... Donato Bini and Robert T Jantzen§ Istituto per Applicazioni della Matematica CNR, I-8013... more ... Donato Bini and Robert T Jantzen§ Istituto per Applicazioni della Matematica CNR, I-80131 Naples, Italy International Center for Relativistic Astrophysics, University of Rome, I-00185 Rome, Italy § Department of Mathematical Sciences, Villanova University, Villanova ...
General Relativity and Gravitation, Vol. 35, No. 3, March 2003 ( C 2003) ... The Bianchi Classifi... more General Relativity and Gravitation, Vol. 35, No. 3, March 2003 ( C 2003) ... The Bianchi Classification in the Sch¨ucking-Behr Approach1 ... A. Krasi nski,2 Christoph G. Behr,3 Engelbert Sch ücking,4 Frank B. Estabrook,5 Hugo D. Wahlquist,6 George FR Ellis,7 Robert Jantzen,8 ...
... 2. THE TAUB-NUT METRIC The metric of the Taub-NUT spacetime [14] in Boyer-Lindquist-like coo... more ... 2. THE TAUB-NUT METRIC The metric of the Taub-NUT spacetime [14] in Boyer-Lindquist-like coor-dinates is ds2 = − −1 (dt + 2l cos θdφ)2 + ( −1 dr2 + dθ2 + sin2 θ dφ2), (1) ... e0 is interpreted as the 4-velocity of the ZAMOs. The ZAMO dual 1-forms are ...
Title: LETTER TO THE EDITOR: Spacetimes with a transitive similarity group. ... Abstract. Not Ava... more Title: LETTER TO THE EDITOR: Spacetimes with a transitive similarity group. ... Abstract. Not Available Reference 0 Reference 1 Reference 2 Reference 3 Reference 4 Reference 5 Reference 6 Reference 7 Reference 8 Reference 9 Reference 10 Reference 11 Reference 12
The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equ... more The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equations in N+1 spacetime dimensions are explicitly shown to have a simple geometric interpretation in the Hamiltonian formulation.
Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous ... more Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous 4-parameter family of surfaces invariant under at least a 1-parameter symmetry group and which contains as various limits spheres, tori, helical tubes, and cylinders, all useful for illustrating various aspects of geometry in a visualizable setting that are important in special and general relativity. In this family the most aesthetically pleasing surfaces come from screw-rotating a plane cross-sectional curve perpendicular to itself, i.e., orthogonal to the tangent vector to a helix. If we impose instead this orthogonality in the Lorentzian geometry of 3-dimensional Minkowski spacetime with a timelike helical "central" world line representing a circular orbit, we can model the Fermi Born rigid model of the classical electron in such an orbit around the nucleus, and visualize the Fermi coordinate grid and its intersection with the world tube of the equatorial circle of the spherical surface of the electron (suppressing one spatial dimension). This leads what we might playfully term "relativistic pasta". This is a useful 2-dimensional stationary spacetime with closed spatial slices on which to illustrate the slicing and threading splittings of general relativity relative to a Killing congruence, like stationary axisymmetric spacetimes including the rotating black hole family.
An investigation of those cases of the generalized Friedmann equation which are solvable in terms... more An investigation of those cases of the generalized Friedmann equation which are solvable in terms of elementary or elliptic functions is under- taken together with a study of the time gauges which allow this to occur. This is accomplished by examining the natural choices of independent and dependent variables in this problem, using manipulations like those of the Kepler problem, which is shown to be equivalent to a generalized Friedmann problem, thus clarifying the similarities between the simplest solutions of each.
The motion of massless spinning test particles is investigated using the Newman-Penrose formalism... more The motion of massless spinning test particles is investigated using the Newman-Penrose formalism within the Mathisson-Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole reduction world line" lies along a principal null direction of an algebraically special vacuum spacetime, the equations of motion can be explicitly integrated. Examples are given for some familiar spacetimes of this type in the interest of shedding some light on the consequences of this model.
The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equ... more The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equations in N+1 spacetime dimensions are explicitly shown to have a simple geometric interpretation in the Hamiltonian formulation.
A recent paper claiming to have found the true general vacuum solu- tion of the locally rotationa... more A recent paper claiming to have found the true general vacuum solu- tion of the locally rotationally symmetric Bianchi type IX spatially ho- mogeneous Einstein equations already found by Taub in 1951 rediscovers that solution. The complete vacuuum solution of the Einstein equations for the locally ro- tationally symmetric Bianchi type IX spatially homogeneous cosmological model found by Abraham Taub
Recent Developments in Theoretical and Experimental General Relativity Gravitation and Relativistic Field Theories, 1999
... Bini, Donato; Jantzen, Robert T.; Merloni, Andrea. Publication: Recent Developments in Theore... more ... Bini, Donato; Jantzen, Robert T.; Merloni, Andrea. Publication: Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, held at the Hebrew University of Jerusalem, 22-27 June, 1997. Edited by Tsvi Piran and Remo ...
... Donato Bini and Robert T Jantzen§ Istituto per Applicazioni della Matematica CNR, I-8013... more ... Donato Bini and Robert T Jantzen§ Istituto per Applicazioni della Matematica CNR, I-80131 Naples, Italy International Center for Relativistic Astrophysics, University of Rome, I-00185 Rome, Italy § Department of Mathematical Sciences, Villanova University, Villanova ...
General Relativity and Gravitation, Vol. 35, No. 3, March 2003 ( C 2003) ... The Bianchi Classifi... more General Relativity and Gravitation, Vol. 35, No. 3, March 2003 ( C 2003) ... The Bianchi Classification in the Sch¨ucking-Behr Approach1 ... A. Krasi nski,2 Christoph G. Behr,3 Engelbert Sch ücking,4 Frank B. Estabrook,5 Hugo D. Wahlquist,6 George FR Ellis,7 Robert Jantzen,8 ...
... 2. THE TAUB-NUT METRIC The metric of the Taub-NUT spacetime [14] in Boyer-Lindquist-like coo... more ... 2. THE TAUB-NUT METRIC The metric of the Taub-NUT spacetime [14] in Boyer-Lindquist-like coor-dinates is ds2 = − −1 (dt + 2l cos θdφ)2 + ( −1 dr2 + dθ2 + sin2 θ dφ2), (1) ... e0 is interpreted as the 4-velocity of the ZAMOs. The ZAMO dual 1-forms are ...
Title: LETTER TO THE EDITOR: Spacetimes with a transitive similarity group. ... Abstract. Not Ava... more Title: LETTER TO THE EDITOR: Spacetimes with a transitive similarity group. ... Abstract. Not Available Reference 0 Reference 1 Reference 2 Reference 3 Reference 4 Reference 5 Reference 6 Reference 7 Reference 8 Reference 9 Reference 10 Reference 11 Reference 12
The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equ... more The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equations in N+1 spacetime dimensions are explicitly shown to have a simple geometric interpretation in the Hamiltonian formulation.
Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous ... more Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous 4-parameter family of surfaces invariant under at least a 1-parameter symmetry group and which contains as various limits spheres, tori, helical tubes, and cylinders, all useful for illustrating various aspects of geometry in a visualizable setting that are important in special and general relativity. In this family the most aesthetically pleasing surfaces come from screw-rotating a plane cross-sectional curve perpendicular to itself, i.e., orthogonal to the tangent vector to a helix. If we impose instead this orthogonality in the Lorentzian geometry of 3-dimensional Minkowski spacetime with a timelike helical "central" world line representing a circular orbit, we can model the Fermi Born rigid model of the classical electron in such an orbit around the nucleus, and visualize the Fermi coordinate grid and its intersection with the world tube of the equatorial circle of the spherical surface of the electron (suppressing one spatial dimension). This leads what we might playfully term "relativistic pasta". This is a useful 2-dimensional stationary spacetime with closed spatial slices on which to illustrate the slicing and threading splittings of general relativity relative to a Killing congruence, like stationary axisymmetric spacetimes including the rotating black hole family.
An investigation of those cases of the generalized Friedmann equation which are solvable in terms... more An investigation of those cases of the generalized Friedmann equation which are solvable in terms of elementary or elliptic functions is under- taken together with a study of the time gauges which allow this to occur. This is accomplished by examining the natural choices of independent and dependent variables in this problem, using manipulations like those of the Kepler problem, which is shown to be equivalent to a generalized Friedmann problem, thus clarifying the similarities between the simplest solutions of each.
The motion of massless spinning test particles is investigated using the Newman-Penrose formalism... more The motion of massless spinning test particles is investigated using the Newman-Penrose formalism within the Mathisson-Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole reduction world line" lies along a principal null direction of an algebraically special vacuum spacetime, the equations of motion can be explicitly integrated. Examples are given for some familiar spacetimes of this type in the interest of shedding some light on the consequences of this model.
The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equ... more The additional conditions satisfied by the generalized Kasner solution of the vacuum Einstein equations in N+1 spacetime dimensions are explicitly shown to have a simple geometric interpretation in the Hamiltonian formulation.
A recent paper claiming to have found the true general vacuum solu- tion of the locally rotationa... more A recent paper claiming to have found the true general vacuum solu- tion of the locally rotationally symmetric Bianchi type IX spatially ho- mogeneous Einstein equations already found by Taub in 1951 rediscovers that solution. The complete vacuuum solution of the Einstein equations for the locally ro- tationally symmetric Bianchi type IX spatially homogeneous cosmological model found by Abraham Taub
Recent Developments in Theoretical and Experimental General Relativity Gravitation and Relativistic Field Theories, 1999
... Bini, Donato; Jantzen, Robert T.; Merloni, Andrea. Publication: Recent Developments in Theore... more ... Bini, Donato; Jantzen, Robert T.; Merloni, Andrea. Publication: Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, held at the Hebrew University of Jerusalem, 22-27 June, 1997. Edited by Tsvi Piran and Remo ...
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