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Register a new userThe static spherically symmetric body in relativistic elasticity
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In this paper is discussed a class of static spherically symmetric solutions of the general relativistic elasticity equations. The main point of discussion is the comparison of two matter models given in terms of their stored energy functionals, i.e., the rule which gives the amount of energy stored in the system when it is deformed. Both functionals mimic (and for small deformations approximate) the classical Kirchhoff-St.Venant materials but differ in the strain variable used. We discuss the behavior of the systems for large deformations.
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An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. Again the formalism requires the knowledge of only one function (instead of two) to generate all possible solutions. To illustrate the method some known cases are recovered.
We study a marginally stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. It turns out that the metric components are separable from the constants of motion along geodesics. We show also that a metric component $g_{rr}$ with a radial coordinate $r$ does not affect MSCOs. This suggests that, as a test of gravity, any ISCO measurement may be put into the same category as gravitational redshift experiments. MSCOs for exact solutions to the Einsteins equation are also mentioned.
In this paper, we systematically study spherically symmetric static spacetimes in the framework of Einstein-aether theory, and pay particular attention to the existence of black holes (BHs). In the present studies we first clarify several subtle issues. In particular, we find that, out of the five non-trivial field equations, only three are independent, so the problem is well-posed, as now generically there are only three unknown functions, {$F(r), B(r), A(r)$, where $F$ and $B$ are metric coefficients, and $A$ describes the aether field.} In addition, the two second-order differential equations for $A$ and $F$ are independent of $B$, and once they are found, $B$ is given simply by an algebraic expression of $F,; A$ and their derivatives. To simplify the problem further, we explore the symmetry of field redefinitions, and work first with the redefined metric and aether field, and then obtain the physical ones by the inverse transformations. These clarifications significantly simplify the computational labor, which is important, as the problem is highly involved mathematically. In fact, it is exactly because of these, we find various numerical BH solutions with an accuracy that is at least two orders higher than previous ones. More important, these BH solutions are the only ones that satisfy the self-consistent conditions and meantime are consistent with all the observational constraints obtained so far. The locations of universal horizons are also identified, together with several other observationally interesting quantities, such as the innermost stable circular orbits (ISCO), the ISCO frequency, and the maximum redshift $z_{max}$ of a photon emitted by a source orbiting the ISCO. All of these quantities are found to be quite close to their relativistic limits.
The measurement of the epicyclic frequencies is a widely used astrophysical technique to infer information on a given self-gravitating system and on the related gravity background. We derive their explicit expressions in static and spherically symmetric wormhole spacetimes. We discuss how these theoretical results can be applied to: (1) detect the presence of a wormhole, distinguishing it by a black hole; (2) reconstruct wormhole solutions through the fit of the observational data, once we have them. Finally, we discuss the physical implications of our proposed epicyclic method.
We derive the equations of motion of a test particle in the equatorial plane around a static and spherically symmetric wormhole influenced by a radiation field including the general relativistic Poynting-Robertson effect. From the analysis of this dynamical system, we develop a diagnostic to distinguish a black hole from a wormhole, which can be timely supported by several and different observational data. This procedure is based on the possibility of having some wormhole metrics, which smoothly connect to the Schwarzschild metric in a small transition surface layer very close to the black hole event horizon. To detect such a metric-change, we analyse the emission proprieties from the critical hypersurface (stable region where radiation and gravitational fields balance) together with those from an accretion disk in the Schwarzschild spacetime toward a distant observer. Indeed, if the observational data are well fitted within such model, it immediately implies the existence of a black hole; while in case of strong departures from such description it means that a wormhole could be present. Finally, we discuss our results and draw the conclusions.
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