arXiv subjects
Publications and source records attributed to M. S. Volkov.
We study the interior structure of the Einstein-Yang-Mills-Dilaton black holes as a function of the dilaton coupling constant $γ\in [0,1]$. For $γ\neq 0$ the solutions have no internal Cauchy horizons and the field amplitudes follow a power law behavior near the singularity. As $γ$ decreases, the solutions develop more and more oscillation cycles in the interior region, whose number becomes infinite in the limit $γ\to 0$.
We analyze the stability properties of the purely magnetic, static solutions to the Einstein--Yang--Mills equations with cosmological constant. It is shown that all three classes of solutions found in a recent study are unstable under spherical perturbations. Specifically, we argue that the configurations have $n$ unstable modes in each parity sector, where $n$ is the number of nodes of the magnetic Yang--Mills amplitude of the background solution. The ``sphaleron--like'' instabilities (odd parity modes) decouple from the gravitational perturbations. They are obtained from a regular Schrödinger equation after a supersymmetric transformation. The body of the work is devoted to the fluctuations with even parity. The main difficulty arises because the Schwarzschild gauge -- which is usually imposed to eliminate the gravitational perturbations from the Yang--Mills equation -- is not regular for solutions with compact spatial topology. In order to overcome this problem, we derive a gauge invariant formalism by virtue of which the unphysical (gauge) modes can be isolated.
We present a numerical classification of the spherically symmetric, static solutions to the Einstein--Yang--Mills equations with cosmological constant $Λ$. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of $Λ$ and the number of nodes, $n$, of the Yang--Mills amplitude. For sufficiently small, positive values of the cosmological constant, $Λ< \Llow(n)$, the solutions generalize the Bartnik--McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values $Λ_{\rm reg}(n) > Λ_{\rm crit}(n)$, the solutions are topologically $3$--spheres, the ground state $(n=1)$ being the Einstein Universe. In the intermediate region, that is for $\Llow(n) < Λ< \Lhig(n)$, there exists a discrete family of global solutions with horizon and ``finite size''.
It is proven that there are precisely $n$ odd-parity sphaleron-like unstable modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.
An infinite family of cornucopions is found within the $SU(2)\times U(1)$ sector of the 4--d heterotic string low-energy theory, the extremal $U(1)$ magnetic dilatonic black hole being the lowest energy state. Non-abelian cornucopions are interpreted as sphalerons associated with potential barriers separating topologically distinct Yang-Mills vacua on the $U(1)$ cornucopion background. A mass formula for non-abelian dilatonic black holes is derived, and the free energy is calculated through the Euclidean action.