859 research outputs found
On 1-Harmonic Functions
Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over R; and every 7-dimensional SO(2) × SO(6)-invariant absolutely area-minimizing integral current in R8 is real analytic. The assumption on the SO(2) × SO(6)-invariance cannot be removed, due to the first counter-example in R8, proved by Bombieri, De Girogi and Giusti
Rigidity of minimal submanifolds in hyperbolic space
We prove that if an -dimensional complete minimal submanifold in
hyperbolic space has sufficiently small total scalar curvature then has
only one end. We also prove that for such there exist no nontrivial
harmonic 1-forms on
Effects of acceleration on the collision of particles in the rotating black hole spacetime
We study the collision of two geodesic particles in the accelerating and
rotating black hole spacetime and probe the effects of the acceleration of
black hole on the center-of-mass energy of the colliding particles and on the
high-velocity collision belts. We find that the dependence of the
center-of-mass energy on the acceleration in the near event-horizon collision
is different from that in the near acceleration-horizon case. Moreover, the
presence of the acceleration changes the shape and position of the
high-velocity collision belts. Our results show that the acceleration of black
holes brings richer physics for the collision of particles.Comment: 7 pages, 2 figures, The corrected version accepted for publication in
EPJ
Interacting Agegraphic Dark Energy
A new dark energy model, named "agegraphic dark energy", has been proposed
recently, based on the so-called K\'{a}rolyh\'{a}zy uncertainty relation, which
arises from quantum mechanics together with general relativity. In this note,
we extend the original agegraphic dark energy model by including the
interaction between agegraphic dark energy and pressureless (dark) matter. In
the interacting agegraphic dark energy model, there are many interesting
features different from the original agegraphic dark energy model and
holographic dark energy model. The similarity and difference between agegraphic
dark energy and holographic dark energy are also discussed.Comment: 10 pages, 5 figures, revtex4; v2: references added; v3: accepted by
Eur. Phys. J. C; v4: published versio
Entropy spectrum of a Kerr anti-de Sitter black hole
The entropy spectrum of a spherically symmetric black hole was derived
without the quasinormal modes in the work of Majhi and Vagenas. Extending this
work to rotating black holes, we quantize the entropy and the horizon area of a
Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area
are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic
invariance in the first way. By addressing the wave function of emitted
(absorbed) particles, the entropy and the area are quantized in the second one.
Both results show that the entropy and the area spectra are equally spaced.Comment: Accepted for publication in The European Physical Journal C, Volume
72, Issue
Hidden symmetries for thermodynamics and emergence of relativity
Erik Verlinde recently proposed an idea about the thermodynamic origin of
gravity. Though this is a beautiful idea which may resolve many long standing
problems in the theories of gravity, it also raises many other problems. In
this article I will comment on some of the problems of Verlinde's proposal with
special emphasis on the thermodynamical origin of the principle of relativity.
It is found that there is a large group of hidden symmetries of thermodynamics
which contains the Poincare group of the spacetime for which space is emergent.
This explains the thermodynamic origin of the principle of relativity.Comment: V1: 4 pages, comments/criticisms welcomed; V2: references added; V3:
typos and minor corrections? V4? substantial changes in Section 3 and other
parts mad
On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications
Let be a strictly increasing function
with . We unify the concepts of -harmonic maps, minimal
hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and
introduce -Yang-Mills fields, -degree, -lower degree, and generalized
Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on
manifolds. When and
the -Yang-Mills field becomes an ordinary Yang-Mills field,
-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus
sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a
manifold respectively. We also introduce the energy functional (resp.
-Yang-Mills functional) and derive the first variational formula of the
energy functional (resp. -Yang-Mills functional) with
applications. In a more general frame, we use a unified method to study the
stress-energy tensors that arise from calculating the rate of change of various
functionals when the metric of the domain or base manifold is changed. These
stress-energy tensors, linked to -conservation laws yield monotonicity
formulae. A "macroscopic" version of these monotonicity inequalities enables us
to derive some Liouville type results and vanishing theorems for forms with
values in vector bundles, and to investigate constant Dirichlet boundary value
problems for 1-forms. In particular, we obtain Liouville theorems for
harmonic maps (e.g. -harmonic maps), and Yang-Mills fields (e.g.
generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain
generalized Chern type results for constant mean curvature type equations for
forms on and on manifolds with the global doubling property
by a different approach. The case and is due to Chern.Comment: 1. This is a revised version with several new sections and an
appendix that will appear in Communications in Mathematical Physics. 2. A
"microscopic" approach to some of these monotonicity formulae leads to
celebrated blow-up techniques and regularity theory in geometric measure
theory. 3. Our unique solution of the Dirichlet problems generalizes the work
of Karcher and Wood on harmonic map
Entropy-Corrected New Agegraphic Dark Energy Model in Horava-Lifshitz Gravity
In this work, we have considered the entropy-corrected new agegraphic dark
energy (ECNADE) model in Horava-Lifshitz gravity in FRW universe. We have
discussed the correspondence between ECNADE and other dark energy models such
as DBI-essence,Yang-Mills dark energy, Chameleon field, Non-linear
electrodynamics field and hessence dark energy in the context of
Horava-Lifshitz gravity and reconstructed the potentials and the dynamics of
the scalar field theory which describe the ECNADE.Comment: 12 page
Yang-Mills Interactions and Gravity in Terms of Clifford Algebra
A model of Yang-Mills interactions and gravity in terms of the Clifford
algebra Cl(0,6) is presented. The gravity and Yang-Mills actions are formulated
as different order terms in a generalized action. The feebleness of gravity as
well as the smallness of the cosmological constant and theta terms are
discussed at the classical level. The invariance groups, including the de
Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations
from either side of an algebraic spinor. Upon symmetry breaking via the Higgs
fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3),
electromagnetic U(1)_EM, and an additional U(1). The first generation leptons
and quarks are identified with even and odd parts of spinor idempotent
projections. There are still several shortcomings with the current model.
Further research is needed to fully recover the standard model results.Comment: 20 pages, to appear in Advances in Applied Clifford Algebra
Entropic Corrections to Coulomb's Law
Two well-known quantum corrections to the area law have been introduced in
the literatures, namely, logarithmic and power-law corrections. Logarithmic
corrections, arises from loop quantum gravity due to thermal equilibrium
fluctuations and quantum fluctuations, while, power-law correction appears in
dealing with the entanglement of quantum fields in and out the horizon.
Inspired by Verlinde's argument on the entropic force, and assuming the quantum
corrected relation for the entropy, we propose the entropic origin for the
Coulomb's law in this note. Also we investigate the Uehling potential as a
radiative correction to Coulomb potential in 1-loop order and show that for
some value of distance the entropic corrections of the Coulomb's law is
compatible with the vacuum-polarization correction in QED. So, we derive
modified Coulomb's law as well as the entropy corrected Poisson's equation
which governing the evolution of the scalar potential . Our study further
supports the unification of gravity and electromagnetic interactions based on
the holographic principle.Comment: 17 pages, 5 figures, accepted in IJT
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