Abstract
In this paper, we study the Jeans analysis in the context of energy–momentum-squared gravity (EMSG). More specifically we find the new Jeans mass for non-rotating infinite mediums as the smallest mass scale for local perturbations that can be stable against its own gravity. Furthermore, for rotating mediums, specifically for rotating thin disks in the context of EMSG, we find a new Toomre-like criterion for the local gravitational stability. Finally, the results are applied to a hyper-massive neutron star, as an astrophysical system. Using a simplified toy model we have shown that, for a positive (negative) value of the EMSG parameter alpha , the system is stable (unstable) in a wide range of alpha . On the other hand, no observational evidence has been reported on the existence of local fragmentation in HMNS. Naturally, this means that EMSG with positive alpha is more acceptable from the physical point of view.
Highlights
Theories of the gravity have been proposed to solve the puzzle [29,30,31,32,33,34,35,36,37]
In this paper, we study the Jeans analysis in the context of energy–momentum-squared gravity (EMSG)
Any cloud or disk is stable if the condition Q > 1 holds. As it was for Jeans instability, it has been shown that the Toomre’s criterion can be used to check the validity of several modified theories of gravity [52,53,54]. Generalizing both criteria for the local stability in the framework of EMSG could provide a very remarkable tool to describe the dynamics of self-gravitating system such as the collapse of spherical clouds, the collapse of massive star into Black Hole and/or the accretion disks around a massive object, leading to new results that could potentially be used to retain/rule out the theory
Summary
We will compute the weak field limit of energy– momentum-squared-gravity (EMSG), recently introduced by [41,42], to study the collapse of a self-gravitating system. Any cloud or disk is stable if the condition Q > 1 holds As it was for Jeans instability, it has been shown that the Toomre’s criterion can be used to check the validity of several modified theories of gravity [52,53,54]. Generalizing both criteria for the local stability in the framework of EMSG could provide a very remarkable tool to describe the dynamics of self-gravitating system such as the collapse of spherical clouds, the collapse of massive star into Black Hole and/or the accretion disks around a massive object, leading to new results that could potentially be used to retain/rule out the theory.
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