Charged anisotropic compact objects by gravitational decoupling

In the present article, we have constructed a static charged anisotropic compact star model of Einstein field equations for a spherically symmetric space-time geometry. Specifically, we have extended the charged isotropic Heintzmann solution to an anisotropic domain. To address this work, we have employed the gravitational decoupling through the so called minimal geometric deformation approach. The charged anisotropic model is representing the realistic compact objects such as $RXJ1856-37$ and $SAX J1808.4-3658(SS2)$. We have reported our results in details for the compact star $RXJ1856-37$ on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, stability conditions, Tolman-Oppenheimer-Volkoff equation and redshift etc

Compact star in Tolman Kuchowicz spacetime in background of Einstein Gauss Bonnet gravity

The present work is devoted to the study of anisotropic compact matter distributions within the framework of 5-dimensional Einstein-Gauss-Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman-Kuchowicz spacetime. The Gauss-Bonnet Lagrangian is coupled to Einstein-Hilbert action through a coupling constant. When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor.Additionally, the behaviour of the subliminal sound speed of the pressure waves in the principal direction of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing causality condition and energy conditions, respectively. All these subjects are supported by mean of physical, mathematical and graphical surve

A generalized Finch-Skea class one static solution

In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components $e^{\nu}$ and $e^{\lambda}$. In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component $g_{rr}$ corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density $\rho$, the radial, and tangential pressures $p_r$ and $p_t$, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The $M-R$ diagram suggests that the solution yields stiffer EoS as parameter $n$ increases. The $M-I$ graph is in agreement with the concepts of Bejgar et al. \cite{bej} that the mass at $I_{max}$ is lesser by few percent (for this solution $\sim 3\%$) from $M_{max}$. This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state.Comment: 14 figures, Accepted in European Physical Journal

Unified first law of thermodynamics in Gauss-Bonnet gravity on an FLRW background

Employing the thermodynamic unified first law through the thermodynamic-gravity conjecture, in this article, we derive for a FLRW universe the Friedmann equations in the framework of Gauss-Bonnet gravity theory. To do this, we project this generalized first law along the Kodama vector field and along the direction of an orthogonal vector to the Kodama vector. The second Friedmann equation is obtained by projecting on the Kodama vector, while the first is obtained by projecting along the flux on the Cauchy hypersurfaces. This result does not assume a priory temperature and an entropy, so the Clausius relation is not used here. Nevertheless, it is used to obtain the corresponding Gauss-Bonnet entropy. In this way, the validity of the generalized second law of thermodynamics is proved for the Gauss-Bonnet gravity theory.Comment: 10 pages, 2 figure

Compact Anisotropic Models in General Relativity by Gravitational Decoupling

Durgapal's fifth isotropic solution describing spherically symmetric and static matter distribution is extended to an anisotropic scenario. To do so we employ the gravitational decoupling through the minimal geometric deformation scheme. This approach allows to split Einstein's field equations in two simply set of equations, one corresponding to the isotropic sector and other to the anisotropic sector described by an extra gravitational source. The isotropic sector is solved by the Dugarpal's model and the anisotropic sector is solved once a suitable election on the minimal geometric deformation is imposes. The obtained model is representing some strange stars candidates and fulfill all the requirements in order to be a well behaved physical solution to the Einstein's field equations

Quantum aspects of the gravitational-gauge vector coupling in the Ho\v{r}ava-Lifshitz theory at the kinetic conformal point

This work presents the main aspects of the anisotropic gravity-vector gauge coupling at all energy scales \i.e., from the IR to the UV point. This study is carry out starting from the 4+1 dimensional Ho\v{r}ava-Lifshitz theory, at the kinetic conformal point.The Kaluza-Klein technology is employed as a unifying mechanism to couple both interactions. Furthermore, by assuming the so-called cylindrical condition, the dimensional reduction to 3+1 dimensions leads to a theory whose underlying group of symmetries corresponds to the diffeomorphisms preserving the foliation of the manifold and a U(1) gauge symmetry. The counting of the degrees of freedom shows that the theory propagates the same spectrum of Einstein-Maxwell theory. The speed of propagation of tensorial and gauge modes is the same, in agreement with recent observations. This point is thoroughly studied taking into account all the $z=1,2,3,4$ terms that contribute to the action. In contrast with the 3+1 dimensional formulation, here the Weyl tensor contributes in a non-trivial way to the potential of the theory. Its complete contribution to the 3+1 theory is explicitly obtained. Additionally, it is shown that the constraints and equations determining the full set of Lagrange multipliers are elliptic partial differential equations of eighth-order. To check and assure the consistency and positivity of the reduced Hamiltonian some restrictions are imposed on the coupling constants. The propagator of the gravitational and gauge sectors are obtained showing that there are not ghost fields, what is more they exhibit the $z=4$ scaling for all physical modes at the high energy level. By evaluating the superficial degree of divergence and considering the structure of the second class constraints, it is shown that the theory is power-counting renormalizable

A new model of regular black hole in (2+1)(2+1) dimensions

We provide a new regular black hole solution in $(2+1)$ dimensions with presence of matter fields in the energy momentum tensor, having its core a flat or (A)dS structure. Since the first law of thermodynamics for regular black holes is modified by the presence of the matter fields, we provide a new version of the first law, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent with the previously known in literature. It is shown that the signs of the variations of the local definition of energy and of the total energy coincide. Furthermore, at infinite, the usual first law $dM=TdS$ is recovered. It is showed that the formalism used is effective to compute the total energy of regular black holes in $(2+1)$ with presence of matter in the energy momentum tensor. This latter suggests the potential applicability of this formalism to calculate the mass of other models of regular black holes in $d \ge 4$ dimensions.Comment: accepted for publication in EP

The structure of Bryant’s empathy index for children: a cross-validation study

The present study examined the structure of Bryant’s Empathy Index (BEI) using different samples for conducting exploratory and confirmatory analyses. The BEI was administered to a sample of 2,714 children (mean age 11.12, SD = 1.59). Exploratory and confirmatory factor analyses showed a three-factor structure: Feelings of Sadness, Understanding Feelings and Tearful Reaction. The results revealed both the multidimensionality of the instrument and appropriate fit indices for the model proposed. Although these results were very similar to those reported in other studies with a Spanish population, the analyses were conducted in a more robust way: with a larger sample and using polychoric correlations and cross validation estimation.El presente estudio examinó la estructura del Bryant’s Empathy Index (BEI), empleando diferentes muestras para llevar a cabo análisis exploratorio y confirmatorio. El BEI se aplicó a una muestra de 2,714 niños (edad media 11,12; DT = 1,59). Análisis exploratorio y confirmatorio revelaron una estructura de tres factores: Sentimientos de Tristeza, Comprensión de Sentimientos y Reacción de Llanto. Los resultados revelaron la multidimensonalidad del instrumento e índices de bondad de ajuste adecuados para el modelo propuesto. Aunque estos resultados eran muy similares a los que aparecen en otros estudios con población española, los análisis se llevaron a cabo de una forma más robusta: con una muestra mayor y empleando correlaciones policóricas y estimación de la validación cruzada