Simple generic extensions of isotropic DurgapalFuloria stars to the anisotropic domain are presented. These anisotropic solutions are obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors by means of the minimal geometric deformation approach are satisfied. Hence the anisotropic field equations are isolated resulting a more treatable set. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, observational effects of such anisotropies when measuring the surface redshift are discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations is shown. In this manner, different anisotropic sectors can be isolated of each other and modeled in a simple and systematic way.

We employ the minimal geometric deformation approach to gravitational decoupling (MGDdecoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object. *

This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordström space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general equation of state, relating the components of the θ-sector in order to obtain the new material contributions and the decoupler function f (r). Besides, we obtain the bounds on the free parameters of the extended solution to avoid new singularities. Furthermore, we show the finitude of all thermodynamic parameters of the solution such as the effective densityρ, radialp r and tangentialp t pressure for different values of parameter α and the total electric charge Q. Finally, the behavior of some scalar invariants, namely the Ricci R and Kretshmann R µνω R µνω scalars are analyzed. It is also remarkable that, after an appropriate limit, the deformed Schwarzschild black hole solution always can be recovered. Although the above is also true, the Schwarzschild solution is described only by the mass M parameter, the Reissner-Nordström solution [2, 3] is characterized by mass M and electric charge Q whereas the Kerr spacetime [4] is painted by mass M and angular momentum J charges. Moreover, the most general solution of this type is the Kerr-Newman space-time [5] characterized by mass M , electric charge Q, and angular momentum J. The existence of these conserved charges is supported by the non-hair conjecture [6], which states that these solutions should not carry any other charges. Nonethe-arXiv:1909.00500v1 [gr-qc]

We study here how the presence of non-zero matter density and a cosmological constant could affect the observation of gravitational waves in pulsar timing arrays. Conventionally, the effect of matter and cosmological constant is included by considering the redshift in frequency due to the expansion. However, there is an additional interesting effect due to the change of coordinates from the ones describing the geometry of the region where waves are produced to the ones used to measure the pulsar timing residuals. This change of coordinates is unavoidable as the strong gravitational field in a black hole merger distorts clocks and rules. Harmonic waves produced in such a merger become anharmonic when detected by a cosmological observer. The effect is tiny but appears to be nevertheless observable for the type of gravitational waves to which pulsar timing arrays are sensitive and for the favoured values of the cosmological parameters.

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose-Einstein condensate of gravitons. In order to do so we extend the Einstein-Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross-Pitaevskii equation describing a graviton Bose-Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is nonzero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose-Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.