical Journal 123: 1111-
1148(2002).
[14] Winter, L.M., Mushotzky, R.F. and Reynolds, C.S., XMM-Newton
Archival Study of the ULX Population in Nearby Galaxies, Astrophysical
Journal 649: 730, 2006.
[15] Munyaneza, F.; R.D. Viollier (2001), The motion of stars near the
Galactic center: A comparison of the black hole and fermion ball
scenarios , Retrieved on 2006-03-25.
[16] Tsiklauri, David; Raoul D. Viollier (1998), Dark matter concentration
in the galactic center, Retrieved on 2006-03-25.
[17] Heusler M, Stationary Black Holes: Uniqueness and beyond , Living
Rev.Relativity1(6), 1998.
[18] Hawking S.W. and Penrose R. The Singularities of Gravitational
Collapse and Cosmology Proc.Roy.Soc.Lon 314(1519): 529548,(1970)
http://www.jstor.org/stable/2416467
[19] Hawking and Stephen, Black Hole Explosions Nature 248(1974): pp.
3031. doi:10.1038/248030a0.
[20] Celotti A., Miller J.C. and Sciama D.W., Astrophysical evidence
for the existence of black holes Class. Quant. Grav. 16 (1999),
http://arxiv.org/abs/astro-ph/9912186.
[21] Chandrasekhar, Subrahmanyan , Mathematical Theory of Black Holes ,
Oxford University Press,1999, ISBN 0-19-850370-9.
[22] Heusler M, Stationary Black Holes: Uniqueness and beyond , Living
Rev.Relativity1(6), 1998.
[23] R. F. Harrington, Field Computation by Moment Methods, New York:
Macmillan, 1968.
[24] M.N.O.Sadiku, Elements of electromagnetics , Third Edition, Oxford
University Press, New York.
[25] Arti Vaish and H. Parthasarathy, Modal Analysis of Waveguide using
Method of Moment, Accepted for publication in HAIT Journal of Science
and Engineering-B, 2007.
[26] Taylor, Edwin F. and Wheeler, John Archibald (2000), Exploring Black
Holes, Addison Wesley Longman, ISBN 0-201-38423-X.
[27] Orosz, J.A et al (2007), A 15.65 solar mass black hole in an eclipsing
binary in the nearby spiral galaxy Messier 33, Nature 449: 872-875.
doi:10.1038/nature06218.
[28] Arti Vaish and H. Parthasarathy, Finite Element Analysis of Propagation
Modes in a Waveguide: Effect of Gravitational Field, Accepted for
publication in HAIT Journal of Science and Engineering-B, 2007.
[1] J. A. Kong, Electromagnetic Wave Theory, 2nd Ed. New York: Wiley,
1990.
[2] K. Murawski, Analytical and Numerical Methods for wave propagation
in fluid media, World Scientific Publishing Co. Pte. Ltd., Vol. 7, series
A, 2002.
[3] P.A.M. Dirac,General Theory of Relativity, second edition, Princeton
University Press, 1996.
[4] Geroch and Robert, General Relativity from A to B, University of Chicago
Press, Chicago, 1981.
[5] Thorne, Kip S.; Misner, Charles and Wheeler, John (1973), Gravitation
, W. H. Freeman and Company, ISBN 0-7167-0344-0.
[6] Wald, Robert M. (1992), Space, Time, and Gravity: The Theory of the
Big Bang and Black Holes, University of Chicago Press, ISBN 0-226-
87029-4.
[7] D. Finkelstein (1958), Past-Future Asymmetry of the Gravitational Field
of a Point Particle, Phys. Rev. 110: 965-967.
[8] Lewis G. F. and Kwan, J. No Way Back: Maximizing Survival Time
Below the Schwarzschild Event Horizon, Publications of the Astronomical
Society of Australia 24 (2): 46-52(2007).
[9] R. P. Kerr, Gravitational field of a spinning mass as an example of
algebraically special metrics , Phys. Rev. Lett. 11, 237 (1963).
[10] Carr B.J. , Primordial Black Holes: Do They Exist and Are They Useful?,
Proceedings of "Inflating Horizon of Particle Astrophysics and Cosmology",
Universal Academy Press Inc and Yamada Science Foundation,
http://arxiv.org/abs/astro-ph/0511743 2005.
[11] McClintock, Jeffrey E.; Shafee, Rebecca; Narayan, Ramesh; Remillard,
Ronald A.; Davis, Shane W. and Li, Li-Xin (2006), The Spin of the Near-
Extreme Kerr Black Hole GRS 1915+105 , Astrophys.J. 652: 518-539,
¡http://arxiv.org/abs/astro-ph/0606076¿.
[12] Page, Ron N. , Hawking Radiation and Black Hole Thermodynamics,
New.J.Phys. 7(203), (2005).
[13] Bloom, J.S., Kulkarni, S. R., Djorgovski, S. G., The Observed Offset
Distribution of Gamma-Ray Bursts from Their Host Galaxies: A Robust
Clue to the Nature of the Progenitors, Astronomical Journal 123: 1111-
1148(2002).
[14] Winter, L.M., Mushotzky, R.F. and Reynolds, C.S., XMM-Newton
Archival Study of the ULX Population in Nearby Galaxies, Astrophysical
Journal 649: 730, 2006.
[15] Munyaneza, F.; R.D. Viollier (2001), The motion of stars near the
Galactic center: A comparison of the black hole and fermion ball
scenarios , Retrieved on 2006-03-25.
[16] Tsiklauri, David; Raoul D. Viollier (1998), Dark matter concentration
in the galactic center, Retrieved on 2006-03-25.
[17] Heusler M, Stationary Black Holes: Uniqueness and beyond , Living
Rev.Relativity1(6), 1998.
[18] Hawking S.W. and Penrose R. The Singularities of Gravitational
Collapse and Cosmology Proc.Roy.Soc.Lon 314(1519): 529548,(1970)
http://www.jstor.org/stable/2416467
[19] Hawking and Stephen, Black Hole Explosions Nature 248(1974): pp.
3031. doi:10.1038/248030a0.
[20] Celotti A., Miller J.C. and Sciama D.W., Astrophysical evidence
for the existence of black holes Class. Quant. Grav. 16 (1999),
http://arxiv.org/abs/astro-ph/9912186.
[21] Chandrasekhar, Subrahmanyan , Mathematical Theory of Black Holes ,
Oxford University Press,1999, ISBN 0-19-850370-9.
[22] Heusler M, Stationary Black Holes: Uniqueness and beyond , Living
Rev.Relativity1(6), 1998.
[23] R. F. Harrington, Field Computation by Moment Methods, New York:
Macmillan, 1968.
[24] M.N.O.Sadiku, Elements of electromagnetics , Third Edition, Oxford
University Press, New York.
[25] Arti Vaish and H. Parthasarathy, Modal Analysis of Waveguide using
Method of Moment, Accepted for publication in HAIT Journal of Science
and Engineering-B, 2007.
[26] Taylor, Edwin F. and Wheeler, John Archibald (2000), Exploring Black
Holes, Addison Wesley Longman, ISBN 0-201-38423-X.
[27] Orosz, J.A et al (2007), A 15.65 solar mass black hole in an eclipsing
binary in the nearby spiral galaxy Messier 33, Nature 449: 872-875.
doi:10.1038/nature06218.
[28] Arti Vaish and H. Parthasarathy, Finite Element Analysis of Propagation
Modes in a Waveguide: Effect of Gravitational Field, Accepted for
publication in HAIT Journal of Science and Engineering-B, 2007.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64867", author = "Arti Vaish and Harish Parthasarathy", title = "Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole", abstract = "This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.
", keywords = "Method of moments, General theory of relativity, Electromagnetism, Metric tensor, schwarzchild metric, Wave Equation.", volume = "4", number = "8", pages = "1230-5", }
