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Papers by Roberto Sussman Livovsky
Monthly Notices of the Royal Astronomical Society, May 17, 2017
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International Journal of Environmental Research and Public Health, Feb 3, 2021
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Journal of Mathematical Physics, 1991
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Physical review, Dec 29, 2008
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Classical and Quantum Gravity, Mar 1, 2012
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Classical and Quantum Gravity, Jul 28, 2015
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Classical and Quantum Gravity, Oct 8, 2013
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General Relativity and Gravitation, Nov 30, 2007
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Classical and Quantum Gravity, Sep 18, 2019
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Journal of Mathematical Physics, Mar 1, 1995
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Classical and Quantum Gravity, Oct 30, 2004
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Classical and Quantum Gravity, Jul 16, 2010
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Journal of Mathematical Physics, May 1, 1987
A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shea... more A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shear-free perfect fluid configurations is derived. It is presented in the form of Jacobian elliptic functions characterized by seven free parameters: five constants and two arbitrary functions of time. This class of solutions is the most general charged version of the class derived by Kustaanheimo and Qvist [Comment. Phys. Math. Helsingf. 13, 12 (1948); Exact Solutions of Einstein’s Field Equations (Cambridge U. P., Cambridge, 1980), Chap. 12, Sec. 2]. It is found that many of the charged particular solutions expressible by elementary functions are new. Particular solutions, including neutral and uniform density solutions, are classified in detail. The physical interpretation of these solutions, including the study of their singularity structure, will be presented in a subsequent paper (Part II).
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Physical review, Aug 26, 2004
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General Relativity and Gravitation, Mar 1, 1985
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Classical and Quantum Gravity, Nov 4, 2011
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Journal of Mathematical Physics, Apr 1, 1988
Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. P... more Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. Phys. 28, 1118 (1987)] are examined in detail. It is shown how the imposition of zero shear restricts the possible choices of equations of state. Two types of singular boundaries arising in these solutions are examined by verifying the local behavior of causal curves approaching these boundaries. For this purpose, a criterion due to C. J. S. Clarke (private communication) is given, allowing one to test the completeness of arbitrary accelerated timelike curves in terms of their acceleration and proper time. One of these boundaries is a spacelike singularity at which causal curves terminate as pressure diverges but matter-energy and charge densities remain finite. At the other boundary, which is timelike if the expansion Θ is finite, proper volume of local fluid elements vanishes as all state variables diverge but causal curves are complete. If Θ diverges at this boundary, a null singularity arises as the end product of the collapse of a two-sphere generated by a given class of timelike curves. The gravitational collapse of bounded spheres matched to a Schwarzschild or Reissner–Nordstro/m exterior is also examined in detail. It is shown that the spacelike singularity mentioned above could be naked under certain parameter choices. Solutions presenting the other boundary produce very peculiar black holes in which the ‘‘surface’’ of the sphere collapses into the above mentioned null singularity, while the ‘‘interior’’ fluid layers avoid this singularity and evolve towards their infinite future.
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Monthly Notices of the Royal Astronomical Society, May 17, 2017
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International Journal of Environmental Research and Public Health, Feb 3, 2021
Bookmarks Related papers MentionsView impact
Journal of Mathematical Physics, 1991
Bookmarks Related papers MentionsView impact
Physical review, Dec 29, 2008
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Classical and Quantum Gravity, Mar 1, 2012
Bookmarks Related papers MentionsView impact
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Classical and Quantum Gravity, Jul 28, 2015
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Classical and Quantum Gravity, Oct 8, 2013
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General Relativity and Gravitation, Nov 30, 2007
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Classical and Quantum Gravity, Sep 18, 2019
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Journal of Mathematical Physics, Mar 1, 1995
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Classical and Quantum Gravity, Oct 30, 2004
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Classical and Quantum Gravity, Jul 16, 2010
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Journal of Mathematical Physics, May 1, 1987
A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shea... more A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shear-free perfect fluid configurations is derived. It is presented in the form of Jacobian elliptic functions characterized by seven free parameters: five constants and two arbitrary functions of time. This class of solutions is the most general charged version of the class derived by Kustaanheimo and Qvist [Comment. Phys. Math. Helsingf. 13, 12 (1948); Exact Solutions of Einstein’s Field Equations (Cambridge U. P., Cambridge, 1980), Chap. 12, Sec. 2]. It is found that many of the charged particular solutions expressible by elementary functions are new. Particular solutions, including neutral and uniform density solutions, are classified in detail. The physical interpretation of these solutions, including the study of their singularity structure, will be presented in a subsequent paper (Part II).
Bookmarks Related papers MentionsView impact
Physical review, Aug 26, 2004
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General Relativity and Gravitation, Mar 1, 1985
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Classical and Quantum Gravity, Nov 4, 2011
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Journal of Mathematical Physics, Apr 1, 1988
Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. P... more Geometrical and physical properties of the solutions derived and classified in Part I [J. Math. Phys. 28, 1118 (1987)] are examined in detail. It is shown how the imposition of zero shear restricts the possible choices of equations of state. Two types of singular boundaries arising in these solutions are examined by verifying the local behavior of causal curves approaching these boundaries. For this purpose, a criterion due to C. J. S. Clarke (private communication) is given, allowing one to test the completeness of arbitrary accelerated timelike curves in terms of their acceleration and proper time. One of these boundaries is a spacelike singularity at which causal curves terminate as pressure diverges but matter-energy and charge densities remain finite. At the other boundary, which is timelike if the expansion Θ is finite, proper volume of local fluid elements vanishes as all state variables diverge but causal curves are complete. If Θ diverges at this boundary, a null singularity arises as the end product of the collapse of a two-sphere generated by a given class of timelike curves. The gravitational collapse of bounded spheres matched to a Schwarzschild or Reissner–Nordstro/m exterior is also examined in detail. It is shown that the spacelike singularity mentioned above could be naked under certain parameter choices. Solutions presenting the other boundary produce very peculiar black holes in which the ‘‘surface’’ of the sphere collapses into the above mentioned null singularity, while the ‘‘interior’’ fluid layers avoid this singularity and evolve towards their infinite future.
Bookmarks Related papers MentionsView impact