Many theories allow existence of higher dimensions that are non compact. Study of stability and structure of stars in such a framework is interesting and explored by different groups. All these studies have been performed for compact objects like white dwarfs, neutron stars, and black holes; all of which exhibit strong field gravity. These studies were mostly analytical and did not give numerical values of observable properties like the mass, radius, gravitational redshift, etc. for the stars. The reason for this is the fact that we do not know the value of the gravitational constant and properties of matter at higher dimensions. In the present work, M. Bagchi provided values of these observables for a few dimensions and discuss possible observational aspects.
Tolman-Oppenheimer-Volkoff equations, are equations which determines the structure of a spherically symmetric body of isotropic material in equilibrium, in general relativity (GR). It is widely used in the study of properties of compact stars.
In her paper, she expressed
these Tolman-Oppenheimer-Volkoff equations in terms of parameters of 4 dimensional spacetime and solved numerically for 4 (n= 1), 5 (n =2), 6 (n =3), and 7 (n = 4) dimensions using a standard equation of state for the neutron star matter derived for the 4 dimensional spacetime.
You can see in above table, it has been shown that with the increase of the dimensionality, the maximum value of the mass of the neutron star decreases and the stars become less compact means 7-D neutron star have mass of just 1.35 compared to 4-D neutron star which has 2.19. While the radius and corresponding central density of the neutron star increases with the increase of the dimensionality. Thus, although the compactness limit decreases with increased dimensionality, neutron stars never violate this limit.
However, it still remains an open question whether low mass neutron stars have just low central density, or they belong to higher dimensions. In principle, if one can measure mass, radius, and gravitational redshift for a neutron star i.e. M, R, z – all three at the same time it would be possible to constrain both the equation of state, central density and the dimension of the spacetime inside that object. This will be an extremely challenging task for observational astronomers, but not impossible by combining timing and spectral analysis of binary pulsars. Where timing analysis of binary pulsars would result in measurements of the mass of the star while the spectral analysis would give the radius (using the value of the mass obtained from timing analysis) and gravitational redshift (if any known spectral line is detected).
References: Manjari Bagchi, “A study of neutron stars in D≥4 dimensions”, ArXiv, pp. 1-8, 2020. arXiv:2010.08928 link: https://arxiv.org/abs/2010.08928
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