Reissner-Nordstrom Spacetime Research Articles

Slowly rotating charged fluid balls and their matching to an exterior domain

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordstrom space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by Garcia. The Garcia solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter C_{2}, characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant C_{2} for the Garcia solution. We conjecture that the Garcia metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.

Charged solutions in 5D Chern-Simons supergravity

A family of solutions with mass and electric charge of five-dimensional Chern-Simons supergravity is displayed. The action contains an extra term that changes the value of the cosmological constant, as considered by Horava. It is shown that the solutions approach asymptotically the Reissner-Nordstrom spacetime. The role of the torsion tensor in providing charged solutions is stressed.

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.

Low-energy sector quantization of a massless scalar field outside a Reissner-Nordström black hole and static sources

We quantize the low-energy sector of a massless scalar field in the Reissner-Nordstrom spacetime. This allows the analysis of processes involving soft scalar particles occurring outside charged black holes. In particular, we compute the response of a static scalar source interacting with Hawking radiation using the Unruh (and the Hartle-Hawking) vacuum. This response is compared with the one obtained when the source is uniformly accelerated in the usual vacuum of the Minkowski spacetime with the same proper acceleration. We show that both responses are in general different in opposition to the result obtained when the Reissner-Nordstrom black hole is replaced by a Schwarzschild one. The conceptual relevance of this result is commented.

Spinning Particles in Reissner–Nordstrom Spacetime

We study pseudo-classical spinning particles in the spacetime of the Reissner–Nordstrom black hole. We derive the constants and the equations of motion and investigate bound state orbits in a plane.

The total space-time of a point charge and its consequences for black holes

Singularities associated with an incomplete space-timeS are not uniquely defined until a boundaryB is attached to it. [The resulting space-time-with-boundary, ¯S ≡S ∪B, will be termed a ‘total’ space-time (TST).] Since an incomplete spacetime is compatible with a variety of boundaries, it follows thatS does not represent a unique universe, but instead corresponds to a family of universes, one for each of its distinct TSTs. It is shown here that the boundary attached to the Reissner-Nordstrom space-time for a point charge is invalid forq 2<m 2. When the correct boundary is used, the resulting TST is inextendible. This implies that the Graves-Brill black hole cannot be produced by gravitational collapse. The same is true of the Kruskal-Fronsdal black hole for the point mass, and for those black holes which reduce to the latter for special values of their parameters.

The Lynden-Bell and Katz definition of gravitational energy: Applications to singular solutions

We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and spherically symmetric space-times which admit a curvature singularity. These are the Tolman V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th of the gravitational radius. We show that the LK definition can still be applied to these solutions despite the presence of a singularity which nonetheless appears to carry no energy in the LK sense. While in the solutions that we mentioned the KL gravitational energy is positive definite everywhere in space time, this is not the case for the overcharged Reissner-Nordstrom space-time. In the latter case in fact the LK energy density becomes negative sufficiently close to the singularity hence we use the positivity criterion to impose a more stringent limit of validity to the Reissner-Nordstrom solution.

What have we learned from two-dimensional models of quantum black holes?

The two-dimensional black hole provides a theoretical laboratory in which the quantum nature of black holes may be probed without the complications of four-dimensional dynamics. It is therefore natural to ask, what have we learned from this model? Much recent work has focused on the semi-classical limit where the black hole is similar to the Schwarzschild solution. However, in this essay, we demonstrate that theexact two-dimensional quantum black hole is non-singular. Instead the singularity is replaced by a surface of time reflection symmetry in an extended space-time. The maximally extended space-time thus consists of an infinite sequence of asymptotically flat regions connected by timelike wormholes, rather analogous to the Reissner-Nordstrom space-time. The implications of this to the apparent loss of quantum information arising from black hole evaporation are also briefly discussed.

Nonsingular Lagrangians for two-dimensional black holes.

We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is possible that quantum deformations of these extremal solutions are the endpoint of Hawking evaporation when the models are coupled to matter, and that the resulting evolution may be studied entirely within the framework of the semiclassical approximation. Numerical work to verify this conjecture is in progress. We point out however that the solutions with non-negative mass always contain Cauchy horizons, and may be sensitive to small perturbations.

An orifice-string in the standard Kaluza-Klein theory

In the standard Kaluza-Klein theory an orifice solution is proposed which can be spliced into a four-dimensional Reissner-Nordstrom space-time. From the point of view of a four-dimensional observer, the obtained orifice solution can be treated as a string moving in a Wheeler superspace of four geometries.

Testing a stability conjecture for Cauchy horizons.

A stability conjecture previously developed to investigate quasiregular and nonscalar curvature singularities is extended here to cover the stability of Cauchy horizons. In particular, the Reissner-Nordstrom spacetime of charged, nonrotating black holes is considered. The conjecture predicts that the addition of infalling null dust with a power-law tail will produce a nonscalar curvature singularity at the Cauchy horizon. This prediction is verified using a Reissner-Nordstrom-Vaidya spacetime studied by Hiscock. The conjecture also predicts that a combination of infalling and outgoing null dust will produce a scalar curvature singularity at the Cauchy horizon. This prediction is verified using the mass inflation results of Poisson and Israel

The instability of the Kerr-like Cauchy horizons

A theorem is proved which shows that under a certain condition called the strong null convergence condition the topological structure of the Cauchy horizons of the type occurring in the Reissner-Nordstrom and Kerr space-times will have to change. This result together with an earlier argument due to Tipler shows that such horizons are unstable.

Quasilocal mass for event horizons

The Dougan-Mason quasilocal mass (1991) is calculated as a function of the angular momentum on a cross section of the event horizon in a Kerr spacetime. The result is compared with results for the quasilocal masses defined by Komar (1959), Hawking (1968), Penrose (1982), Ludvigsen-Vickers (1983), Bergqvist-Ludvigsen (1991), and Kulkarni-Chellathurai-Dadhich (1988). The same study is also made for spheres in a Reissner-Nordstrom spacetime. It is shown that no definition is equivalent to any other in both these situations, and this might be because of difficulties in defining mass in general relativity at the quasilocal level.

Speed of a freely falling particle in Reissner-Nordstrom spacetime

The speed of a particle freely falling in Reissner-Nordstrom spacetime as measured by an observer at spatial infinity is investigated which reveals some curious aspects of the spacetime.

Spin precession of a charged particle in Reissner-Nordstrom spacetime

The spin precession frequency of a charged particle confined to the equatorial plane in a circular orbit in Reissner-Nordstrom spacetime as a function of radial distance from the central object is investigated. In order to see the difference in behaviour for particles with different e/m 0 and g values we consider the case of electron and proton separately. The spin precession frequency in the flat space limit puts a lower bound to Landé's g value.

Glueing Reissner-Nordstrom spacetimes along charged shells of matter

The authors generalise the results of Dray and 't Hooft (1986) by showing how to join two or more Reissner-Nordstrom spacetimes with different charges and masses along null cylinders representing charged shells of massless matter. Conservation laws are then used to give a rigorous definition of the charge and energy of the shells. They point out that their results are not confined to general relativity but that there is also a special relativistic analogue of a collapsing charged shell.

On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordstrom space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.

Curvature, causality and completeness in space-times with causally complete spacelike slices

Let S be a spacelike slice (defined formally in Section 2) in a space-time M. We will say that S is future causally complete in M if for each p ε J+(S) the closure in S of the set J-(p) ∩ S is compact. Define past causal completeness time-dually. Then S is causally complete if it is both future and past causally complete. A compact spacelike slice is necessarily causally complete, as is any Cauchy surface, but the concept of causal completeness is much broader than either of these two conditions. For example the slices t = const. ≠ 0 in the space-time obtained by removing the origin from Minkowski space are causally complete, although they are neither Cauchy nor compact. The slice t = 0 in the previous example and the hyperboloid in Minkowski space (where (t, x1, …, xn) are standard inertial coordinates) are examples of slices which are not causally complete. Physically speaking, an edgeless slice S is future causally complete if the information from S which reaches a point in the future of S comes from a finite nonsingular region in S. The Maximal Reissner-Nordstrom space-time is a well-known example in which this finiteness condition is not fulfilled by any of its asymptotically flat partial Cauchy surfaces. Indeed for any such partial Cauchy surface S, J-(p) ∩ S is non-compact for any p ε H+(S). However, as has been discussed in the literature (e.g. [17], p. 625 f), it is believed that the Cauchy horizon in this situation is unstable with respect to perturbations of the initial data on S.

Self-interaction and massive vector field in the Schwarzschild space-time

Using a multipole expansion, we determine formally the massive vector field generated by a point source held fixed in the Schwarzschild space-time. We prove that its limit, when the mass of the Proca field goes to zero, does not tend to the corresponding massless vector field. In this limit we evaluate the expression of the self-force acting on the particle. The result is in accordance with that of Vilenkin, without the assumption that the point source is at a large distance from the horizon, that we extend to the case of a Reissner-Nordstrom space-time. We also investigate a further case: a point source within a spherical shell of matter for which the Proca field tends to the corresponding massless vector field.

Vacuum polarization in Reissner Nordstrom spacetime

In this letter, the vacuum energy momentum tensor of a massive scalar field in Reissner Nordstrom spacetime is calculated.