Static spherically symmetric solutions to Einstein-Maxwell dilaton field equations in D dimensions (original) (raw)

Class of Einstein-Maxwell dilatons, an ansatz for new families of rotating solutions

Classical and Quantum Gravity, 2000

The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a "Hamiltonian"is obtained, which allows to rewrite the dynamical equations in terms of three complex functions only. Using an ansatz resembling the one used by the harmonic maps ansatz, we express these three functions in terms of the harmonic parameters, studying the cases where these parameters are real, and when they are complex. For each case, the set of equations in terms of these harmonic parameters is derived, and several classes of solutions to the Einstein-Maxwell with arbitrary coupling constant to a dilaton field are presented. Most of the known solutions of charged and dilatonic black holes are contained as special cases and can be non-trivially generalized in different ways.

Spherically Symmetric Solutions in Higher-Derivative Gravity

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type 'no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to 'vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as 'wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.

On static spherical symmetric solutions of the Bach-Einstein gravitational field equations

Astronomische Nachrichten: A Journal on all Fields of Astronomy, 1985

For field equations of 4th order, following from a Lagrangian "Ricci scalar plus Weyl scalar", it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = 0 and r = ∞ resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme. Für die Feldgleichungen 4. Ordnung, die aus einem Lagrangeausdruck "Ricci-Skalar plus Weyl-Skalar" folgen, wird unter Zuhilfenahme von Methoden der Nicht-Standard-Analysis gezeigt, daß in einer Umgebung des Minkowskiraumes keine statischen kugelsymmetrischen Lösungen existieren. Damit wird erstmals neben den bekannten lokalen Entwicklungen um r = 0 und r = ∞ eine globale Aussageüber die Existenz solcher Lösungen getroffen. Anschließend wird dies Ergebnis im Zusammenhang mit Einstein's Teilchenprogramm diskutiert.

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

General Relativity and Gravitation, 2005

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.

On Spherically Symmetric Solutions of the Einstein-Maxwell Field Equations

General Letters in Mathematics

In literature many solution of Einstein-Maxwell's equations have been found. We consider the spherically symmetric geometry and classify the solutions of Einstein-Maxwell's equations by considering the null/non-null electromagnetic field and isotropic/anisotropic matter with the help of Segre type of spherical symmetric spacetime.

Spherically symmetric solutions of Einstein + non-polynomial gravities

General Relativity and Gravitation, 2008

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.