scholarly journals Null shells and double layers in quadratic gravity

2021 ◽  
Vol 2081 (1) ◽  
pp. 012020
Author(s):  
I D Ivanova
Keyword(s):  
Spherical Geometry ◽  
External Pressure ◽  
Double Layers ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Least Action Principle ◽  
Motion Equations ◽  
Least Action ◽  
Quadratic Gravity ◽  
Singular Hypersurface

Abstract For a singular hypersurface of arbitrary type in quadratic gravity motion equations were obtained using only the least action principle. It turned out that the coefficients in the motion equations are zeroed with a combination corresponding to the Gauss-Bonnet term. Therefore it does not create neither double layers nor thin shells. It has been demonstrated that there is no “external pressure” for any type of null singular hypersurface. It turned out that null spherically symmetric singular hupersurfaces in quadratic gravity cannot be a double layer, and only thin shells are possible. The system of motion equations in this case is reduced to one which is expressed through the invariants of spherical geometry along with the Lichnerowicz conditions. Spherically symmetric null thin shells were investigated for spherically symmetric solutions of conformal gravity as applications, in particular, for various vacua and Vaidya-type solutions.

scholarly journals Spherically symmetric double layers in Weyl+Einstein gravity

2019 ◽  
Vol 28 (13) ◽  
pp. 1941007 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
Double Layer ◽  
Curvature Tensor ◽  
Extrinsic Curvature ◽  
Einstein Gravity ◽  
Double Layers ◽  
Spherically Symmetric ◽  
Weyl Formula ◽  
Matching Conditions ◽  
Quadratic Gravity ◽  
Singular Hypersurface

We study the matching conditions on singular hypersurfaces in Weyl[Formula: see text]Einstein gravity. Unlike General Relativity, the so-called quadratic gravity allows the existence of a double layer, i.e. the derivative of [Formula: see text]-function. This double layer is a purely geometrical phenomenon and it may be treated as the purely gravitational shock wave. The mathematical formalism was elaborated by Senovilla for generic quadratic gravity. We derived the matching conditions for the spherically symmetric singular hypersurface in the Weyl[Formula: see text]Einstein gravity. It was found that in the presence of the double layer, the matching conditions contain an arbitrary function. One of the consequences of such freedom is that a trace of the extrinsic curvature tensor of a singular hypersurface is necessarily equal to zero. We suggested that the [Formula: see text] and [Formula: see text] components of the surface matter energy–momentum tensor of the shell describe energy flow [Formula: see text] and momentum transfer [Formula: see text] of particles produced by the double layer itself. Moreover, the requirement of the zero trace of the extrinsic curvature tensor (mentioned above) implies that [Formula: see text], and this fact also supports our suggestion, because it means that for the observer sitting on the shell, particles will be seen created by pairs, and the sum of their momentum transfers must be zero. We found also that the spherically symmetric null double layer in the Weyl[Formula: see text]Einstein gravity does not exist at all.

scholarly journals Junction conditions in quadratic gravity: thin shells and double layers

2016 ◽  
Vol 33 (10) ◽  
pp. 105008 ◽  
Author(s):  
Borja Reina ◽  
José M M Senovilla ◽  
Raül Vera
Keyword(s):  
Double Layers ◽  
Thin Shells ◽  
Junction Conditions ◽  
Quadratic Gravity

scholarly journals Double Layer in the Quadratic Gravity and the Least Action Principle

2020 ◽  
Vol 51 (4) ◽  
pp. 730-734
Author(s):  
V. A. Berezin ◽  
V. Yu. Dokuchaev ◽  
Yu. N. Eroshenko ◽  
A. L. Smirnov
Keyword(s):  
Double Layer ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Quadratic Gravity

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Phase reconstruction by the weighted least action principle

2006 ◽  
Vol 8 (3) ◽  
pp. 279-289 ◽  
Author(s):  
Chungmin Lee ◽  
John Lowengrub ◽  
Jacob Rubinstein ◽  
Xiaoming Zheng
Keyword(s):  
Action Principle ◽  
Phase Reconstruction ◽  
Least Action Principle ◽  
Least Action

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

scholarly journals LUKEWARM BLACK HOLES IN QUADRATIC GRAVITY

2011 ◽  
Vol 26 (14) ◽  
pp. 999-1007 ◽  
Author(s):  
JERZY MATYJASEK ◽  
KATARZYNA ZWIERZCHOWSKA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Fourth Order ◽  
Spherically Symmetric ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Quadratic Gravity ◽  
De Sitter Universe ◽  
Electrically Charged

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.

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