Construction of Sources for Majumdar-Papapetrou Spacetimes

Varela, Víctor

doi:10.1023/a:1026014114308

Cited by 21 publications

(30 citation statements)

References 32 publications

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“…A different development was taken by Das [41], who relying on the work of Majumdar [37], put dust particles on the point particles positions, evading the black hole horizons. Several other authors have further analyzed the properties of Majumdar-Papapetrou systems [42,43,44,45,46,47]. Bonnor and collaborators [48,49,50,51,52] in a series of papers have shown and studied important new solutions of Majumdar-Papapetrou equations and properties of the system.…”

Section: Introductionmentioning

confidence: 99%

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

Lemos

Zanchin

2006

Journal of Mathematical Physics

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During the 1990s a large amount of work was dedicated to studying general relativity coupled to non-Abelian Yang-Mills type theories. Several remarkable results were accomplished. In particular, it was shown that the magnetic monopole, a solution of the Yang-Mills-Higgs equations can indeed be coupled to gravitation. For a low Higgs mass it was found that there are regular monopole solutions, and that for a sufficiently massive monopole the system develops an extremal magnetic Reissner-Nordström quasi-horizon with all the matter fields laying inside the horizon. These latter solutions, called quasi-black holes, although non-singular, are arbitrarily close to having a horizon, and for an external observer it becomes increasingly difficult distinguish these from a true black hole as a critical solution is approached. However, at precisely the critical value the quasi-black hole turns into a degenerate spacetime. On the other hand, for a high Higgs mass, a sufficiently massive monopole develops also a quasi-black hole, but at a critical value it turns into an extremal true horizon, now with matter fields showing up outside. One can also put a small Schwarzschild black hole inside the magnetic monopole, the configuration being an example of a non-Abelian black hole. Surprisingly, Majumdar-Papapetrou systems, Abelian systems constructed from extremal dust (pressureless matter with equal charge and energy densities), also show a resembling behavior. Previously, we have reported that one can find Majumdar-Papapetrou solutions which are everywhere nonsingular, but can be arbitrarily close of being a black hole, displaying the same quasi-black hole behavior found in the gravitational magnetic monopole solutions. With the aim of better understanding the similarities between gravitational magnetic monopoles and MajumdarPapapetrou systems, here we study a particular system, namely a system composed of two extremal electrically charged spherical shells (or stars, generically) in the Einstein−Maxwell−MajumdarPapapetrou theory. We first review the gravitational properties of the magnetic monopoles, and then compare with the gravitational properties of the double extremal electric shell system. These quasi-black hole solutions can help in the understanding of true black holes, and can give some insight into the nature of the entropy of black holes in the form of entanglement.

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Section: Introductionmentioning

confidence: 99%

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

Lemos

Zanchin

2006

Journal of Mathematical Physics

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“…Helmholtz type equation which can be solved, in the case the pressure is zero see also [45]. These are thus extensions of Bonnor stars, stars that include charged matter, non-extremal, and pressure.…”

Section: Further Connectionsmentioning

confidence: 99%

Bonnor stars indspacetime dimensions

Lemos¹,

Zanchin

2008

Phys. Rev. D

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Bonnor stars are regular static compact configurations in equilibrium, composed of an extremal dust fluid, i.e., a charged dust fluid where the mass density is equal to the charge density in appropriate units and up to a sign, joined to a suitable exterior vacuum solution, both within Newtonian gravity and general relativity.In four dimensions, these configurations obey the Majumdar-Papapetrou system of equations, in one case, the system is a particular setup of Newtonian gravity coupled to Coulomb electricity and electrically charged matter or fluid, in the other case, the system is a particular setup of general relativity coupled to Maxwell electromagnetism and electrically charged matter or fluid, where the corresponding gravitational potential is a specially simple function of the electric potential field and the fluid, when there is one, is made of extremal dust. Since the Majumdar-Papapetrou system can be generalized to d spacetime dimensions, as has been previously done, and higher dimensional scenarios can be important in gravitational physics, it is natural to study this type of Bonnor solutions in higher dimensions, d ≥ 4. As a preparation, we analyze Newton-Coulomb theory with an electrically charged fluid in a Majumdar-Papapetrou context, in d = n + 1 spacetime dimensions, with n being the number of spatial dimensions. We show that 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 where they are distinct. We study a class of spherically symmetric Bonnor stars within this theory. Under sufficient compactification they form point mass charged Newtonian singularities. We then study the analogue type systems in the Einstein-Maxwell theory with an electrically charged fluid. Drawing on our previous work on the d-dimensional Majumdar-Papapetrou system, we restate some properties of this system. We obtain spherically symmetric Bonnor star solutions in d = n + 1 spacetime dimensions. We show that these stars, under sufficient compactification, form d-dimensional quasi-black holes. We also show that in the appropriate low gravity limit theses solutions turn into the solutions of Newtonian gravity, i.e., they are quasi-Newtonian Bonnor stars. In this connection, we note that the star solutions in Majumdar-Papapetrou Newtonian gravity, when contrasted to those solutions in Majumdar-Papapetrou general relativity, display clearly the branching off of the high density objects that may arise in the strong field regime of each theory, mild singularities in one theory, quasi-black holes in the other. Another important feature worth of mention is that, 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 in h...

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“…Our previous contribution [1] was devoted to the study of static charged dust solutions of the Einstein-Maxwell equations. The derivation of the solutions was based on three main assumptions: (i) the spacetime metric has the conformastatic form…”

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confidence: 99%

“…The extension of the Majumdar-type class of solutions to include static charged perfect fluid sources is easily achieved using a modified version of the charged dust procedure outlined in [1]. In this case the conformastatic metric (1) is assumed again, but h ij is allowed to have non-vanishing Riemannian curvature.…”

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Neutral perfect fluids of Majumdar-type in general relativity

Varela

2005

Gen Relativ Gravit

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We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations, proposed by Ida to include charged perfect fluid sources. We impose the equation of state ρ + 3p = 0 and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges Q and −Q. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.Our previous contribution [1] was devoted to the study of static charged dust solutions of the Einstein-Maxwell equations. The derivation of the solutions was based on three main assumptions: (i) the spacetime metric has the conformastatic formwhere Latin indices indicate 1, 2, 3; (ii) the background three-dimensional metric h ij is Euclidean; (iii) h ij and V depend only on the space-like coordinates x 1 , x 2 , x 3 . As a consequence, the corresponding static solutions of the Einstein-Maxwell-charged dust equations satisfied a linear relation between V and the Coulombian potential A 0 . We will refer to solutions of the field equations with such a linear relationship as being of

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Construction of Sources for Majumdar-Papapetrou Spacetimes

Cited by 21 publications

References 32 publications

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

Gravitational magnetic monopoles and Majumdar-Papapetrou stars

Bonnor stars indspacetime dimensions

Neutral perfect fluids of Majumdar-type in general relativity

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