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E. Kyriakopoulos

Publications and source records attributed to E. Kyriakopoulos.

9 recordsLinked to original sources
arXiv2022

Regular Interior Solutions to the Solution of Kerr which Satisfy the Weak and the Strong Energy Conditions

The line element of a class of solutions which match to the solution of Kerr on an oblate spheroid if the two functions $ F(r)$ and $H(r)$ on which it depends satisfy certain matching conditions is presented. The non vanishing components of the Ricci tensor $R_{μν}$, the Ricci scalar $ R$, the second order curvature invariant $K$, the eigenvalues of the Ricci tensor, the energy density $μ$, the tangential pressure $P_{\perp}$, and the quantity $μ+P_{\perp}$ are calculated. A function $F(r)$ is given for which $R$ and $K$ and therefore the solutions are regular. The function $ H(r) $ should be such that the solution it gives satisfies at least the Weak Energy Conditions (WEC). Several $H(r)$ are given explicitly for which the resulting solutions satisfy the WEC and also the Strong Energy Conditions (SEC) and the graphs of their $μ$, $P_{\perp}$ and $μ+P_{\perp}$ for certain values of their parameters are presented. It is shown that all solutions of the class are anisotropic fluid solutions and that there are no perfect fluid solutions in the class.

gr-qc↗
arXiv2016

Regular Spherically Symmetric Interior Solution To Schwarzschid's Solution Which Satisfies The Weak Energy Conditions

We present a simple spherically symmetric and regular solution of Einstein's equations with two parameters $k$ and $M$, which matches to Schwarzschild's solution, satisfies the weak energy conditions in the interior region and for small $r$ behaves like the de Sitter solution. Its energy density $ρ$ and its radial pressure $p_r$ satisfy the relation $ρ+p_r=0$. For some values of $k/M$ the solution does not have an event horizon and the event horizon of Schwarzschild's solution is inside the matching surface. Therefore it describes the formation of a gravitational soliton, which is shown to be stable. Gravitational solitons are related to dark matter. For the other values of $k/M$ it is a regular black hole solution.

gr-qc↗
arXiv2016

Rotating Anisotropic Fluid Solutions

An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the eigenvalues of this tensor and the energy-momentum tensor of the solutions are given explicitly. All have the ring singularity of Kerr's solution and in addition the solution one more singularity and some solutions of the family additional singularities.The solution matches to the extremal solution of Kerr on two surfaces, which are thin shells and for proper values of the parameters of the solution approximate oblate spheroids. One of these surfaces has positive surface density. The solutions of the family satisfy the matching conditions with the solution of Kerr on two pair of surfaces, which are again thin shells. The surface density of one pair of surfaces is given explicitly. Also for proper values of the parameters of the solutions the surfaces of the other pair approximate oblate spheroids.

gr-qc↗
arXiv2014

Family Of Rotating Anisotropic Fluid Solutions which Match to Kerr's Solution

We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{μν}$ the eigenvalues of the tensor $R_μ^ν$ and the energy-momentum tensor $T_{μν}$ of the solutions are given explicitly. All members of the family have the ring singularity of Kerr's solution and most of them one or two more singularities. The solutions can be matched to the solution of Kerr on three closed surfaces, which for proper values of the parameters of the solutions approximate oblate spheroids. All matching surfaces are thin shells. For some values of a constant the surface density in one of them is positive everywhere and in this surface and in its interior all energy conditions are satisfied.

gr-qc↗
arXiv2009

Rotating Black Hole Solutions with Axion Dilaton and Two Vector Fields and Solutions with Metric and Fields of the Same Form

We present two rotating black hole solutions with axion $ξ$, dilaton $ϕ$ and two U(1) vector fields. By applying the "Newman-Janis trick" to a metric with 3 arbitrary parameters we find a rotating metric $g_{μν}$ with 4 such parameters $(M, a, Q_E, Q_M)$, and then a solution with this $g_{μν}$ as metric. Our solution is asymptotically flat and has angular momentum $J=M a$, gyromagnetic ratio $g=2$, two horizons, the singularities of Kerr's solution, axion and dilaton singular only for $r=a\cosθ=0$. Applying to the solution we have found the $S-$duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metric, each vector field and the $λ=ξ+ie^{-2ϕ}$ of our solutions and the solution of : Sen for $Q_E$, Sen for $Q_E$ and $Q_M$, Kerr-Newman for $Q_E$ and $Q_M$, Kerr, Ref. 9, STW, GM-GHS, Reissner-Nordström,Schwarzschild are the same function of $a$, and two functions $ρ^2=r(r+b)+a^2\cos^2θ$ and $Δ=ρ^2-2Mr+c$, of $a$, $b$ and two functions, and of $a$, $b$ and $d$ respectively, where $a$, $b$, $c$ and $d$ are constants. It is shown that from our solutions a number of known solutions can be obtained, which together with our solutions are listed in an Appendix. Also it is shown that all solutions which are mentioned in the paper satisfy all energy conditions, and mass formulae are obtained for them.

gr-qc↗
arXiv2006

Black Holes in Models with Dilaton Field and Electric or Electric and Magnetic Charges

Exact static spherically symmetric charged black holes in four dimensions are presented. One of them has only electric charge and another electric and magnetic charges. In these solutions the metric is asymptotically flat, has two horizons, irremovable singularity only at $r=0$, and the dilaton field is singular only at $r=0$. The solution with electric charge only is characterized by three free parameters, the ADM mass, the electric charge and an additional free parameter. It can be considered as a modification of the GHS-GM solution obtained by changing the coupling between dilaton and electromagnetic field. The general dyonic solution is again characterized by three free parameters, the ADM mass, the magnetic charge and an additional free parameter, which is not the electric charge. According to a definition of the no-hair conjecture the solutions are "hairy".A very interesting special case of the dyonic solution is characterized by three free parameters, the ADM mass and the electric and the magnetic charges. The solutions satisfy the dominant as well as the strong energy condition outside and on the external horizon.

gr-qc↗
arXiv2006

Black Hole in a Model with Dilaton and Monopole Fields

We present an exact black hole solution in a model having besides gravity a dilaton and a monopole field. The solution has three free parameters, one of which can be identified with the monopole charge, and another with the ADM mass. The metric is asymptotically flat and has two horizons and irremovable singularity only at $r=0$. The dilaton field is singular only at $r=0$. The dominant and the strong energy condition are satisfied outside and on the external horizon. According to a formulation of the no hair conjecture the solution is "hairy". Also the well know GHS-GM solution is obtained from our solution for certain values of its parameters.

gr-qc↗
arXiv2001

Bäcklund Transformations of Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

Clairin's method of obtaining Bäcklund transformations is applied to Einstein's field equations for the interior of a uniformly rotating stationary axisymmetric perfect fluid. It is shown that for arbitrary pressure $p$ and mass density $μ$ the method does not give non-trivial Bäcklund transformations, while if $μ+ 3p =0$ it gives the transformation of Ehlers.

gr-qc↗