Abstract
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we define a duality transformation which interchanges active and passive electric parts. It implies interchange of roles of Ricci and Einstein curvatures. Further by modifying the vacuum/flat equation we construct spacetimes dual to the Schwarzschild solution and flat spacetime. The dual spacetimes describe the original spacetimes with global monopole charge and global texture. The duality so defined is thus intimately related to the topological defects and also renders the Schwarzschild field asymptotically non-flat which augurs well with Mach’s Principle.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
It is a matter of great pleasure and privilege to have known Jayant Narlikar and worked with him closely in setting up IUCAA. With deep affection and feeling I dedicate this work to him on his completing 60 years.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M.A.G. Bonilla and J.M.M. Senovilla, 1997, Gen. Rel.Grav. 29, 91.
N. Dadhich, 1999, Mod. Phys. Letts. A 14, 337, 759.
N. Dadhich, L.K. Patel and R. Tikekar (1998) Class. Quantum Grav. 15, L27.
N. Dadhich, 1995, GR-14 Abstracts, A.98.
N. Dadhich, 1997, On the Schwarzschild field, gr-qc/9704068.
M. Barriola and A. Vilenkin, 1989, Phys. Rev. Lett. 63, 341.
R.L. Davis, 1987, Phys. Rev. D 35, 3705.
N. Turok, 1989, Phys. Rev. Lett. 63, 2625.
T.W.B. Kibble, 1979, J. Phys. A 9, 1347.
A. Vilenkin, 1985, Phys. Rep. 121, 263.
N. Dadhich & K. Narayan, 1998, Gen. Rel.Grav. 30, L1133.
D. Harari & C. Lousto, 1990, Phys. Rev. D 42, 2626.
G.W. Gibbons, M.E. Oritz, F. Ruiz Ruiz & T.M. Samols, 1992, Nucl. Phys. B 385, 127.
N. Dadhich, K. Narayan & U.A. Yajnik, 1998, Pramana 50, 307.
R.J. Gott III and M.J. Rees (1987) Mon. Not. Roy. astr. Soc. 227, 453.
E.W. Kobl, 1989, Astrophys. J. 344, 543.
M Kamionkowski & N. Toumbas, 1996, Phys. Rev. Lett. 77, 587.
V. Sahni, 1991, Phys. Rev. D 43, R301.
D. Notzold, 1991, Phys. Rev. D 43, R961.
D. V. Ahluwalia, 1998, Mod. Phys. Letts. A 13, 1397.
A.K. Raychaudhuri, 1955, Phys.Rev. 90, 1123.
M. Nouri-Zonoz, N. Dadhich & D. Lynden-Bell, 1999, Class. Quant. Gra. 16, 1.
N. Dadhich and L. K. Patel (1999) Gravo-electric dual of the Kerr solution, submitted.
K.B. Marathe and G. Martucci (1998) Nuovo Cim. B113, 1175.
N. Dadhich and K.B. Marathe (1998) Electromagnetic resolution of curvature and gravitational instantons, submitted to Nuovo Cim.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Dadhich, N. (2000). Dual Spacetimes, Mach’s Principle and Topological Defects. In: Dadhich, N., Kembhavi, A. (eds) The Universe. Astrophysics and Space Science Library, vol 244. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4050-8_8
Download citation
DOI: https://doi.org/10.1007/978-94-011-4050-8_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5784-4
Online ISBN: 978-94-011-4050-8
eBook Packages: Springer Book Archive