A new class of viable and exact solutions of EFEs with Karmarkar conditions: an application to cold star modeling

Abstract

In this work we present a theoretical framework within Einstein’s classical general relativity which models stellar compact objects such as PSR J1614–2230 and SAX J1808.4–3658. The Einstein field equations are solved by assuming that the interior of the compact object is described by a class I spacetime. The so-called Karmarkar condition arising from this requirement is integrated to reduce the gravitational behaviour to a single generating function. By appealing to physics we adopt a form for the gravitational potential which is sufficiently robust to accurately describe compact objects. Our model satisfies all the requirements for physically realistic stellar structures.

Uncharged and charged anisotropic like-Durgapal stellar models with vanishing complexity

“…For this we set q = 0 in Eqs. (47), (48) and (49). We use the g tt metric coefficient as a seed known solution…”

“…Setting q = 0 in Eqs. (47), (48) and (49) we use the g tt metric coefficient as a seed (a well-behaved known solution) that will allow us to obtain the complete solution of the problem considered. So, we start with the metric temporal function, The vanishing complexity condition (38), as before, translates into a relationship between the metric variables and enables us to find the radial metric coefficient, given by…”

“…In the case of considering stellar objects that have a net electric charge, obviously, we have another degree of freedom or indeterminacy that must be satisfied. In this regard, we need to provide (in addition to the boundary or initial conditions) extra information related to the local physics or restrictions on the metric variables such as the conformally flat [41,42] or the arXiv:2208.10260v1 [gr-qc] 18 Aug 2022 2 Karmarkar condition which allow to choose one of the metric functions as generator of the total solution [43] (see, also [44][45][46][47][48][49]). In the same direction, a relevant and well known concept in physics as is the complexity, applied to the scope of General Relativity, can perfectly be considered to provide the extra necessary information.…”

Anisotropic star models in the context of vanishing complexity

“…For instance, polytropic equations of state (see [9,10] and references therein) that were first considered in the Newtonian regime to study white dwarfs [11,12], has been generalized to model anisotropic spheres in General Relativity [13][14][15][16][17][18][19][20][21][22][23][24]. Besides, physical conditions that restrict the metric variables have also been fully used such as the Karmarkar condition which allows to choose one of the metric functions as generator of the total solution [25] (for recent developments see, [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41], for example). Another example is the conformally flat condition which takes into account the vanishing of the Weyl tensor [15,42].…”

Complexity factor for black holes in the framework of the Newman–Penrose formalism

“…Many studies have been carried out in order to establish the appropriate conditions that, in addition to allowing the system to be closed, lead us to obtain real physical models that may be used to describe compact objects. Most of the conditions are given by means of state equations that intent to describe the local physics properties of the relativistic fluids what stars are made of, but there may be other possibilities, like plausible heuristic conditions over the metric variables which perfectly work to close and solve the system of field equations (see [3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein). Following this scheme, we can use the relevant concept of complexity (in the realm of general relativity) for self-gravitating relativistic fluids, as a condition that provides extra information which can categorize the system.…”