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Register a new userA combined Majumdar-Papapetrou-Bonnor field as extreme limit of the double-Reissner-Nordstrom solution
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The general extreme limit of the double-Reissner-Nordstrom solution is worked out in explicit analytical form involving prolate spheroidal coordinates. We name it the combined Majumdar-Papapetrou-Bonnor field to underline the fact that it contains as particular cases the two-body specialization of the well-known Majumdar-Papapetrou solution and Bonnors three-parameter electrostatic field. To the latter we give a precise physical interpretation as describing a pair of non-rotating extremal black holes with unequal masses and unequal opposite charges kept apart by a strut, the absolute values of charges exceeding the respective (positive) values of masses.
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The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanced transformation. Moreover a new analytical exact solution is built adding the NUT charge to a double charged black hole, at equilibrium. It describes the non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the near-horizon analysis, its microscopic entropy, according to the Kerr/CFT correspondence, is found and the second law of black hole thermodynamics is discussed.
We investigate the positions of stable circular massive particle orbits in the Majumdar--Papapetrou dihole spacetime with equal mass. In terms of qualitative differences of their sequences, we classify the dihole separation into five ranges and find four critical values as the boundaries. When the separation is relatively large, the sequence on the symmetric plane bifurcates, and furthermore, they extend to each innermost stable circular orbit in the vicinity of each black hole. In a certain separation range, the sequence on the symmetric plane separates into two parts. On the basis of this phenomenon, we discuss the formation of double accretion disks with a common center. Finally, we clarify the dependence of the radii of marginally stable circular orbits and innermost stable circular orbits on the separation parameter. We find a discontinuous transition of the innermost stable circular orbit radius. We also find the separation range at which the radius of the innermost stable circular orbit can be smaller than that of the stable circular photon orbit.
The maximally extended Reissner--Nordstrom (RN) manifold with $e^2 < m^2$ begs for attaching a material source to it that would preserve the infinite chain of asymptotically flat regions and evolve through the wormhole between the RN singularities. So far, the attempts were discouraging. Here we try one more possible source -- a solution found by Ruban in 1972 that is a charged generalisation of an inhomogeneous Kantowski--Sachs-type dust solution. It can be matched to the RN solution, and the matching surface must stay all the time between the two RN event horizons. However, shell crossings do not allow even half a cycle of oscillation between the maximal and the minimal size.
We start from a static, spherically symmetric space-time in the presence of an electrostatic field and construct the mini-superspace Lagrangian that reproduces the well known Reissner - Nordstrom solution. We identify the classical integrals of motion that are to be mapped to quantum observables and which are associated with the mass and charge. Their eigenvalue equations are used as supplementary conditions to the Wheeler-DeWitt equation and a link is provided between the existence of an horizon and to whether the spectrum of the observables is fully discrete or not. For each case we provide an orthonormal basis of states as emerges through the process of canonical quantization.
We study black holes produced by the collapse of a spherically symmetric charged scalar field in asymptotically flat space. We employ a late time expansion and show decaying fluxes of radiation through the event horizon imply the black hole must contain a null singularity on the Cauchy horizon and a central spacelike singularity.
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