924 research outputs found
Spacetime Slices and Surfaces of Revolution
Under certain conditions, a -dimensional slice of a
spherically symmetric black hole spacetime can be equivariantly embedded in
-dimensional Minkowski space. The embedding depends on a real parameter
that corresponds physically to the surface gravity of the black hole
horizon.
Under conditions that turn out to be closely related, a real surface that
possesses rotational symmetry can be equivariantly embedded in 3-dimensional
Euclidean space. The embedding does not obviously depend on a parameter.
However, the Gaussian curvature is given by a simple formula: If the metric is
written , then
\K_g=-{1/2}\phi''(r).
This note shows that metrics and occur in dual pairs, and that
the embeddings described above are orthogonal facets of a single phenomenon. In
particular, the metrics and their respective embeddings differ by a Wick
rotation that preserves the ambient symmetry.
Consequently, the embedding of depends on a real parameter. The ambient
space is not smooth, and is inversely proportional to the cone angle
at the axis of rotation. Further, the Gaussian curvature of is given
by a simple formula that seems not to be widely known.Comment: 15 pages, added reference
The Hubble Slow Roll Expansion for Multi Field Inflation
We examine the dynamics of inflation driven by multiple, interacting scalar
fields and derive a multi field version of the Hubble slow roll expansion. We
show that the properties of this expansion naturally generalize those of the
single field case. We present an analogous hierarchy of slow roll parameters,
and derive the system of ``flow'' equations that describes their evolution, and
show that when this system is truncated at finite order, it can always be
solved exactly. Lastly, we express the scalar and tensor perturbation spectra
in terms of the slow roll parameters
On the Suppression of Parametric Resonance and the Viability of Tachyonic Preheating after Multi-Field Inflation
We investigate the feasibility of explosive particle production via
parametric resonance or tachyonic preheating in multi-field inflationary models
by means of lattice simulations. We observe a strong suppression of resonances
in the presence of four-leg interactions between the inflaton fields and a
scalar matter field, leading to insufficient preheating when more than two
inflatons couple to the same matter field. This suppression is caused by a
dephasing of the inflatons that increases the effective mass of the matter
field.
Including three-leg interactions leads to tachyonic preheating, which is not
suppressed by an increase in the number of fields. If four-leg interactions are
sub-dominant, we observe a slight enhancement of tachyonic preheating. Thus, in
order for preheating after multi-field inflation to be efficient, one needs to
ensure that three-leg interactions are present. If no tachyonic contributions
exist, we expect the old theory of reheating to be applicable.Comment: v2: reference added, identical with PRD version, 23 pages, 3 figure
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