Abstract
We present a simple, analytic and straightforward method to elucidate the effects produced by polytropic fluids on any other gravitational source, no matter its nature, for static and spherically symmetric spacetimes. As a direct application, we study the interaction between polytropes and perfect fluids coexisting inside a self-gravitating stellar object.
Highlights
The study of self-gravitating systems is of great importance in the context of general relativity
Since the Gravitational Decoupling approach (GD) [4,5] is precisely designed for coupling/decoupling gravitational sources in general relativity, we will see that, it is possible to elucidate the role played by each gravitational source, without resorting to any numerical protocol or perturbation scheme, as explained in the paragraph
In order to be as self-contained as possible, and to clarify the reader any potential confusion about what we developed between Eqs. (2)–(31), we describe the intrinsic relationship between gravitational decoupling and energy exchange for coupled/decoupled relativistic fluids
Summary
The study of self-gravitating systems is of great importance in the context of general relativity. It would be very useful to see how relevant is the role that each fluid, represented by their respective energy–momentum tensor Tμi ν in (1), plays on a selfgravitating system, as well as how these gravitational sources interact with each other This would allow, for instance, detecting which source dominates over the others, and rule out any equation of state incompatible with the dominant source. 211 Page 2 of 11 and much more realistic,[1] indicates an exchange of energy between these sources that, in principle, would be impossible to quantify or at least describe in some detail The reason for this is that the Bianchi identities do not introduce additional information beyond Einstein’s equations.
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