scholarly journals Localized deformation for initial data sets with the dominant energy condition

2020 ◽  
Vol 59 (1) ◽  
Author(s):  
Justin Corvino ◽  
Lan-Hsuan Huang
Keyword(s):  
Initial Data ◽  
Energy Condition ◽  
Dominant Energy Condition ◽  
Data Sets ◽  
Localized Deformation

scholarly journals Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

2019 ◽  
Vol 30 (13) ◽  
pp. 1940003
Author(s):  
Yaohua Wang ◽  
Xiao Zhang
Keyword(s):  
Initial Data ◽  
Energy Condition ◽  
Positive Energy ◽  
Dominant Energy Condition ◽  
Data Sets ◽  
De Sitter

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

scholarly journals USING (4+1) SPLIT AND ENERGY CONDITIONS TO STUDY THE INDUCED MATTER IN 5D RICCI-FLAT COSMOLOGY

2007 ◽  
Vol 22 (05) ◽  
pp. 985-994 ◽  
Author(s):  
YONGLI PING ◽  
HONGYA LIU ◽  
LIXIN XU
Keyword(s):  
Energy Condition ◽  
Energy Conditions ◽  
Dominant Energy Condition ◽  
Strong Energy Condition ◽  
Ricci Flat ◽  
Strong Energy ◽  
Expansion Of The Universe ◽  
Frw Models ◽  
Induced Matter ◽  
The Universe

We use (4+1) split to derive the 4D induced energy density ρ and pressure p of the 5D Ricci-flat cosmological solutions which are characterized by having a bounce instead of a bang. The solutions contain two arbitrary functions of time t and, therefore, are mathematically rich in giving various cosmological models. By using four known energy conditions (null, weak, strong, and dominant) to pick out and study physically meaningful solutions, we find that the 4D part of the 5D solutions asymptotically approaches to the standard 4D FRW models and the expansion of the universe is decelerating for normal induced matter for which all the four energy conditions are satisfied. We also find that quintessence might be normal or abnormal, depending on the parameter w of the equation of state. If -1 ≤ w < -1/3, the expansion of the universe is accelerating and the quintessence is abnormal because the strong energy condition is violated while other three are satisfied. For phantom, all the four energy conditions are violated. Before the bounce, all the four energy conditions are violated, implying that the cosmic matter before the bounce could be explained as a phantom that has a large negative pressure and makes the universe bouncing. In the early times after the bounce, the dominant energy condition is violated, while the other three are satisfied, and so the cosmic matter could be explained as a super-luminal acoustic matter.

scholarly journals Initial data sets for the Schwarzschild spacetime

2007 ◽  
Vol 75 (2) ◽  
Author(s):  
Alfonso García-Parrado Gómez-Lobo ◽  
Juan A. Valiente Kroon
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Schwarzschild Spacetime

scholarly journals Violation of the Dominant Energy Condition in Geometrodynamics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 400
Author(s):  
Vladimir Lasukov
Keyword(s):  
Black Holes ◽  
Dark Energy ◽  
Energy Condition ◽  
Dominant Energy Condition ◽  
Isotropic Energy ◽  
Cosmological Singularity ◽  
Dominant Condition ◽  
Field Theoretical Model ◽  
Over Time

It is shown that in Einstein’s theory and in the theory of gravity with Logunov constraints, there is a field-theoretical model of dark energy that is consistent with the observational data indicating that the Hubble value increases over time. In the developed model of dark energy, the isotropic energy dominant condition is violated. It solves the problem of the cosmological singularity and the singularity of “black holes”. The compact configuration of the scalar field can generate a flux of particles by the pairs of particles production mechanism from the vacuum by a field of barrier and in the process of transformation of thermal energy (Hawking radiation) and acceleration energy into radiation. The scalars can play the role of the so-called “black holes” with no singularity inside themselves.

scholarly journals Evolution of thin shells in D-dimensional general relativity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950069 ◽  
Author(s):  
Marcos A. Ramirez ◽  
Daniel Aparicio
Keyword(s):  
Energy Condition ◽  
Cosmic Censorship ◽  
Einstein Equations ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Spherically Symmetric ◽  
Barotropic Fluids ◽  
Large Shell ◽  
Asymptotic Dynamics ◽  
Electrovacuum Solution

In this paper, we consider singular timelike spherical hypersurfaces embedded in a [Formula: see text]-dimensional spherically symmetric bulk spacetime which is an electrovacuum solution of Einstein equations with cosmological constant. We analyze the different possibilities regarding the orientation of the gradient of the standard [Formula: see text] coordinate in relation to the shell. Then we study the dynamics according to Einstein equations for arbitrary matter satisfying the dominant energy condition. In particular, we thoroughly analyze the asymptotic dynamics for both the small and large-shell-radius limits. We also study the main qualitative aspects of the dynamics of shells made of linear barotropic fluids that satisfy the dominant energy condition. Finally, we prove weak cosmic censorship for this class of solutions.

scholarly journals ON THE STATIC SPACETIME OF A SINGLE POINT CHARGE

2011 ◽  
Vol 23 (03) ◽  
pp. 309-346 ◽  
Author(s):  
A. SHADI TAHVILDAR-ZADEH
Keyword(s):  
Single Point ◽  
Energy Condition ◽  
Weak Field ◽  
Charge Ratio ◽  
Dominant Energy Condition ◽  
Total Charge ◽  
Spherically Symmetric ◽  
Time Axis ◽  
Weak Field Limit ◽  
Test Charge

Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding spherically symmetric, asymptotically flat, electrostatic spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We also prove the uniqueness of these solutions in the spherically symmetric class, and we conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.

scholarly journals Rotating thin shells in (2 + 1)-dimensional asymptotically AdS spacetimes: Mechanical properties, machian effects, and energy conditions

2015 ◽  
Vol 24 (09) ◽  
pp. 1542022 ◽  
Author(s):  
José P. S. Lemos ◽  
Francisco J. Lopes ◽  
Masato Minamitsuji
Keyword(s):  
Energy Momentum Tensor ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Junction Conditions ◽  
Rest Energy ◽  
Inertial Frames ◽  
Ads Spacetime

In this paper, a rotating thin shell in a (2 + 1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2 + 1) dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy–density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy–momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2 + 1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

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