16,482 research outputs found

### Existence of minimal surfaces of arbitrary large Morse index

We show that in a closed 3-manifold with a generic metric of positive Ricci
curvature, there are minimal surfaces of arbitrary large Morse index, which
partially confirms a conjecture by F. Marques and A. Neves. We prove this by
analyzing the lamination structure of the limit of minimal surfaces with
bounded Morse index.Comment: One figure, final versio

### A maximum principle for free boundary minimal varieties of arbitrary codimension

We establish a boundary maximum principle for free boundary minimal
submanifolds in a Riemannian manifold with boundary, in any dimension and
codimension. Our result holds more generally in the context of varifolds.Comment: revised version, to appear in Comm. Anal. Geo

### Ghost free massive gravity with singular reference metrics

An auxiliary metric (reference metric) is inevitable in massive gravity
theory. In the scenario of gauge/gravity duality, a singular reference metric
corresponds to momentum dissipations, which describes the electric and heat
conductivity for normal conductors. We demonstrate in detail that the massive
gravity with singular reference metric is ghost-free.Comment: 6pages, no figur

### Absolutely split metacyclic groups and weak metacirculants

Let $m,n,r$ be positive integers, and let $G=\langle a\rangle: \langle
b\rangle \cong \mathbb{Z}_n: \mathbb{Z}_m$ be a split metacyclic group such
that $b^{-1}ab=a^r$. We say that $G$ is {\em absolutely split with respect to
$\langle a\rangle$} provided that for any $x\in G$, if $\langle
x\rangle\cap\langle a\rangle=1$, then there exists $y\in G$ such that
$x\in\langle y\rangle$ and $G=\langle a\rangle: \langle y\rangle$. In this
paper, we give a sufficient and necessary condition for the group $G$ being
absolutely split. This generalizes a result of Sanming Zhou and the second
author in [arXiv: 1611.06264v1]. We also use this result to investigate the
relationship between metacirculants and weak metacirculants.
Metacirculants were introduced by Alspach and Parsons in $1982$ and have been
a rich source of various topics since then. As a generalization of this classes
of graphs, Maru\v si\v c and \v Sparl in 2008 posed the so called weak
metacirculants. A graph is called a {\em weak metacirculant} if it has a
vertex-transitive metacyclic automorphism group. In this paper, it is proved
that a weak metacirculant of $2$-power order is a metacirculant if and only if
it has a vertex-transitive split metacyclic automorphism group. This provides a
partial answer to an open question in the literature

### Quasinormal Modes and Late-Time Tails of Canonical Acoustic Black Holes

In this paper, we investigate the evolution of classical wave propagation in
the canonical acoustic black hole by numerical method and discuss the details
of tail phenomenon. The oscillating frequency and damping time scale both
increase with the angular momentum $l$. For the lower $l$, numerical results
show the lowest WKB approximation gives the most reliable result. We also find
that time scale of the interim region from ringing to tail is not affected
obviously by changing $l$.Comment: 5 pages, 6 figure

### Anisotropy of incommensurate spin and charge fluctuations in detwinned YBa$_2$Cu$_3$O$_{6+\delta}$

Motivated by a recent neutron scattering experiment on detwinned
YBa$_2$Cu$_3$O$_{6+\delta}$ superconductor, we examine the frequency and doping
dependence of the anisotropy in the spin and charge fluctuation arising from
the coupling between the plane and the chain. Starting from the two-dimensional
$t$-$t^{'}$-$J$ model and using the random-phase approximation (RPA), we find a
pronounced anisotropy of the incommensurate (IC) peaks in the spin channel,
namely the peak intensity at the $(\pi\pm\delta,\pi)$ direction is stronger
than that at the $(\pi,\pi\pm\delta)$ direction in a wide frequency range from
$\omega=0.2J$ to the resonance frequency $\omega_r=0.35J$. Above the resonance
frequency, the IC peaks reemerge. Their intensities shift to the diagonal
direction and no anisotropy exists along the two diagonal directions. We find
that this anisotropy is robust with respect to the possible variation of the
RPA correction factor and to the dopings. The charge fluctuation is also found
to be incommensurate for all energies considered and peak at $(0,\delta)$ and
$(\delta,0)$. An anisotropy in its IC peak intensity along the $k_x$ and the
$k_y$ direction exists, but in sharp contrast to the spin channel, the maximum
intensity of the IC peak is along the $k_y$ direction. Moreover, the IC peak in
the charge channel exhibits an upward dispersion, in contrast to the downward
dispersion below the spin resonance frequency for the spin IC peak. We explain
these features based on the effect of the plane-chain coupling on the topology
of the Fermi surface.Comment: 8 page

### De Sitter ground state of scalar-tensor gravity and its fluctuation with dust

An exact de Sitter solution of scalar-tensor gravity is found, in which the
non-minimal coupling scalar is rolling along a non-constant potential. Based on
this solution, a dust-filled FRW universe is explored in frame of scalar-tensor
gravity. The effective dark energy induced by the sole non-minimal scalar can
be quintessence-like, phantom-like, and more significantly, can cross the
phantom divide. The rich and varied properties of scalar-tensor gravity even
with only one scalar is shown in this article.Comment: 9 pages, 9fig

### Global monopoles in the Brans-Dicke theory

A gravitating global monopole produces a repulsive grativational field
outside the core in addition to a solid angular deficit in the Brans-Dicke
theory. As a new feature, the angular deficit is dependent on the values of
\phi_{\infty} and \omega, where \phi_{\infty} is asymptotic value of scalar
field in space-like infinity and \omega is the Brans-Dicke parameter.Comment: Latex 6 pages, To be published in Phys. Rev.

### Black hole solutions in de Rham-Gabadadze-Tolley massive gravity

We present a detailed study of the static spherically symmetric solutions in
de Rham-Gabadadze-Tolley (dRGT) theory. Since the diffeomorphism invariance can
be restored by introducing the St\"{u}ckelberg fields $\phi^a$, there is new
invariant $I^{ab}=g^{\mu\nu}\partial_{\mu}\phi^a\partial_\nu\phi^b$ in the
massive gravity, which adds to the ones usually encountered in general
relativity (GR). In the unitary gauge $\phi^a=x^\mu\delta_\mu^a$, any inverse
metric $g^{\mu\nu}$ that has divergence including the coordinate singularity in
GR would exhibit a singularity in the invariant $I^{ab}$. Therefore, there is
no conventional Schwarzschild metric if we choose unitary gauge. In this paper,
we obtain a self-consistent static spherically symmetric ansatz in the
nonunitary gauge. Under this ansatz, we find that there are seven solutions
including the Schwarzschild solution, Reissner-Nordstr\"{o}m solution and five
other solutions. These solutions may possess an event horizon depending upon
the physical parameters (Schwarzschild radius $r_s$, scalar charge $S$ and/or
electric charge $Q$). If these solutions possess an event horizon, we show that
the singularity of $I^{ab}$ is absent at the horizon. Therefore, these
solutions may become candidates for black holes in dRGT.Comment: 12pages, no figur

### MOND cosmology from entropic force

We derive the MOND cosmology which is uniquely corresponding to the original
MOND at galaxy scales via entropic gravity method.
It inherits the key merit of MOND, that is, it reduces the baryonic matter
and non-baryonic dark matter into baryonic matter only.
For the first time we obtain the critical parameter in MOND, i.e., the
transition acceleration $a_c$ at cosmological scale.
We thus solve the long-standing coincidence problem $a_c\sim cH_{0}$. More
interestingly, a term like age-graphic dark energy emerges naturally.
In the frame of this MOND cosmology, we only need baryonic matter to describe
both dark matter and dark energy in standard cosmology.Comment: 4 pages, several references added, to appear in PL

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