Majumdar-Papapetrou Spacetimes Research Articles

Tidal Forces in Majumdar-Papapetrou Spacetimes

Tidal disruption events occur when astrophysical objects are destroyed by black holes due to strong tidal force effects. Tidal forces have been studied in a variety of black hole spacetimes, including Reissner-Nordström and Kerr spacetimes. Despite the vast literature on the subject, tidal forces around black holes in static equilibrium have never been investigated before. The aim of this work is to fill in this gap and explore tidal forces in the Majumdar-Papapetrou spacetime describing two extremely charged binary black holes in equilibrium. We focus on tidal forces associated with radial and circular geodesics of massive neutral particles moving on the plane equidistant to the black holes. In particular, we study the behavior of the tidal forces as a function of the distance from the black holes and as a function of the energy of the geodesics. We also investigate the numerical solutions of the geodesic deviation equation for different initial conditions.

Energy extraction from non-coalescing black hole binaries

We define and sketch the generalized ergosphere of the Majumdar-Papapetrou (MP) spacetime. In particular, we demonstrate the existence of closed orbits of negative energy that live outside the event horizon of such a spacetime. Relying on the Penrose process mechanism, we use these orbits to illustrate the possibility of energy extraction from a MP binary black hole by particle scattering. We also analyze the efficiency of the process, and construct explicit examples that optimize the extraction of energy. Lastly, we show how such concepts can be extended to a pair of non-coalescing Kerr black holes described by the Cabrera-Munguia, Manko and Ruiz (CMMR) metric.

Stable circular orbits in higher-dimensional multi–black-hole spacetimes

We consider the dynamics of particles, particularly focusing on circular orbits in the higher-dimensional Majumdar-Papapetrou (MP) spacetimes with two equal mass black holes. It is widely known that in the 5D Schwarzschild-Tangherlini and Myers-Perry backgrounds, there are no stable circular orbits. In contrast, we show that in the 5D MP background, stable circular orbits can always exist when the separation of two black holes is large enough. More precisely, for a large separation, stable circular orbits exist from the vicinity of horizons to infinity; for a medium one, they appear only in a certain finite region bounded by the innermost stable circular orbit and the outermost stable circular orbit outside the horizons; for a small one, they do not appear at all. Moreover, we show that in MP spacetimes in more than 5D, they do not exist for any separations.

Transversely trapping surfaces: Dynamical version

Abstract We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill–Lindquist initial data and in the Majumdar–Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality $A_0\le 4\pi (3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [Prog. Theor. Exp. Phys. 2017, 033E01 (2017)] and a static/stationary transversely trapping surface [Prog. Theor. Exp. Phys. 2017, 063E01 (2017)], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions.

Electrogeodesics in the di-hole Majumdar-Papapetrou spacetime

We investigate the (electro-)geodesic structure of the Majumdar-Papapetrou solution representing static charged black holes in equilibrium. We assume only two point sources, thus imparting spacetime axial symmetry. We study electrogeodesics both on and off the equatorial plane and explore the stability of circular trajectories via the geodesic deviation equation. In contrast to the classical Newtonian situation, we find regions of spacetime admitting two different angular frequencies for a given radius of the circular electrogeodesic. We look both at the weak- and near-field limits of the solution. We use analytic as well as numerical methods in our approach.

Particle acceleration by Majumdar–Papapetrou di-hole

We explore the multi-black hole spacetimes from the perspective of the ultra-high energy particle collisions. Such a discussion is limited to the spacetimes containing a single black hole so far. We deal with the Majumdar–Papapetrou solution representing a system consisting of two identical black holes in the equilibrium. In order to identify the conditions suitable for the process of high energy collisions, we consider particles confined to move on the equatorial plane towards the axis of symmetry with the zero angular momentum. We consider collision between the particles moving in opposite directions at the location midway between the black holes on the axis. We show that the center of mass energy of collision between the particles increases with the decrease in the separation between the black holes and shows divergence in the limit where the separation goes to zero. We estimate the size of the region close to the central point on the equatorial plane where it would be possible to have high energy collisions and show that this region has a reasonably large spatial extent. We further explore the process of high energy collisions with the general geodesics with arbitrary angular momentum on the equatorial plane away from the central point. Although in this paper we deal with the Majumdar–Papapetrou spacetime which serves as a toy example representing multiple black holes, we speculate on the possibility that the ultra-high energy collisions would also occur in the more general setting like colliding black holes, when distance between the black holes is extremely small, which can in principle be verified in the numerical relativity simulations.

Anomaly and the self-energy of electric charges

We study the self energy of a charged particle located in a static D-dimensional gravitational field. We show that the energy functional for this problem is invariant under an infinite dimensional (gauge) group of transformations parameterized by one scalar function of (D-1)-variables. We demonstrate that the problem of the calculation of the self energy for a pointlike charge is equivalent to the calculation of the fluctuations $<\psi^2>$ for an effective (D-1)-dimensional Euclidean quantum field theory. Using point-splitting regularization we obtain an expression for the self energy and show, that it possesses anomalies. Explicit calculation of the self energy and its anomaly is done for the higher dimensional Majumdar-Papapetrou spacetimes.

Self-energy of a scalar charge near higher-dimensional black holes

We study the problem of self-energy of charges in higher-dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher-dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires nonzero value in odd-dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin of the conformal anomalies in quantum field theory in even-dimensional spacetimes.

Scalar and electromagnetic fields of static sources in higher dimensional Majumdar-Papapetrou spacetimes

We study massless scalar and electromagnetic fields from static sources in a static higher-dimensional spacetime. Exact expressions for static Green's functions for such problems are obtained in the background of the Majumdar-Papapetrou solutions of the Einstein-Maxwell equations. Using this result, we calculate the force between two scalar or electric charges in the presence of one or several extremally charged black holes in equilibrium in the higher-dimensional spacetime.

Relativistic Euler’s three-body problem, optical geometry, and the golden ratio

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the ${\mathbb{Z}}_{2}$ invariant solution, with Arnowitt-Deser-Misner mass ${M}_{\mathrm{ADM}}=2{M}_{\mathrm{K}}$, where ${M}_{\mathrm{K}}$ is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic submanifold. The existence and radii of circular photon orbits in this submanifold are studied, as functions of the distance $2L$ between the two black holes. For $L\ensuremath{\rightarrow}0$ there are two such orbits, corresponding to $r=3{M}_{\mathrm{ADM}}$ and $r=2{M}_{\mathrm{ADM}}$ in Schwarzschild coordinates. As the distance increases, it is shown that the two photon orbits approach one another and merge when ${M}_{\mathrm{K}}=\ensuremath{\varphi}L$, where $\ensuremath{\varphi}$ is the golden ratio. Beyond this distance there exist no circular photon orbits. The two null orbits delimit a forbidden band for timelike circular orbits, which is interpreted in terms of optical geometry. For large $L$, timelike circular orbits are allowed everywhere, as in the analogous Newtonian problem. The analysis is generalized by considering a ${\mathbb{Z}}_{2}$ invariant Weyl solution with an array of $N$ black holes and also by charging the black holes, which connects the Weyl solution to a Majumdar-Papapetrou spacetime.

Publisher’s Note: Multishell model for Majumdar-Papapetrou spacetimes [Phys. Rev. D72, 024032 (2005)

Exact solutions to static and non-static Einstein-Maxwell equations in the presence of extremely charged dust embedded on thin shells are constructed. Singularities of multi-black hole Majumdar-Papapetrou and Kastor-Trashen solutions are removed by placing the matter on thin shells. Double spherical thin shell solution is given as an illustration and the matter densitiies on the shells are derived.

Multishell model for Majumdar-Papapetrou spacetimes

Exact solutions to static and nonstatic Einstein-Maxwell equations in the presence of extremely charged dust embedded on thin shells are constructed. Singularities of multi-black-hole Majumdar- Papapetrou and Kastor-Traschen solutions are removed by placing the matter on thin shells. Double spherical thin shell solution is given as an illustration and the matter densities on the shells are derived.

Construction of Sources for Majumdar-Papapetrou Spacetimes

We study Majumdar-Papapetrou solutions for the 3+1 Einstein-Maxwell equations, with charged dust acting as the external source for the fields. The spherically symmetric solution of G\"{u}rses is considered in detail. We introduce new parameters that simplify the construction of class $C^1$, singularity-free geometries. The arising sources are bounded or unbounded, and the redshift of light signals allows an observer at spatial infinity to distinguish these cases. We find out an interesting affinity between the conformastatic metric and some homothetic, matter and Ricci collineations. The associated non-Noetherian symmetries provide us with distinctive solutions that can be used to construct non-singular sources for Majumdar-Papapetrou spacetimes.}

Sources for the Majumdar-Papapetrou space-times

Einstein's field equations are solved exactly for static charged dust distributions. These solutions generalize the Majumdar-Papapetrou metrics. Maxwell's equations lead to the equality of charge and mass densities of the dust distrubition. Einstein's equations reduce to a nonlinear version of Poisson's equation.

Traversable Wormholes in Geometries of Charged Shells.

We construct a static axisymmetric wormhole from the gravitational field of two charged shells which are kept in equilibrium by their electromagnetic repulsion. For large separations the exterior tends to the Majumdar-Papapetrou spacetime of two charged particles. The interior of the wormhole is a Reissner-Nordstr\"om black hole matching to the two shells. The wormhole is traversable and connects to the same asymptotics without violation of energy conditions. However, every point in the Majumdar-Papapetrou region lies on a closed timelike curve.

Horizon instability of extremal black holes

We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This result holds in particular for extremal Kerr-Newman and Majumdar-Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon.