On the Construction of Global Models Describing Rotating Bodies; Uniqueness of the Exterior Gravitational Field (original) (raw)
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The studies in general relativity of rotating finite objects in equilibrium have usually focused on the case when they are truly isolated, this is, the models to describe finite objects are embedded in an asymptotically flat exterior vacuum. Known results ensure the uniqueness of the vacuum exterior field by using the boundary data for the exterior field given at the surface of the object plus the decay of the exterior field at infinity. The final aim of the present work is to study the consequences on the interior models by changing the boundary condition at infinity to one accounting for the embedding of the object in a cosmological background. Considering first the FLRW standard cosmological backgrounds, we are studying the general matching of FLRW with stationary axisymmetric spacetimes in order to find the new boundary condition for the vacuum region. Here we present the first results.
arXiv (Cornell University), 2018
We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a "phase transition" on the surface R = 2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.
Advances in High Energy Physics, 2018
We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution is static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a “phase transition” on the surface R=2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.
International Journal of Theoretical & Computational Physics, 2021
In general theory of relativity, Einstein's field equations relate the geometry of space-time with the distribution of matter within it. These equations were first published by Einstein in the form of a tensor equation which related the local space-time curvature with the local energy and momentum within this space-time. In this article, Einstein's geometrical field equations interior and exterior to astrophysically real or hypothetical distribution of mass within a spherical geometry were constructed and solved for field whose gravitational potential varies with time, radial distance and polar angle. The exterior solution was obtained using power series. The metric tensors and the solution of the Einstein's exterior field equations used in this work has only one arbitrary function f(t,r,θ) , and thus put the Einstein's geometrical theory of gravitation on the same bases with the Newton's dynamical theory of gravitation. The gravitational scalar potential f(t,r,θ) obtained in this research work to the order of c o, c-2 , contains Newton dynamical gravitational scalar potential and post Newtonian additional terms much importance as it can be applied to the study of rotating bodies such as stars. The interior solution was obtained using weak field and slow-motion approximation. The obtained result converges to Newton's dynamical scalar potential with additional time factor not found in the well-known Newton's dynamical theory of gravitation which is a profound discovery with the dependency on three arbitrary functions. Our result obeyed the equivalence principle of Physics.
Exterior gravitational field of a rotating deformed mass
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We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein–Euler equations, that is, the Einstein equations together with the energy–momentum tensor of a barotropic perfect fluid. Although the reduced system of equations for the potentials in the co-rotating co-ordinate system is known, we derive the system of equations for potentials in the so called zero angular momentum observer co-ordinate system. We newly give a proof of the equivalence between the reduced system and the full system of Einstein equations. It is done under the assumption that the angular velocity is constant on the support of the density. Also the consistency of the equations of the system is analyzed. On this basic theory we construct on the whole space the stationary asymptotically flat metric generated by a slowly rotating compactly supported perfect fluid with vacuum boundary.
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General Relativity and Gravitation, 2013
We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) ǫ+(1−n)p = ǫ 0. This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois-Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist's metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr's metric.
International Journal of Engineering Science, 2003
Using the symmetry reduction approach we have herein examined, under continuous groups of transformations, the invariance of Einstein exterior equations for stationary axisymmetric and rotating case, in conventional and nonconventional forms, that is a coupled system of nonlinear partial differential equations of second order. More specifically, the said technique yields the invariant transformation that reduces the given system of partial differential equations to a system of nonlinear ordinary differential equations (nlodes) which, in the case of conventional form, is reduced to a single nlode of second order. The first integral of the resulting nlode has been obtained via invariant-variational principle and NoetherÕs theorem and involves an integration constant. Depending upon the choice of the arbitrary constant two different forms of the exact solutions are indicated. The generalized forms of Weyl and Schwarzschild solutions for the case of no spin have also been deduced as particular cases. Investigation of nonconventional form of Einstein exterior equations has not only led to the recovery of solutions obtained through conventional form but it also yields physically important asymptotically flat solutions. In a particular case, a single third order nlode has been derived which evidently opens up the possibility of finding many further interesting solutions of the exterior field equations.