14 research outputs found
On the existence of topological hairy black holes in SU(N) EYM theory with a negative cosmological constant
We investigate the existence of black hole solutions of four dimensional su(N) EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically symmetric spacetimes. We prove the existence of non-trivial solutions for any integer N, with N−1 gauge degrees of freedom. Specifically, we prove two results: existence of solutions for fixed values of the initial parameters and as |Λ|→∞, and existence of solutions for any Λ<0 in some neighbourhood of existing trivial solutions. In both cases we can prove the existence of `nodeless' solutions, i.e. such that all gauge field functions have no zeroes; this fact is of interest as we anticipate that some of them may be stable
On the global existence of hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups
We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called 'regular case'. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well researched adS su(N) system. We find the analysis differs from the asymptotically flat case in some important ways:
the biggest difference is that for Λ < 0, solutions are much less constrained as r → ∞, making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the su(N) case proved important to stability
Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black-hole solutions to the stationary Einstein
equations has been steadily increasing, sometimes in unexpected ways. In
particular, it has turned out that not all black-hole-equilibrium
configurations are characterized by their mass, angular momentum and global
charges. Moreover, the high degree of symmetry displayed by vacuum and
electro-vacuum black-hole spacetimes ceases to exist in self-gravitating
non-linear field theories. This text aims to review some developments in the
subject and to discuss them in light of the uniqueness theorem for the
Einstein-Maxwell system.Comment: Major update of the original version by Markus Heusler from 1998.
Piotr T. Chru\'sciel and Jo\~ao Lopes Costa succeeded to this review's
authorship. Significantly restructured and updated all sections; changes are
too numerous to be usefully described here. The number of references
increased from 186 to 32
Classification of non-Riemannian doubled-yet-gauged spacetime
Assuming covariant fields as the `fundamental' variables,
Double Field Theory can accommodate novel geometries where a Riemannian metric
cannot be defined, even locally. Here we present a complete classification of
such non-Riemannian spacetimes in terms of two non-negative integers,
, . Upon these backgrounds, strings become
chiral and anti-chiral over and directions respectively, while
particles and strings are frozen over the directions. In
particular, we identify as Riemannian manifolds, as
non-relativistic spacetime, as Gomis-Ooguri non-relativistic string,
as ultra-relativistic Carroll geometry, and as Siegel's
chiral string. Combined with a covariant Kaluza-Klein ansatz which we further
spell, leads to Newton-Cartan gravity. Alternative to the conventional
string compactifications on small manifolds, non-Riemannian spacetime such as
, may open a new scheme of the dimensional reduction from ten to
four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in
(2.51) correcte