Relativistic star solutions in higher-dimensional pseudospheroidal space-time

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 (lambda) 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 lambda. One obtains a physically interesting solution satisfying the acoustic condition when lambda lies in the range lambda > (D + 1)/(D - 3) for the space-time dimensions ranging from D = 4 to 8 and (D + 1)/(D - 3) < lambda < (D (2) - 4D + 3)/(D (2) - 8D - 1) for space-time dimensions a parts per thousand yen9. The non-negativity of the energy density (rho) constrains the parameter with a lower limit (lambda > 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.