Bonnor stars in d spacetime dimensions

Abstract

Bonnor stars are regular static compact configurations in equilibrium, composed of an extremal dust fluid, a charged dust fluid where the mass density is equal to the charge density, joined to an exterior vacuum solution, within Newtonian gravity and general relativity. In four dimensions, they obey the corresponding Majumdar-Papapetrou system, where the gravitational potential is a simple function of the electric potential field and the fluid, when there is one, is made of extremal dust. The Majumdar-Papapetrou system can be generalized to d spacetime dimensions. Thus, it is natural to study Bonnor solutions in higher d dimensions. We analyze Newton-Coulomb theory with an electrically charged fluid in a Majumdar-Papapetrou context, in d=n+1 spacetime dimensions, n the number of spatial dimensions. Within the Newtonian theory, in vacuum, the Majumdar-Papapetrou relation for the gravitational potential in terms of the electric potential, and its related Weyl relation, are equivalent, in contrast with general relativity. We study a class of spherically symmetric Bonnor stars. Under sufficient compactification they form point mass charged Newtonian singularities. We study the analogue systems in the Einstein-Maxwell theory with an electrically charged fluid. We restate some properties of this system and obtain spherically symmetric Bonnor star solutions in d=n+1 spacetime dimensions. These stars, under compactification, form quasi-black holes. Whereas there are no solutions for Newtonian or relativistic stars supported by degenerate pressure in higher dimensions, higher dimensional Bonnor stars, supported by electric repulsion, do indeed have solutions within Newtonian gravity and general relativity. So the existence of stars depends on the number of dimensions and on the underlying field content.

48 pages, 5 figues, references added, minor changes

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