Relativistic polytropic models of charged anisotropic compact objects

In this paper, we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity (\begin{document}${\rm GR}$\end{document}). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state (\begin{document}${\rm EoS}$\end{document}). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., \begin{document}$\eta= \dfrac{1}{2},~ \dfrac{2}{3},~ 1$\end{document}, and \begin{document}$ 2 $\end{document}. Next, numerous physical characteristics of these considered models were studied via graphical analysis, and they were found to obey all the essential conditions for astrophysical compact objects. Furthermore, such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear, quadratic, and polytropic \begin{document}${\rm EoS}$\end{document}     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Singularities of noncompact charged objects

We formulate a model of noncompact spherical charged objects in the framework of noncommutative field theory. The Einstein-Maxwell field equations are solved with charged anisotropic fluid. We choose matter and charge densities as functions of two parameters instead of defining these quantities in terms of Gaussian distribution function. It is found that the corresponding densities and the Ricci scalar are singular at origin, whereas the metric is nonsingular, indicating a spacelike singularity. The numerical solution of the horizon equation implies that there are two or one or no horizon(s) depending on the mass. We also evaluate the Hawking temperature, and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.     

Relativistic compact objects in isotropic coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati-type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic-type fluid with an equation of statep =γρ is discussed in detail.     

Casimir forces between arbitrary compact objects

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.     

Extended gravitational decoupled charged anisotropic solutions

In this paper, we study exact charged anisotropic spherical solutions through extended geometric deformation technique. For this purpose, we consider the singularity-free Krori–Barua solution and extend it to attain two analytical anisotropic models in the presence of the electromagnetic field. We examine energy bounds as well as causality condition for the star Her X-I to analyze the viability of the obtained solutions. It is found that both models show realistic behavior as they satisfy all physical constraints as well as stability criterion. We conclude that the extended gravitational decoupling approach provides more stable results for the stellar system in contrast to minimal geometric deformation.     

Physics of accretion flows around compact objects

Several physical and astrophysical problems related to accretion onto black holes and neutron stars are briefly reviewed. I discuss the observed differences between these two types of compact objects in quiescent Soft X-ray Transients. Then I review the status of various non-standard objects suggested as an alternative to black holes. Finally, I present new results and a suggestion about the nature of the jet activity in Active Galactic Nuclei. To cite this article: J.-P. Lasota, C. R. Physique 8 (2007).     

A conformally flat realistic anisotropic model for a compact star

A physically realistic stellar model with a simple expression for the energy density and conformally flat interior is found. The relations between the different conditions are used without graphic proofs. It may represent a real pulsar.     

Generalised model for anisotropic compact stars

In the present investigation an exact generalised model for anisotropic compact stars of embedding class 1 is sought with a general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass–radius relation, stability of the models, in connection to their validity. It is observed that the model presented here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates RXJ 1856-37, SAX J 1808.4-3658 (SS1) and SAX J 1808.4-3658 (SS2) are concerned.     

Relativistic models of a class of compact objects

A class of general relativistic solutions in isotropic spherical polar coordinates which describe compact stars in hydrostatic equilibrium are discussed. The stellar models obtained here are characterized by four parameters, namely, ??, k, A and R of geometrical significance related to the inhomogeneity of the matter content of the star. The stellar models obtained using the solutions are physically viable for a wide range of values of the parameters. The physical features of the compact objects taken up here are studied numerically for a number of admissible values of the parameters. Observational stellar mass data are used to construct suitable models of the compact stars.     

Tail wavelets in merger of binary compact objects

We present a model for tail wavelets, a phenomenon known as "echo" in the literature. The tail wavelet may appear in signal reconnaissances in the merger of binary compact objects, including black holes and neutron stars. We show that the dark matter surrounding the compact objects lead to a speculated tail wavelet following the main gravitational wave(GW). We demonstrate that the radiation pressure of the main wave is fully capable of pushing away the surrounding matter to some altitude, and splashing down of the matter excites the tail wavelet after ringing down of the main wave. We illustrate this concept in a simplified model, where numerical estimations are conducted on the specific distribution of dark matter outside the black hole horizon and the threshold values in accordance with observations. We study the full back reaction of the surrounding dark matter to the metric and find that the effect on to the tail wavelets is insignificant. We reveal the fine difference between the tail wavelets of a dressed and a bare black hole. We demonstrate that the tail wavelet can appear as a natural phenomenon in the frame of general relativity, without invoking modified gravities or quantum effects.     

A new family of high-order compact upwind difference schemes with good spectral resolution

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.     

A new family of high-order compact upwind difference schemes with good spectral resolution

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.     

Accretion processes for general spherically symmetric compact objects

The European Physical Journal C - LArGe is a Gerda low-background test facility to study novel background suppression methods in a low-background environment, for future application in the Gerda...     

A new model for spherically symmetric charged compact stars of embedding class 1

In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant \(A=0\), which shows that our solutions represent the so-called ‘electromagnetic mass model’ [17], and, secondly, the metric function \(\nu (r)\), for the limit n tending to infinity, converts to \(\nu (r)=C{r}^{2}+ ln~B\), which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence.