scholarly journals Bubbling of Almost-harmonic Maps between 2-spheres at Points of Zero Energy Density

2004 ◽  
pp. 33-42 ◽  
Author(s):  
Peter Topping
Keyword(s):  
Energy Density ◽  
Harmonic Maps ◽  
Zero Energy

scholarly journals Cosmological Constant from the Entropy Balance Condition

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Merab Gogberashvili
Keyword(s):  
Dark Energy ◽  
Energy Density ◽  
Apparent Horizon ◽  
Critical Density ◽  
Zero Energy ◽  
Dark Energy Density ◽  
Event Horizons ◽  
Balance Condition ◽  
Quantum Particles ◽  
Hubble Horizon

In the action formalism variations of metric tensors usually are limited by the Hubble horizon. On the contrary, variations of quantum fields should be extended up to the event horizon, which is the real boundary of the spacetime. As a result the entanglement energy of quantum particles across the apparent horizon is missed in the cosmological equations written for the Hubble volume. We identify this missing boundary term with the dark energy density and express it (using the zero energy assumption for the finite universe) as the critical density multiplied by the ratio of the Hubble and event horizons radii.

Stability and constant boundary-value problems of harmonic maps with potential

2000 ◽  
Vol 68 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Qun Chen
Keyword(s):  
Riemannian Manifold ◽  
Energy Density ◽  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
General Class ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Boundary Value ◽  
The Stability ◽  
Harmonic Maps With Potential

AbstractLet M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

scholarly journals Freely falling observer and black hole radiation

2014 ◽  
Vol 29 (11) ◽  
pp. 1450052 ◽  
Author(s):  
Wontae Kim ◽  
Edwin J. Son
Keyword(s):  
Black Hole ◽  
Energy Density ◽  
Event Horizon ◽  
Negative Energy ◽  
Positive Energy ◽  
Energy Curve ◽  
Zero Energy ◽  
Negative Energy Density ◽  
Black Hole Radiation

We find radiation in an infalling frame and present an explicit analytic evidence of the failure of no drama condition by showing that an infalling observer finds an infinite negative energy density at the event horizon. The negative and positive energy density regions are divided by the newly defined zero-energy curve (ZEC). The evaporating black hole is surrounded by the negative energy which can also be observed in the infalling frame.

scholarly journals Field-angle dependence of the zero-energy density of states in the unconventional heavy-fermion superconductor CeCoIn5

2004 ◽  
Vol 16 (3) ◽  
pp. L13-L19 ◽  
Author(s):  
H Aoki ◽  
T Sakakibara ◽  
H Shishido ◽  
R Settai ◽  
Y nuki ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Of States ◽  
Heavy Fermion ◽  
Zero Energy ◽  
Angle Dependence ◽  
Heavy Fermion Superconductor

Zero-energy density effect in stopping power of carbon

1984 ◽  
Vol 80 (3-4) ◽  
pp. 261-271 ◽  
Author(s):  
C. J. Tung ◽  
C. Lin
Keyword(s):  
Energy Density ◽  
Density Effect ◽  
Stopping Power ◽  
Zero Energy

scholarly journals A Unified Cosmological Model for Solution of Problems of Cosmological Constant, Cosmic Coincidence, Energy Conservation, Flatness and Homogeneity of Horizon

2021 ◽  
Author(s):  
Biswaranjan Dikshit
Keyword(s):  
Energy Density ◽  
Cosmological Model ◽  
Energy Conservation ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Zero Energy ◽  
Cosmological Constant Problem ◽  
Coincidence Problem ◽  
Horizon Problem

Cosmological constant problem is the difference by a factor of ~10123 between quantum mechanically calculated vacuum energy density and astronomically observed value. Cosmic coincidence problem questions why matter energy density is of the same order as the present vacuum energy density (former is ~32% and latter is ~68%). Recently, by quantizing zero-point field of space, we have developed a cosmological model that predicts correct value of vacuum and non-vacuum energy density. In this paper, we remove some earlier assumptions and develop a generalized version of our cosmological model to solve three more problems viz. energy conservation, flatness and horizon problem along with the above two. For creation of universe without violating law of energy conservation, net energy of the universe including (negative) gravitational potential energy must be zero. However, in conventional method, its quantitative proof needs the space to be exactly flat i.e. zero-energy universe is a consequence of flatness. But, in this paper, we will prove a zero-energy universe without using flatness of space and then show that flatness is actually a consequence of zero energy density. Finally, using our model we solve the horizon problem of universe. Although cosmic inflation can explain the flatness of space and uniformity of horizon by invoking inflaton field, it cannot predict the present value of vacuum energy density or matter density. But, our cosmological model solves in an unified manner all the above mentioned five problems viz. cosmological constant problem, cosmic coincidence problem, energy conservation, flatness and horizon problem.

scholarly journals The Energy Density Gap of Harmonic Maps between Finsler Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Jingwei Han ◽  
Yao-yong Yu ◽  
Jing Yu
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Harmonic Maps ◽  
Finsler Manifold ◽  
Rigidity Theorem ◽  
Moving Frame ◽  
Finsler Manifolds ◽  
Variation Formula ◽  
Smooth Maps

We study the energy density function of nondegenerate smooth maps with vanishing tension field between two real Finsler manifolds. Firstly, we get a variation formula of energy density function by using moving frame. With this formula, we obtain a rigidity theorem of nondegenerate map with vanishing tension field from the Finsler manifold to the Berwald manifold.

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