scholarly journals ON THE DETECTION OF SCALAR FIELD INDUCED SPACE–TIME TORSION

2002 ◽  
Vol 17 (07) ◽  
pp. 421-428 ◽  
Author(s):  
T. DERELI ◽  
R. W. TUCKER
Keyword(s):  
Scalar Field ◽  
Alternative Hypothesis ◽  
Space Time ◽  
Current Time ◽  
Civita Connection ◽  
Test Particles ◽  
Perihelion Shift ◽  
Theories Of Gravity ◽  
Levi Civita Connection

We argue that the geodesic hypothesis based on autoparallels of the Levi–Cività connection may need refinement in the scalar–tensor theories of gravity. Based on a reformulation of the Brans–Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans–Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans–Dicke scalar field couples significantly to matter and test particles move on such worldlines, the current time keeping methods based on the conventional geodesic hypothesis may need refinement.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

scholarly journals A NON-GEODESIC MOTION IN THE R-1 THEORY OF GRAVITY TUNED WITH OBSERVATIONS

2008 ◽  
Vol 23 (02) ◽  
pp. 109-114 ◽  
Author(s):  
CHRISTIAN CORDA
Keyword(s):  
Dark Matter ◽  
High Order ◽  
Ricci Scalar ◽  
Geodesic Motion ◽  
General Picture ◽  
Test Particles ◽  
Pioneer Anomaly ◽  
Theories Of Gravity ◽  
Theory Of Gravity

In the general picture of high order theories of gravity, recently, the R-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R-1 function of the Ricci scalar and the matter Lagrangian. The result is a non-geodesic motion of test particles which, in principle, could be connected with Dark Matter and Pioneer anomaly problems.

Noncommutative scalar field in de Sitter space–time and pair creation process

2021 ◽  
Vol 36 (02) ◽  
pp. 2150011
Author(s):  
Nabil Mehdaoui ◽  
Lamine Khodja ◽  
Salah Haouat
Keyword(s):  
Scalar Field ◽  
Chemical Potential ◽  
De Sitter Space ◽  
Space Time ◽  
Pair Creation ◽  
De Sitter ◽  
Creation Process ◽  
Scalar Particles ◽  
Constant Electromagnetic Field

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

Entropy in a d-dimensional charged black hole

2018 ◽  
Vol 33 (27) ◽  
pp. 1850159 ◽  
Author(s):  
Shad Ali ◽  
Xin-Yang Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Space Time ◽  
Charged Black Hole ◽  
Schwarzschild Black Hole ◽  
Proportionality Coefficient ◽  
Proportional Relation ◽  
Hamiltonian Analysis ◽  
Interior Volume

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.

ON THE GAUSS–BONNET FORMULA IN RIEMANN–FINSLER GEOMETRY

2002 ◽  
Vol 34 (3) ◽  
pp. 329-340 ◽  
Author(s):  
BRAD LACKEY
Keyword(s):  
Finsler Space ◽  
Finsler Geometry ◽  
Euler Class ◽  
Constant Volume ◽  
Finsler Spaces ◽  
Chern Connection ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Riemannian Case ◽  
Torsion Free

Using Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel–Levi–Civita connection in the Riemannian case), this result extends the Gauss–Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.

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