Relativistic star solutions in higher-dimensional pseudospheroidal space-time

Abstract

We obtain relativistic solutions of a class of compact stars in hydrostatic equilibrium in higher dimensions by assuming a pseudospheroidal geometry for the spacetime. The space-time geometry is assumed to be (D − 1) pseudospheroid immersed in a D-dimensional Euclidean space. The spheroidicity parameter (λ) plays an important role in determining the equation of state of the matter content and the maximum radius of such stars. It is found that the core density of compact objects is approximately proportional to the square of the space-time dimensions (D), i.e., core of the star is denser in higher dimensions than that in conventional four dimensions. The central density of a compact star is also found to depend on the parameter λ. One obtains a physically interesting solution satisfying the acoustic condition when λ lies in the range λ > (D + 1)/(D − 3) for the space-time dimensions ranging from D = 4 to 8 and (D + 1)/(D − 3) < λ < (D 2 − 4D + 3)/(D 2 − 8D − 1) for space-time dimensions ≥9. The non-negativity of the energy density (ρ) constrains the parameter with a lower limit (λ > 1). We note that in the case of a superdense compact object the number of space-time dimensions cannot be taken infinitely large, which is a different result from the braneworld model.

Possibility of higher-dimensional anisotropic compact star

“…However, in the literature there is some evidence available in favor of extra dimensions in compact stars [45][46][47][48][49][50].…”

Compact stars on pseudo-spheroidal spacetime compatible with observational data

“…Further, the red shift at the centre z c and on the boundary z R are both positive and finite. (2011); Chattopadhyay and Paul (2010); Chattopadhyay et al (2012). In this paper, we have obtained a new class of solutions to Einstein's field equations for a spherically symmetric anisotropic distribution of matter and have shown that our model can fit to the observational data of a number of well studied pulsars ( Gangopadhyay et al (2013)).…”

“…);Tikekar (1999);Tikekar and Thomas (2005);Thomas et al (2005);Thomas and Ratanpal (2007);Paul et al (2011);Chattopadhyay and Paul (2010);Chattopadhyay et al (2012)). …”

A new class of solutions of anisotropic charged distributions on pseudo-spheroidal spacetime

“…This spacetime, known as pseudo-spheroidal spacetime, has been studied by number of researchers Tikekar and Thomas (1998, 1999; Thomas et al (2005); Thomas and Ratanpal (2007);Paul et al (2011);Paul and Chattopadhyay (2010); Chattopadhyay and Paul (2012) have found that it can accommodate compact superdense stars.…”