John Carminati | Deakin University (original) (raw)

Papers by John Carminati

Research paper thumbnail of The validity of Huygens' principle for the conformally invariant scalar wave equation, Maxwell's equations and Weyl's neutrino equation on Petrov type D and type III space-times

Physics Letters, Nov 1, 1986

... 1923 ). [2] J. Carminati and RG McLenaghan, Phys. Lett. A 105 (1984) 351. 324 [ 3 ] J. Carmin... more ... 1923 ). [2] J. Carminati and RG McLenaghan, Phys. Lett. A 105 (1984) 351. 324 [ 3 ] J. Carminati and RG McLenaghan, Ann. Inst. Henri Poincare, Phys. Theor. ... 3. J. Carminati and RG McLenaghan ,Ann. Inst. Henri Poincaré. Phys. Theor. 44 (1986), p. 115. 4. P. Günther Wiss. ...

Research paper thumbnail of Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times

Annales De L Institut Henri Poincare-physique Theorique, 1991

Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equa... more Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times

Research paper thumbnail of An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle

An explicit determination of the Petrov type N spacetimes on which the conformally invariant scal... more An explicit determination of the Petrov type N spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle Annales de l'I. H. P., section A, tome 44, n o 2 (1986), p. 115-153 <http://www.numdam.org/item?id=AIHPA_1986__44_2_115_0> © Gauthier-Villars, 1986, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Research paper thumbnail of The validity of Huygens' principle on type N space-times

It is shown that a necessary condition for the validity of Huygens' principle for the confor... more It is shown that a necessary condition for the validity of Huygens' principle for the conformally invariant scalar wave equation, or Maxwell's equations, or Weyl's neutrino equation on any Petrov type N space-time is that the space-time be conformally related to a special complex recurrent space-time.

Research paper thumbnail of The Validity of Huygens' Principle for the Wave Equation on Curved Space-time

Research paper thumbnail of The Validity of Huygens' Principle on Type II Space-Times

Research paper thumbnail of The automatic conversion of spinor equations to dyad form in MAPLE

General Relativity and Gravitation, Sep 1, 1992

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated... more A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.

Research paper thumbnail of Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space

Journal of Mathematical Physics, Nov 1, 1991

In a recent comment Sneddon discussed the set of fourteen algebraic invariants of the Riemann cur... more In a recent comment Sneddon discussed the set of fourteen algebraic invariants of the Riemann curvature tensor in four dimensions. The focus was rectification of an error (in the form of lack of independence) in an earlier construction and the presentation of a corrected set suitable for application. Several authors who have worked on this problem were mentioned. The comment, however, did not mention the work of Narlikar and Karmarkar who presented a set of invariants well before the earliest work cited in the comment. The original publication by Narlikar and Karmarkar may not be readily available so we list and make a few comments on their set.

Research paper thumbnail of Determination of all Petrov type-N space-times on which the conformally invariant scalar wave equation satisfies Huygen's principle

Physics Letters, Oct 1, 1984

It is shown that the conformally invariant wave equation on a Petrov type-N space-time satisfies ... more It is shown that the conformally invariant wave equation on a Petrov type-N space-time satisfies Huygens' principle if and only if the space-time is conformally related to a plane wave space-time. Hadamard [ 1 ] posed the general problem, as yet unsolved, of determining up to equivalence all the secondorder linear hyperbolic partial differential equations in n independent variables that satisfy Huygens' principle in the strict sense. We recall that such an equation may be written in coordinate invariant form as

Research paper thumbnail of On the problem of algebraic completeness for the invariants of the Riemann tensor. II

Journal of Mathematical Physics, 2002

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] f... more We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space–times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space–time.

Research paper thumbnail of Herlt metrics and gravitational-electrostatic balance in general relativity

General Relativity and Gravitation, Aug 1, 1992

The balance problem in general relativity is reviewed. The transformation connecting the Herlt eq... more The balance problem in general relativity is reviewed. The transformation connecting the Herlt equations for electrovacuum and the Weyl equations for axially symmetric vacuum is given. This yields a new exact solution for the superposition of two separated Reissner-NordstrSm sources with a balance condition which depends upon their separation distance. This result has potential implications for averting gravitational collapse. Details of the singularity structure are also presented.

Research paper thumbnail of Petrov Type III, Shear-Free Perfect Fluid Space-Times in General Relativity

General Relativity and Gravitation, Jul 1, 1989

Research paper thumbnail of Shear-free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

Classical and Quantum Gravity, Jul 4, 2007

We show that shearfree perfect fluids obeying an equation of state p = (γ − 1)µ are non-rotating ... more We show that shearfree perfect fluids obeying an equation of state p = (γ − 1)µ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Research paper thumbnail of Type D perfect-fluid spacetimes with a non-null electromagnetic field. I

Classical and Quantum Gravity, Sep 1, 1990

The author investigates completely aligned, Petrov type D solutions of the Einstein-Maxwell field... more The author investigates completely aligned, Petrov type D solutions of the Einstein-Maxwell field equations, which have a perfect fluid and an (non-null) electromagnetic field as source, subject to the additional assumption that the magnetic part of the Weyl tensor relative to the fluid 4-velocity, is zero. The author indicates how all such solutions may be naturally classified into two classes, depending on whether or not the invariants associated with the Weyl, trace-free Ricci and Maxwell tensors are independent. A detailed study, centred about conditions for zero vorticity in the fluid flow, is carried out on the functionally independent class. Further, we present new solutions, which belong to this class, some of which may be of interest in the study of gravitational collapse as well as possibly providing suitable cosmological models for early epochs of our Universe.

Research paper thumbnail of Shear-free perfect fluids in general relativity: III. Petrov type III spacetimes

Classical and Quantum Gravity, Jul 1, 1996

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Shear-free perfect fluids in general relativity: IV. Petrov type III spacetimes

Classical and Quantum Gravity, May 1, 1997

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Shear‐free perfect fluids in general relativity II. Aligned, Petrov type III space‐times

Journal of Mathematical Physics, Oct 1, 1990

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Conversion of Spinor Equations to Dyad Form in Maple

General Relativity and Gravitation, Jul 1, 1989

Research paper thumbnail of Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations

Analysis and Mathematical Physics, Sep 13, 2013

A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equatio... more A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equations within a thin rotating spherical shell were found as invariant and approximately invariant solutions. The model is used to describe a simple zonally averaged atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows. The model is superimposed by a stationary latitude dependent flow. Under the assumption of no friction, the perturbed model describes zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. In terms of nonlinear modeling for the NS equations, two small parameters are chosen for the viscosity and the rate of the earth’s rotation and exact solutions in terms of elementary functions are found using approximate symmetry analysis. It is shown that approximately invariant solutions are also valid in the absence of the flow perturbation to a zonally averaged mean flow.

Research paper thumbnail of On the non-uniqueness of solutions in the modelling of steady wind flows

Computers & Fluids, Feb 1, 1995

The two-dimensional, steady, turbulent Navier-Stokes Equations are explored for the case of a log... more The two-dimensional, steady, turbulent Navier-Stokes Equations are explored for the case of a logarithmic profile. A general, analytical solution technique is presented, using potential functions; it contains two arbitrary functions. Example solutions are derived with the symbolic manipulator Maple; they show various shear stress profiles derived from a single form for the velocity profile. These stress variations occur within an

Research paper thumbnail of The validity of Huygens' principle for the conformally invariant scalar wave equation, Maxwell's equations and Weyl's neutrino equation on Petrov type D and type III space-times

Physics Letters, Nov 1, 1986

... 1923 ). [2] J. Carminati and RG McLenaghan, Phys. Lett. A 105 (1984) 351. 324 [ 3 ] J. Carmin... more ... 1923 ). [2] J. Carminati and RG McLenaghan, Phys. Lett. A 105 (1984) 351. 324 [ 3 ] J. Carminati and RG McLenaghan, Ann. Inst. Henri Poincare, Phys. Theor. ... 3. J. Carminati and RG McLenaghan ,Ann. Inst. Henri Poincaré. Phys. Theor. 44 (1986), p. 115. 4. P. Günther Wiss. ...

Research paper thumbnail of Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times

Annales De L Institut Henri Poincare-physique Theorique, 1991

Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equa... more Consequences of the validity of Huygens' principle for the conformally invariant scalar wave equation, Weyl's neutrino equation and Maxwell's equations on Petrov type II space-times

Research paper thumbnail of An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle

An explicit determination of the Petrov type N spacetimes on which the conformally invariant scal... more An explicit determination of the Petrov type N spacetimes on which the conformally invariant scalar wave equation satisfies Huygens' principle Annales de l'I. H. P., section A, tome 44, n o 2 (1986), p. 115-153 <http://www.numdam.org/item?id=AIHPA_1986__44_2_115_0> © Gauthier-Villars, 1986, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Research paper thumbnail of The validity of Huygens' principle on type N space-times

It is shown that a necessary condition for the validity of Huygens' principle for the confor... more It is shown that a necessary condition for the validity of Huygens' principle for the conformally invariant scalar wave equation, or Maxwell's equations, or Weyl's neutrino equation on any Petrov type N space-time is that the space-time be conformally related to a special complex recurrent space-time.

Research paper thumbnail of The Validity of Huygens' Principle for the Wave Equation on Curved Space-time

Research paper thumbnail of The Validity of Huygens' Principle on Type II Space-Times

Research paper thumbnail of The automatic conversion of spinor equations to dyad form in MAPLE

General Relativity and Gravitation, Sep 1, 1992

A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated... more A new package in the symbolic algebra system MAPLE is presented for the conversion of complicated spinor equations to their expansions with respect to a normalized spinor dyad. By following a simple index convention, we obtain a powerful computational tool with a straightforward and easy to use syntax. A number of examples, including nontrivial applications of the package to recent research, are provided.

Research paper thumbnail of Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space

Journal of Mathematical Physics, Nov 1, 1991

In a recent comment Sneddon discussed the set of fourteen algebraic invariants of the Riemann cur... more In a recent comment Sneddon discussed the set of fourteen algebraic invariants of the Riemann curvature tensor in four dimensions. The focus was rectification of an error (in the form of lack of independence) in an earlier construction and the presentation of a corrected set suitable for application. Several authors who have worked on this problem were mentioned. The comment, however, did not mention the work of Narlikar and Karmarkar who presented a set of invariants well before the earliest work cited in the comment. The original publication by Narlikar and Karmarkar may not be readily available so we list and make a few comments on their set.

Research paper thumbnail of Determination of all Petrov type-N space-times on which the conformally invariant scalar wave equation satisfies Huygen's principle

Physics Letters, Oct 1, 1984

It is shown that the conformally invariant wave equation on a Petrov type-N space-time satisfies ... more It is shown that the conformally invariant wave equation on a Petrov type-N space-time satisfies Huygens' principle if and only if the space-time is conformally related to a plane wave space-time. Hadamard [ 1 ] posed the general problem, as yet unsolved, of determining up to equivalence all the secondorder linear hyperbolic partial differential equations in n independent variables that satisfy Huygens' principle in the strict sense. We recall that such an equation may be written in coordinate invariant form as

Research paper thumbnail of On the problem of algebraic completeness for the invariants of the Riemann tensor. II

Journal of Mathematical Physics, 2002

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] f... more We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space–times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space–time.

Research paper thumbnail of Herlt metrics and gravitational-electrostatic balance in general relativity

General Relativity and Gravitation, Aug 1, 1992

The balance problem in general relativity is reviewed. The transformation connecting the Herlt eq... more The balance problem in general relativity is reviewed. The transformation connecting the Herlt equations for electrovacuum and the Weyl equations for axially symmetric vacuum is given. This yields a new exact solution for the superposition of two separated Reissner-NordstrSm sources with a balance condition which depends upon their separation distance. This result has potential implications for averting gravitational collapse. Details of the singularity structure are also presented.

Research paper thumbnail of Petrov Type III, Shear-Free Perfect Fluid Space-Times in General Relativity

General Relativity and Gravitation, Jul 1, 1989

Research paper thumbnail of Shear-free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

Classical and Quantum Gravity, Jul 4, 2007

We show that shearfree perfect fluids obeying an equation of state p = (γ − 1)µ are non-rotating ... more We show that shearfree perfect fluids obeying an equation of state p = (γ − 1)µ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Research paper thumbnail of Type D perfect-fluid spacetimes with a non-null electromagnetic field. I

Classical and Quantum Gravity, Sep 1, 1990

The author investigates completely aligned, Petrov type D solutions of the Einstein-Maxwell field... more The author investigates completely aligned, Petrov type D solutions of the Einstein-Maxwell field equations, which have a perfect fluid and an (non-null) electromagnetic field as source, subject to the additional assumption that the magnetic part of the Weyl tensor relative to the fluid 4-velocity, is zero. The author indicates how all such solutions may be naturally classified into two classes, depending on whether or not the invariants associated with the Weyl, trace-free Ricci and Maxwell tensors are independent. A detailed study, centred about conditions for zero vorticity in the fluid flow, is carried out on the functionally independent class. Further, we present new solutions, which belong to this class, some of which may be of interest in the study of gravitational collapse as well as possibly providing suitable cosmological models for early epochs of our Universe.

Research paper thumbnail of Shear-free perfect fluids in general relativity: III. Petrov type III spacetimes

Classical and Quantum Gravity, Jul 1, 1996

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Shear-free perfect fluids in general relativity: IV. Petrov type III spacetimes

Classical and Quantum Gravity, May 1, 1997

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Shear‐free perfect fluids in general relativity II. Aligned, Petrov type III space‐times

Journal of Mathematical Physics, Oct 1, 1990

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a baro... more Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p = pew) satisfying w + p=/=O, are investigated. It is shown that if the ac~ele~ation of the fluid is orthogonal to the two-spaces spanned by the repeated principal null duectlOn ofthe Weyl tensor and the fluid four-velocity, or ifthe fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid's volume expansion is zero.

Research paper thumbnail of Conversion of Spinor Equations to Dyad Form in Maple

General Relativity and Gravitation, Jul 1, 1989

Research paper thumbnail of Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations

Analysis and Mathematical Physics, Sep 13, 2013

A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equatio... more A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equations within a thin rotating spherical shell were found as invariant and approximately invariant solutions. The model is used to describe a simple zonally averaged atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows. The model is superimposed by a stationary latitude dependent flow. Under the assumption of no friction, the perturbed model describes zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. In terms of nonlinear modeling for the NS equations, two small parameters are chosen for the viscosity and the rate of the earth’s rotation and exact solutions in terms of elementary functions are found using approximate symmetry analysis. It is shown that approximately invariant solutions are also valid in the absence of the flow perturbation to a zonally averaged mean flow.

Research paper thumbnail of On the non-uniqueness of solutions in the modelling of steady wind flows

Computers & Fluids, Feb 1, 1995

The two-dimensional, steady, turbulent Navier-Stokes Equations are explored for the case of a log... more The two-dimensional, steady, turbulent Navier-Stokes Equations are explored for the case of a logarithmic profile. A general, analytical solution technique is presented, using potential functions; it contains two arbitrary functions. Example solutions are derived with the symbolic manipulator Maple; they show various shear stress profiles derived from a single form for the velocity profile. These stress variations occur within an