The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison

We review recent results concerning the spherically symmetric Einstein-scalar field system with positive cosmological constant. We do so by comparing with the classical results of Christodoulou concerning the asymptotically flat case (vanishing cosmological constant) and by discussing some of the issues which have emerged since the publication of our main results. Concerning the positive cosmological constant case, we also sketch an alternative proof of global in (Bondi) time existence, based on energy estimates, which is presumably more flexible and, consequently, amenable to generalizations; other potential improvements and generalizations of our main results are also discussed.     

The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant

We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored.The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity.We investigate several conceptual and technical details that might be of interest for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar, which simplifies the analysis tremendously.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.     

The character of an anisotropic and spherically symmetric star in the presence of a cosmological constant

From the gravitational structure equations of an anisotropic and spherically symmetric star in the presence of a cosmological constant, we derive the inequality which limits the mass-radius ratio, imposing energy conditions on the matter, From this inequality, we display how the cosmological constant modifies the Buchdahl limit, and express the bounds on both the mass-radius ratio and surface redshiR in terms of the ratio between the cosmological constant and mean energy density of the star.     

Higher dimensional spherically symmetric inhomogeneous cosmological model with heat flow

We study spherically symmetric inhomogeneous cosmological model with heat flow in higher dimensional space-time and present a class of solutions in which the velocity field is shear-free. Some of these solutions are analogous to the known solutions in 4-dimension while some are totally new.     

A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.     

Higher-dimensional Florides-like solution with cosmological constant

N-dimensional generalization of Florides' interior solution with cosmological constant and Kotller's exterior solution are presented here. The case of uniform density configuration is also considered. One can get back the solutions in four-dimensional space-time by puttingN=4 in the solutions presented here.     

Vaidya's spherically symmetric radiating solution

Conclusions An analysis of Vaidya's solution has shown that it cannot describe electromagnetic radiation in a gravitational field: the Einstein-Maxwell equations for this solution are incompatible.The neutrino treatment of this solution is somewhat dubious.An investigation using the Rodichev energy tensor and Petrov's classification indicates that there is also no gravitational radiation in this solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 130–132, November, 1971.In conclusion the authors wish to thank V. I. Rodichev for valuable discussions of this work.     

Algebraically special vacuum gravitational fields with a cosmological constant

A general view is given of the Petrov type II metric with a cosmological constant to an accuracy of two complex functions of three variables which are related by four differential equations. As a consequence the form of the metric is obtained for types III and N which are specified by one complex function satisfying three differential equations. A particular solution is given as an example of an accurate solution of type II with a cosmological constant. State University, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 102–108, June, 1996.     

General solution of the spherically symmetric Yang-Mills equations

A general solution of the spherically symmetric Yang-Mills equations is presented.     

A spherically symmetric solution of the Maxwell-Einstein equations

A spherically symmetric solution of the already unified field theory ofRainich (i.e. of the source-free Maxwell-Einstein equations) is presented which represents a static massless charged particle. It is not equivalent to the Reissner-Nordström solution with zero mass, although both metrics repel uncharged test particles.On leave of absence from the Department of Mathematics, The University, Bristol.     

New solution of the cosmological constant problems

We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) to a field which can take many possible values. Variation gives a new integral constraint equation for the classical value of the effective CC that dominates the wave function of the Universe. The expected value of the effective CC, is calculated from measurable quantities to be O(t(U)(-2)) as observed, where t(U) is the present age of the Universe in Planck units. This also leads to a falsifiable prediction for the observed spatial curvature parameter of Ω(k0) = -0.0055. Our proposal requires no fine-tunings or extra dark-energy fields but suggests a new view of time evolution.     

Charged spherically symmetric solution in Mikhail-Wanas field theory

A set of coupled differential equations obtained by Wanas in the Mikhail-Wanas generalized field theory is completely integrated.     

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.     

Signature change, vacuum condensation and cosmological constant

We proposes an alternative model of duality symmetry, based on the previously obtained divergence theory, including an scalar field, an internal vector and a metric signature. At some small scale an effective scalar field equation has appeared whose potential acts like a Higgs one, where the metric signature plays the role of an order parameter. Non-vanishing Vacuum condensation of this Higgs field occurs once a signature change from Euclidean to Lorentzian is formed. The mass scale of Higgs field excitations around this vacuum may contribute, in the Lorentzian sector, to the cosmological constant, in agreement with observations.     

Topological defect solutions in the spherically symmetric space-time admitting conformal motion

In this paper, we have examined strings with monopole and electric field and domain walls with matter and electric field in the spherically symmetric space-time admitting a one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for a spherically symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.