11,732 research outputs found
Energy in ghost-free massive gravity theory
The detailed calculations of the energy in the ghost-free massive gravity
theory is presented. The energy is defined in the standard way within the
canonical approach, but to evaluate it requires resolving the Hamiltonian
constraints, which are known, in general, only implicitly. Fortunately, the
constraints can be explicitly obtained and resolved in the spherically
symmetric sector, which allows one to evaluate the energy. It turns out that
the energy is positive for globally regular and asymptotically flat fields
constituting the "physical sector" of the theory. In other cases the energy can
be negative and even unbounded from below, which suggests that the theory could
be still plagued with ghost instability. However, a detailed inspection reveals
that the corresponding solutions of the constraints are either not globally
regular or not asymptotically flat. Such solutions cannot describe initial data
triggering ghost instability of the physical sector. This allows one to
conjecture that the physical sector could actually be protected from the
instability by a potential barrier separating it from negative energy states.Comment: 35 pages, minor improvements, an appendix adde
On the instabilities of the static, spherically symmetric SU(2) Einstein-Yang-Mills-Dilaton solitons and black holes
We prove that the number of odd parity instabilities of the n-th SU(2)
Einstein-Yang-Mills-Dilaton soliton and black hole equals n.Comment: Added reference
De Sitter vacua in ghost-free massive gravity theory
We present a simple procedure to obtain all de Sitter solutions in the
ghost-free massive gravity theory by using the Gordon ansatz. For these
solutions the physical metric can be conveniently viewed as describing a
hyperboloid in 5D Minkowski space, while the flat reference metric depends on
the Stuckelberg field that satisfies the equation
. This equation has infinitely many
solutions, hence there are infinitely many de Sitter vacua with different
physical properties. Only the simplest solution with has been previously
studied since it is manifestly homogeneous and isotropic, but it is unstable.
However, other solutions could be stable. We require the timelike isometry to
be common for both metrics, and this gives physically distinguished solutions
since only for them the canonical energy is time-independent. We conjecture
that these solutions minimize the energy and are therefore stable. We also show
that in some cases solutions can be homogeneous and isotropic in a non-manifest
way such that their symmetries are not obvious. All of this suggests that the
theory may admit viable cosmologies.Comment: 14 pages, 1 figure, references adde
Instability Proof for Einstein-Yang-Mills Solitons and Black Holes with Arbitrary Gauge Groups
We prove that static, spherically symmetric, asymptotically flat soliton and
black hole solutions of the Einstein-Yang-Mills equations are unstable for
arbitrary gauge groups, at least for the ``generic" case. This conclusion is
derived without explicit knowledge of the possible equilibrium solutions.Comment: 26 pages, LATEX, no figure
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