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Register a new userIsotropization and change of complexity by gravitational decoupling
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We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b) generate new solutions for self-gravitating distributions with the same or vanishing complexity factor. A few working examples are given for illustrative purposes.
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In this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by the Minimal Geometric Deformation approach. We use the complexity factor as a complementary condition to close the system of differential equations. It is shown that for a polynomial complexity the resulting solution can be matched with two different modified-vacuum geometries.
In this work we obtain an anisotropic neutron star solution by gravitational decoupling starting from a perfect fluid configuration which has been used to model the compact object PSR J0348+0432. Additionally, we consider the same solution to model the Binary Pulsar SAX J1808.4-3658 and X-ray Binaries Her X-1 and Cen X-3 ones. We study the acceptability conditions and obtain that the MGD--deformed solution obey the same physical requirements as its isotropic counterpart. Finally, we conclude that the most stable solutions, according to the adiabatic index and gravitational cracking criterion, are those with the smallest compactness parameters, namely SAX J1808.4-3658 and Her X-1.
Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge generating these transformations. Under the above conditions i) and ii), this charge consistently increases the entropy from the minimum value given by the Schwarzschild geometry. As a direct application, we find a non-trivial extension of the Reissner-Nordstrom black hole showing a surprisingly simple horizon. Finally, the non-linear electrodynamics generating this new solution is fully specified.
We study several aspects of the extended thermodynamics of BTZ black holes with thermodynamic mass $M=alpha m + gamma frac{j}{ell}$ and angular momentum $J = alpha j + gamma ell m$, for general values of the parameters $(alpha, gamma)$ ranging from regular ($alpha=1, gamma=0$) to exotic ($alpha=0, gamma=1$). We show that there exist two distinct behaviours for the black holes, one when $alpha > gamma$ (mostly regular), and the other when $gamma < alpha$ (mostly exotic). We find that the Smarr formula holds for all $(alpha, gamma)$. We derive the corresponding thermodynamic volumes, which we find to be positive provided $alpha$ and $gamma$ satisfy a certain constraint. The dependence of pressure on volume is unremarkable and strictly decreasing when $alpha > gamma$, but a maximum volume emerges for large $Jgg T$ when $gamma > alpha$; consequently an exotic black hole of a given horizon circumference and temperature can exist in two distinct anti de Sitter backgrounds. We compute the reverse isoperimetric ratio, and study the Gibbs free energy and criticality conditions for each. Finally we investigate the complexity growth of these objects and find that they are all proportional to the complexity of the BTZ black hole. Somewhat surprisingly, purely exotic BTZ black holes have vanishing complexity growth.
Using the gravitational decoupling by the minimal geometric deformation approach, we build an anisotropic version of the well-known Tolman VII solution, determining an exact and physically acceptable interior two-fluid solution that can represent behavior of compact objects. Comparison of the effective density and density of the perfect fluid is demonstrated explicitly. We show that the radial and tangential pressure are different in magnitude giving thus the anisotropy of the modified Tolman VII solution. The dependence of the anisotropy on the coupling constant is also shown.
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