scholarly journals Gravity in a warped 6D world with an extra 2D sphere

2019 ◽  
Vol 28 (02) ◽  
pp. 1950029
Author(s):  
Akira Kokado ◽  
Takesi Saito
Keyword(s):  
Differential Equation ◽  
Einstein Equation ◽  
Infinite Series ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Special Choice ◽  
Higher Dimensional ◽  
General Energy ◽  
Yukawa Potentials ◽  
Matter Fields

Corrections to Newton’s inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here, we give a model of a warped 6D world with an extra 2D sphere. We take a general energy–momentum tensor, which does not depend on a special choice of bulk matter fields. The 6D Einstein equation reduces to the spheroidal differential equation, which can be easily solved. The gravitational potential in our 4D universe is calculated to be composed of infinite series of massive Yukawa potentials coming from the KK mode, together with Newton’s inverse law. The series of Yukawa type potentials converges well to behave as [Formula: see text] near [Formula: see text].

scholarly journals VACUUM POLARIZATION IN A COSMIC STRING SPACETIME INDUCED BY FLAT BOUNDARY

2011 ◽  
Vol 03 ◽  
pp. 434-445
Author(s):  
EUGÊNIO R. BEZERRA DE MELLO ◽  
ARAM A. SAHARIAN
Keyword(s):  
Cosmic String ◽  
Vacuum Polarization ◽  
Energy Momentum Tensor ◽  
Neumann Boundary ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Massive Scalar ◽  
Expectation Values ◽  
Massive Scalar Field ◽  
Higher Dimensional

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string.

Vacuum polarization in the background of conical singularity

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040030
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Dimensional Spacetime ◽  
Higher Dimensional

We consider the gravity-induced effects associated with a massless scalar field living in a higher-dimensional spacetime being the tensor product of Minkowski space and spherically-symmetric space with angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole or cosmic string with flat extra dimensions, where the deficit of solid angle is proportional to Newton constant and tension. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green’s function and compute it to the leading order. With the use of this Green’s function we compute the renormalized vacuum expectation value of the scalar-field’s energy-momentum tensor. We make some general note on the linear-on-curvature part of the trace of even coefficients of Schwinger-deWitt expansion.

scholarly journals General approach to the Lagrangian ambiguity in f(R, T) gravity

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
G. A. Carvalho ◽  
F. Rocha ◽  
H. O. Oliveira ◽  
R. V. Lobato
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Unknown Variable ◽  
Stress Energy ◽  
The Standard Model ◽  
Theories Of Gravity ◽  
Matter Fields

AbstractThe f(R, T) gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, R, and the trace of the stress–energy tensor, T; its field equations also depend on matter Lagrangian, $$\mathscr {L}_{m}$$ L m . In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the $$\mathscr {L}_{m}$$ L m dependence from f(R, T) gravity field equations by generalizing the approach of Moraes in Ref. [1]. We also propose a general approach where we argue that the trace of the energy–momentum tensor must be considered an “unknown” variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy–momentum tensor of the f(R, T) gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

scholarly journals The Motion of Spinless Particles in General Relativity

1978 ◽  
Vol 31 (1) ◽  
pp. 105
Author(s):  
LJ Gregory ◽  
AH Klotz
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Geodesic Equations ◽  
General Energy

A technique is developed, which uses a general energy-momentum tensor, to derive the equations of motion in general relativity. This enables the geodesic equations for spinless particles to be deduced.

scholarly journals Forces in Schwarzschild, Vaidya and generalized Vaidya spacetimes

2021 ◽  
Vol 2081 (1) ◽  
pp. 012036
Author(s):  
Vitalii Vertogradov
Keyword(s):  
Perfect Fluid ◽  
Einstein Equation ◽  
Coordinate Transformation ◽  
Energy Momentum Tensor ◽  
Naked Singularity ◽  
Momentum Tensor ◽  
Geodesic Equation ◽  
Singularity Formation ◽  
Schwarzschild Spacetime ◽  
Leading Term

Abstract In this paper we investigate how the leading term in the geodesic equation in Schwarzschild spacetime changes under the coordinate transformation to Eddington-Finkelstein coordinates. This term corresponds to the Newton force of attraction. Also we consider this term when we add the energy-momentum tensor of the form of the null dust and the null perfect fluid into right-hand side of the Einstein equation. We estimate the value of this force in Vaidya spacetime when the naked singularity formation occurs. Also we give conditions in generalized Vaidya spacetime when this force of attraction is replaced by the force of repulsion.

On Hypermomentum in General Relativity I. The Notion of Hypermomentum

1976 ◽  
Vol 31 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Friedrich W. Hehl ◽  
G. David Kerlick ◽  
Paul von der Heyde
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Spin Angular Momentum ◽  
Relativistic Field ◽  
Rank Tensor ◽  
General Relativistic ◽  
Matter Fields

Abstract In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor ⊿ijk of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws.

The Einstein equation for signature type changing spacetimes

1994 ◽  
Vol 446 (1926) ◽  
pp. 115-126 ◽  
Keyword(s):  
Scalar Field ◽  
Uniqueness Theorem ◽  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Energy Momentum Tensor ◽  
Local Existence ◽  
Momentum Tensor ◽  
Existence And Uniqueness Theorem ◽  
Local Existence And Uniqueness ◽  
Type Change

We give a local existence and uniqueness theorem for solutions of Einstein’s equations with dust energy momentum tensor in the class of m -dimensional, analytic, transverse, signature type changing spacetimes where the initial condi­tions are given on the hypersurface of signature type change. We also prove a similar theorem in the case that the energy momentum tensor represents a scalar field.

A FORMAL APPROACH TO MACHIAN GENERAL RELATIVITY

2002 ◽  
Vol 11 (09) ◽  
pp. 1347-1354 ◽  
Author(s):  
PAUL S. WESSON ◽  
SANJEEV S. SEAHRA ◽  
HONGYA LIU
Keyword(s):  
General Relativity ◽  
Test Particle ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Formal Approach ◽  
Global Properties ◽  
Higher Dimensional ◽  
Complex Wave ◽  
Local Properties ◽  
Theories Of Gravity

We take Mach's principle to mean that the local properties of a test particle should depend on the global properties of the geometry. Using a complex wave-like metric and an appropriate redefinition of the energy-momentum tensor, we show this to be possible in principle within the context of general relativity. We outline implications for higher-dimensional theories of gravity.

scholarly journals Emergent gravity from hidden sectors and TT deformations

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
P. Betzios ◽  
E. Kiritsis ◽  
V. Niarchos
Keyword(s):  
Energy Momentum Tensor ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Emergent Gravity ◽  
Expectation Value ◽  
Higher Dimensional ◽  
The Standard Model ◽  
Emergent Theory ◽  
Effective Description

Abstract We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive the general effective description of such dynamics, and apply it to the case where a hidden theory generates gravity that is coupled to the Standard Model. In the linearized description, generically, such gravity is massive with the presence of an extra scalar degree of freedom. The propagators of both the spin-two and spin-zero modes are positive and well defined. The associated emergent gravitational theory is a bi-gravity theory, as is (secretly) the case in holography. The background metric on which the QFTs are defined, plays the role of dark energy and the emergent theory has always as a solution the original background metric. In the case where the hidden theory is holographic, the overall description yields a higher-dimensional bulk theory coupled to a brane. The effective graviton on the brane has four-dimensional characteristics both in the UV and IR and is always massive.

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