Papers by Taxiarchis Papakostas
arXiv (Cornell University), Jun 11, 2024
This paper is the initial part of a comprehensive study of spacetimes that admit the canonical fo... more This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein's equations that exhibit hidden symmetries or to identify the hidden symmetries in already known spacetimes that may emerge during the resolution process. In this preliminary paper, we first introduce the canonical forms of Killing tensor, based on a geometrical approach to classify the canonical forms of symmetric 2-rank tensors, as postulated by R. V. Churchill. Subsequently, the derived integrability conditions of the canonical forms serve as additional equations transforming the underdetermined system of equations, comprising of Einstein's Field Equations and the Bianchi Identities (in vacuum with Λ), into an over-determined one. Using a null rotation around the null tetrad frame we manage to simplify the system of equations to the point where the geometric characterization (Petrov Classification) of the extracted solutions can be performed and their null congruences can be characterized geometrically. Therein, we obtain multiple special algebraic solutions according to the Petrov classification (D, III, N, O) where some of them appeared to be new. The latter becomes possible since our analysis is embodied with the usage of the Newman-Penrose formalism of null tetrads.
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arXiv (Cornell University), Sep 7, 2023
The study of the Canonical Forms of the Killing Tensor concerns the simultaneous resolving of the... more The study of the Canonical Forms of the Killing Tensor concerns the simultaneous resolving of the Integrability Conditions of the Killing Tensor along with the Einstein's Field Equations employing the framework of Newman-Penrose Formalism. We present all the Petrov Types admitting the 2nd and 3rd Canonical Forms of Killing Tensor in Vacuum in the frame of General Theory of Relativity. During the investigation of the Type D solution of 2nd Canonical form of the Killing Tensor the Carter's Case [D] solution in Vacuum emerged. 1 The indices µ, ν take the values 1,2,3,4. First things first, in the Section 3 we describe the main points of the appointed formalism. The Newman-Penrose Formalism it is a widely known formalism which use null tetrads and was presented by Newman and and and and et. al [8]. It was found in order to describe the gravitational radiation in the frame of GR but proved to have much more usefulness. We initiate the treatment of the problem in Section 4, where we are going to unravel the setup of the problem. The main steps of the resolving procedure concerns the collection of the Killing equations and the production of the Integrability Conditions, which we able to obtain via the commutation relations of the directional derivatives of the formalism. The Killing equations dictate the initial spins annihilation and expressions that correlate the spin themselves. In the same time we demand by the eigenvalues of the Killing tensor to be general, so any unnecessary annihilation of the directional derivatives of the eigenvalues is not a desired outcome. Next a rotation around our null base tetrads is implied since it seems unbearable for someone to extract any results without further simplifications. The latter provides us with the Key relations. Based upon the latter we resulting to the geometric classification of the emerged solutions, the Petrov Classification denotes the geometric nature of the solution we have to solve. Till this point our investigation based in the simultaneous admitting of both Killing Tensors K 2 , K 3 . In the section 5 though we are going to give up with this simultaneous admission of both Killing tensors and we will consider a relation between the spin coefficients. The lattter forbids the existence of K 3 tensor (q=-1). With the implication of Frobenius Theorem of integrability we set up our vector basis which depend by random functions. The determination of these functions finally resulting to Carter's case [D]. The next section referred to the analysis of the solution which takes place in Section 6. Scoping to gain physical knowledge about the solution necessary reductions have to be operated on . At the last section the equations of geodesics are presented along with the characterization of the eigenvalues of the Killing Tensor in respect to constants of motion. Finally the Appendices A,B demonstrate proofs that would impede the flow of our syllogism if we emplaced them in the main body of the article.
arXiv: General Relativity and Quantum Cosmology, 2018
We present the matching of two solutions belonging both to Carter's family [A] of metrics.The... more We present the matching of two solutions belonging both to Carter's family [A] of metrics.The interior solution has been found by one of us [1] and represents an anisotropic fluid, the exterior solution is the vacuum member of Carter's family of metrics [2].We study the model resulting from the matching procedure and we give some perspectives of our work.15 pages
Bulletin de la Classe des sciences, 1983
Résumé. — Nous explicitons les espaces-temps solutions des équations d'Einstein qui admettent... more Résumé. — Nous explicitons les espaces-temps solutions des équations d'Einstein qui admettent un tenseur de Killing avec une caractéristique de Sègre [(11) (11)], dont les valeurs propres λ, et λ2 ne sont pas des constantes et pour lesquels (t + ï)Ǫ — Ǫ) + 0. En général les espaces en question n'admettent pas de groupe d'isométries et ils sont une généralisation des espaces de B. Carter ; nous trouvons la condition nécessaire et suffisante pour l'existence d'un groupe d'isométries abélien à deux paramètres à orbites isotropes ou non isotropes (G2). Nous examinons les deux cas séparément et nous faisons une étude systématique pour le cas du G2 à orbites non isotropes.
International Journal of Modern Physics D, 2001
We present a stationary axisymmetric solution belonging to Carter's family [Ã] of spaces and ... more We present a stationary axisymmetric solution belonging to Carter's family [Ã] of spaces and representing an anisotropic fluid configuration
Annals of Geophysics, Apr 24, 2012
Observational studies from rock fractures to earthquakes indicate that fractures and many large e... more Observational studies from rock fractures to earthquakes indicate that fractures and many large earthquakes are preceded by accelerating seismic release rates (accelerated seismic deformation). This is characterized by cumulative Benioff strain that follows a power law time-to-failure relation of the form C(t) = K + A(T f -t) m , where T f is the failure time of the large event, and m is of the order of 0.2-0.4. More recent theoretical studies have been related to the behavior of seismicity prior to large earthquakes, to the excitation in proximity of a spinodal instability. These have show that the power-law activation associated with the spinodal instability is essentially identical to the power-law acceleration of Benioff strain observed prior to earthquakes with m = 0.25-0.3. In the present study, we provide an estimate of the generic local distribution of cracks, following the Wackentrapp-Hergarten-Neugebauer model for mode I propagation and concentration of microcracks in brittle solids due to remote stress. This is a coupled system that combines the equilibrium equation for the stress tensor with an evolution equation for the crack density integral. This inverse type result is obtained through the equilibrium equations for a solid body. We test models for the local distribution of cracks, with estimation of the stress tensor in terms of the crack density integral, through the Nash-Moser iterative method. Here, via the evolution equation, these estimates imply that the crack density integral grows according to a (T f -t) 0.3 -law, in agreement with observations.
Journal of Modern Physics, 2015
We present a class of axially symmetric and stationary spaces foliated by a congruence of surface... more We present a class of axially symmetric and stationary spaces foliated by a congruence of surfaces of revolution. The class of solutions considered is that of Carter's family [A] of spaces and we try to find a solution to Einstein's equations in the presence of a perfect fluid with heat flux. This approach is an attempt to find an interior solution that could be matched to a corresponding exterior solution across a surface of zero hydrostatic pressure. The presence of a congruence of surfaces of revolution, described as the quotient space of the commoving observers, can be useful to the determination of the surface of zero pressure. Finally we present two formal solutions representing ellipsoids of revolutions.
Recent Developments in Gravity - Proceedings of the 10th Hellenic Relativity Conference, 2003
... 10. T. Papacostas, Bull. Sci. Acad. R. Belg., LXIX, 495 (1983). 11. T. Papacostas, Int. J. of... more ... 10. T. Papacostas, Bull. Sci. Acad. R. Belg., LXIX, 495 (1983). 11. T. Papacostas, Int. J. of Mod. Phys. D, 10, 869-879 (2001). 12. JA Wheeler et al.," Gravitation", Freeman, San Francisco (1973). 13. S. Weinberg, Gravitation and Cosmology, John Whiley and Sons (1972).
Contemporary Mathematics, 1997
International Journal of Modern Physics D, 1998
We present a new perfect fluid solution belonging to (1,1) subfamily of Hauser–Mahlist spaces, ri... more We present a new perfect fluid solution belonging to (1,1) subfamily of Hauser–Mahlist spaces, rigidly rotating, type D in Petrov classification which reduces to the Wahlquist metric for particular values of our constants of integration. Unfortunately it is characterized by the equation of state of the Wahlquist solution: e + 3p = constant .
A generalization of the notion of surfaces of revolution in the spaces of General Relativity is p... more A generalization of the notion of surfaces of revolution in the spaces of General Relativity is presented. We apply this definition to the case of Carter's family [A] of solutions and we study the Kerr's metric with respect the above mentioned foliation.
Journal of Physics: Conference Series, 2009
ABSTRACT We use the notion of ellipsoidal spaces in General Relativity and obtain the correspondi... more ABSTRACT We use the notion of ellipsoidal spaces in General Relativity and obtain the corresponding Einstein's equations in the case of a perfect fluid with heat flux. We present the integration of the resulting equations and two families of solutions.
Journal of Physics: Conference Series, 2005
ABSTRACT We define the notion of a surface of revolution in the curved spaces of General Relativi... more ABSTRACT We define the notion of a surface of revolution in the curved spaces of General Relativity and we present the corresponding Einstein's equations in the case of an anisotropic fluid with bulk and shear viscosity and heat conduction. We indicate a method of integration and some particular solutions.
Journal of Physics: Conference Series, 2013
We consider the spacetime of a perfect fluid described by the Einstein-Euler equations. We assume... more We consider the spacetime of a perfect fluid described by the Einstein-Euler equations. We assume given spatial growth for the fluid and spacetime initial data and estimate the temporal evolution of the spatial growth rates through the wave equations derived for the fluid and spacetime data.
Journal of Physics: Conference Series, 2013
These proceedings include contributions from speakers of the conference. T Papakostas and D Pliak... more These proceedings include contributions from speakers of the conference. T Papakostas and D Pliakis, as members of the local organizing committee, wish to express their gratitude to all the participants of the conference for the warm atmosphere they created.
Journal of Mathematical Physics, 1991
The Einstein equations coupled with a spherically symmetric time-dependant scalar field are solve... more The Einstein equations coupled with a spherically symmetric time-dependant scalar field are solved. The problem of two distinct cases is reduced and the first of them is successfully solved completely, the resulting solutions being cosmological models. For the second one which is static, only a partial solution is found.
Journal of Mathematical Physics, 1989
A five-parameter family of solutions is investigated, describing the collision of plane-fronted i... more A five-parameter family of solutions is investigated, describing the collision of plane-fronted impulsive gravitational and shock electromagnetic waves. In the interaction region, to the future of the collision, it is a locally known solution of the Einstein–Maxwell electrovacuum equations of Petrov type D. The collision results in the formation of a Cauchy horizon. Extensions of the space-time are constructed beyond the Cauchy horizon and beyond certain two-dimensional surfaces that are mere coordinate singularities. It is found that in the extended space-time the following may occur: (i) no curvature singularities, (ii) two-dimensional spacelike curvature singularities, and (iii) two-dimensional timelike curvature singularities, according to the ranges of the parameters of the solution.
Journal of Mathematical Physics, 1988
In this paper a special case of Hauser–Malliot (HM) space-times is examined in the presence of a ... more In this paper a special case of Hauser–Malliot (HM) space-times is examined in the presence of a perfect fluid source. The obtained solutions are all known except for a generalization of a stationary axisymmetric solution found by Kramer [Class. Quantum Gravit. 1, L3 (1984)].
General Relativity and Gravitation, 1988
We present a perfect fluid solution of Einstein's equations, admitting a Killing tensor with ... more We present a perfect fluid solution of Einstein's equations, admitting a Killing tensor with Segre characteristics [(11)(11)] and two commuting spacelike Killing fields. The Equation of state has no physical meaning but is the same as that of the Wahlquist solution,e+3p=constant, which admits the same Killing tensor, as our solution, although the two Killing fields are timelike and spacelike, respectively.
Proc. of the 3rd IASME/WSEAS Int. Conf. on Energy, Environment, Ecosystems and Sustainable Development, Agios Nikolaos, Greece, July, Jul 27, 2007
Abstract:-In this paper the wind field of the broader area of Chania is statistically analyzed. T... more Abstract:-In this paper the wind field of the broader area of Chania is statistically analyzed. This analysis is based over one year's hourly averaged measurements of the wind speed and direction, obtained from a network of five Automated Meteorological Stations operating in the greater area of Chania. Firstly, a descriptive statistical analysis of wind speed and direction is performed, which includes the availability of data, the calculation of mean wind speeds, monthly and diurnal variations along with the distribution by wind direction. The ...
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Papers by Taxiarchis Papakostas