scholarly journals A CLASS OF COLLISIONS OF PLANE IMPULSIVE LIGHT-LIKE SIGNALS IN GENERAL RELATIVITY

2002 ◽  
Vol 11 (06) ◽  
pp. 933-945 ◽  
Author(s):  
C. BARRABÈS ◽  
P. A. HOGAN
Keyword(s):  
General Relativity ◽  
Systematic Study ◽  
Necessary Conditions ◽  
Weyl Curvature ◽  
Collision Problem ◽  
Special Cases ◽  
Homogeneous Plane

We present a systematic study of collisions of homogeneous, plane- fronted, impulsive light-like signals which do not interact after head-on collision. For the head-on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be noninteracting after collision. We then solve the collision problem in the general case when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.

scholarly journals L’innovation et le modèle du commerce néo-technologique dans l’espace des caractéristiques de Lancaster

2009 ◽  
Vol 55 (3) ◽  
pp. 342-359
Author(s):  
Petr Hanel
Keyword(s):  
Necessary Conditions ◽  
New Product ◽  
Efficient Production ◽  
Numerical Example ◽  
Special Cases ◽  
Welfare Implications ◽  
Efficient Consumption

Lancaster's case of innovation in consumption technology is formalized and extended to include beside of the criterion of efficient consumption also the criterion of efficient production. The two criteria has to be met before an invention can be commercialized economically. Trade provoked by an innovation in consumption technology—a new product—is analyzed on a simple numerical example. Necessary conditions and some welfare implications of the neo-technology trade are presented. The approach is sufficiently general to encompass trade based on cost reducing innovation as well as existing trade models as special cases.

Optimal allocation of relevations in coherent systems

2021 ◽  
Vol 58 (4) ◽  
pp. 1152-1169
Author(s):  
Rongfang Yan ◽  
Jiandong Zhang ◽  
Yiying Zhang
Keyword(s):  
Optimal Allocation ◽  
Necessary Conditions ◽  
Stochastic Order ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Usual Stochastic Order ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Allocation Strategies

AbstractIn this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

scholarly journals Some Cosmological Solutions of a New Nonlocal Gravity Model

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 917
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Alexey S. Koshelev ◽  
Zoran Rakic ◽  
Jelena Stankovic
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Analytic Function ◽  
Cosmological Constant ◽  
Explicit Form ◽  
Gravity Model ◽  
Necessary Conditions ◽  
Equations Of Motion ◽  
Nonlocal Operator ◽  
Cosmological Solutions

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G ∫ [ R − 2 Λ + ( R − 4 Λ ) F ( □ ) ( R − 4 Λ ) ] − g d 4 x , where F ( □ ) = ∑ n = 1 + ∞ f n □ n is an analytic function of the d’Alembertian □. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ ≠ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e Λ 4 t 2 , that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one a ( t ) = A e Λ t 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F ( □ ) , which satisfies obtained necessary conditions.

Rigid frames in general relativity

1965 ◽  
Vol 283 (1394) ◽  
pp. 343-355 ◽  
Keyword(s):  
General Relativity ◽  
Sufficient Conditions ◽  
Classification Theorem ◽  
Noether Theorem ◽  
Projection Technique ◽  
Field Equations ◽  
Rigid Frame ◽  
Special Cases ◽  
Rigid Frames ◽  
Physical Consequences

Properties of a congruence of time-like curves are investigated, by means of a projection technique due to Cattaneo. Born’s requirement of vanishing spatial rate of strain ensures that the congruence defines a rigid frame. Einstein’s field equations impose further conditions, whose physical consequences are explored. Sufficient conditions are given for the extension of the Herglotz-Noether classification theorem to general relativity. The case is investigated in which the curves of the congruence are the orbits of a group of motions. Validity of the Herglotz-Noether theorem is shown to be associated with the existence of a certain type of motion. Finally, some properties of two important special cases of rigid frames—isometric and irrotational motions—are examined.

scholarly journals Injectivity of linear combinations in $\mathcal{B}(\mathcal{H})$

2021 ◽  
Vol 37 ◽  
pp. 359-369
Author(s):  
Marko Kostadinov
Keyword(s):  
Linear Combination ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Combinations ◽  
Special Cases ◽  
Sufficient And Necessary Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

The aim of this paper is to provide sufficient and necessary conditions under which the linear combination $\alpha A + \beta B$, for given operators $A,B \in {\cal B}({\cal H})$ and $\alpha, \beta \in \mathbb{C}\setminus \lbrace 0 \rbrace$, is injective. Using these results, necessary and sufficient conditions for left (right) invertibility are given. Some special cases will be studied as well.

Embedding properties of weighted Besov-type spaces

2015 ◽  
Vol 13 (05) ◽  
pp. 507-553 ◽  
Author(s):  
Wen Yuan ◽  
Dorothee D. Haroske ◽  
Leszek Skrzypczak ◽  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Necessary Conditions ◽  
Muckenhoupt Weight ◽  
Exponential Weights ◽  
Special Cases ◽  
Type Spaces ◽  
Sufficient And Necessary Conditions ◽  
Weighted Besov Spaces ◽  
Dyadic Cubes ◽  
Besov Type Spaces

In this paper, we consider the embeddings of weighted Besov spaces [Formula: see text] into Besov-type spaces [Formula: see text] with w being a (local) Muckenhoupt weight, and give sufficient and necessary conditions on the continuity and the compactness of these embeddings. As special cases, we characterize the continuity and the compactness of embeddings in case of some polynomial or exponential weights. The proofs of these conclusions strongly depend on the geometric properties of dyadic cubes.

Dark matter (energy) may be indistinguishable from modified gravity (MOND)

2017 ◽  
Vol 26 (12) ◽  
pp. 1743010 ◽  
Author(s):  
C. Sivaram
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Modified Gravity ◽  
Observational Evidence ◽  
Negative Results ◽  
Newtonian Dynamics ◽  
Special Cases ◽  
The Universe ◽  
Matter Energy

For Newtonian dynamics to hold over galactic scales, large amounts of dark matter (DM) are required which would dominate cosmic structures. Accounting for the strong observational evidence that the universe is accelerating requires the presence of an unknown dark energy (DE) component constituting about 70% of the matter. Several ingenious ongoing experiments to detect the DM particles have so far led to negative results. Moreover, the comparable proportions of the DM and DE at the present epoch appear unnatural and not predicted by any theory. For these reasons, alternative ideas like MOND and modification of gravity or general relativity over cosmic scales have been proposed. It is shown in this paper that these alternate ideas may not be easily distinguishable from the usual DM or DE hypotheses. Specific examples are given to illustrate this point that the modified theories are special cases of a generalized DM paradigm.

scholarly journals Are Naked Singularities Forbidden by the Second Law of Thermodynamics?

1997 ◽  
Vol 12 (32) ◽  
pp. 2415-2419 ◽  
Author(s):  
Sukratu Barve ◽  
T. P. Singh
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Second Law Of Thermodynamics ◽  
Physical Principle ◽  
Classical General Relativity ◽  
Second Law ◽  
Weyl Curvature ◽  
Naked Singularities

By now, many examples of naked singularities in classical general relativity are known. It may, however, be that a physical principle over and above the general theory prevents the occurrence of such singularities in nature. Assuming the validity of the Weyl curvature hypothesis, we propose that naked singularities are forbidden by the second law of thermodynamics.

scholarly journals Plane symmetric cosmological micro model in modified theory of Einstein’s general relativity

2003 ◽  
pp. 163-176 ◽  
Author(s):  
U.K. Panigrahi ◽  
R.C. Sahu
Keyword(s):  
General Relativity ◽  
Coupling Parameter ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Level ◽  
Micro Model ◽  
Plane Symmetric ◽  
Homogeneous Plane ◽  
Modified Theory ◽  
Einstein’S General Relativity

In this paper, we have investigated an anisotropic homogeneous plane symmetric cosmological micro-model in the presence of massless scalar field in modified theory of Einstein's general relativity. Some interesting physical and geometrical aspects of the model together with singularity in the model are discussed. Further, it is shown that this theory is valid and leads to Ein?stein's theory as the coupling parameter ? ?>? 0 in micro (i.e. quantum) level in general.

Sign in / Sign up

Export Citation Format

Share Document