scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

scholarly journals Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-27 ◽  
Author(s):  
Waldyr A. Rodrigues ◽  
Samuel A. Wainer
Keyword(s):  
Equations Of Motion ◽  
Killing Vector ◽  
De Sitter Space ◽  
Momentum Conservation ◽  
Space Time ◽  
Relativity Theory ◽  
De Sitter ◽  
Metric Tensor ◽  
Clifford Bundle ◽  
Time Structures

We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM), a submanifold of a 5-dimensional pseudo-Euclidean (5dPE) equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structuresMdSLandMdSTPare introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example,MdSLis not supposed to be the model of any gravitational field in the General Relativity Theory (GRT). Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

scholarly journals Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Rachel A. Rosen ◽  
Luca Santoni
Keyword(s):  
Black Hole ◽  
Explicit Form ◽  
Equations Of Motion ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Black Hole Background ◽  
Massless Spin ◽  
Higher Dimensional ◽  
Massless Fields

Abstract We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrödinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number L = 1 in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.

scholarly journals ACCELERATING UNIVERSE AS WINDOW FOR EXTRA DIMENSIONS

2006 ◽  
Vol 21 (31) ◽  
pp. 6491-6511 ◽  
Author(s):  
D. PANIGRAHI ◽  
S. CHATTERJEE ◽  
Y. Z. ZHANG
Keyword(s):  
Equations Of State ◽  
Equations Of Motion ◽  
Relative Magnitude ◽  
Matter Field ◽  
Smooth Transition ◽  
Accelerating Universe ◽  
De Sitter ◽  
Fifth Dimension ◽  
Higher Dimensional ◽  
New Interpretation

Homogeneous cosmological solutions are obtained in five-dimensional (5D) space–time assuming equations of state p = kρ and p1 = γρ where p is the isotropic 3-pressure and p1, that for the fifth dimension. Using different values for the constants k and γ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy by hand. We also extend a recent work of Mohammedi where using a special form of the extra dimensional scale factor a new interpretation of the higher dimensional equations of motion is given and the concept of an effective 4D pressure is introduced. Interestingly the 5D matter field remains regular while the effective negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Relevant to point out that in this case our cosmology apparently mimics the well-known quintessence scenario fuelled by a generalized Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter-like one takes place. Depending on the relative magnitude of the different constants appearing in our solutions we show that some of the cases are amenable to the desirable property of dimensional reduction.

MOSE FOR EUS-GUIDED PANCREATIC TISSUE ACQUISITION: THE THIRD WAY

2020 ◽  
Author(s):  
T Togliani ◽  
I Breoni ◽  
V Davì ◽  
N Mantovani ◽  
A Savioli ◽  
...  
Keyword(s):  
Pancreatic Tissue ◽  
Third Way ◽  
The Third ◽  
Tissue Acquisition

Overcoming “The Third Way” Concept

2006 ◽  
pp. 126-134
Author(s):  
L. Evstigneeva ◽  
R. Evstigneev
Keyword(s):  
Economic Research ◽  
Economic Uncertainty ◽  
Third Way ◽  
The Third ◽  
Linear Approach ◽  
The World ◽  
Non Linear

“The Third Way” concept is still widespread all over the world. Growing socio-economic uncertainty makes the authors revise the concept. In the course of discussion with other authors they introduce a synergetic vision of the problem. That means in the first place changing a linear approach to the economic research for a non-linear one.

Practical Truth

2018 ◽  
Author(s):  
David Charles
Keyword(s):  
Nicomachean Ethics ◽  
Third Way ◽  
The Third ◽  
Two Component ◽  
Major Competitor ◽  
Additional Support

This paper concerns Aristotle’s discussion of practical truth in Nicomachean Ethics VI.2.1139a17–b5. The essay falls into five sections. In the first three, I outline two styles of interpretation of Aristotle’s remarks and suggest that one of them (which I call ‘the third way’) gives a better reading than that offered by its major competitor (which I call ‘the two-component’ view). In the fourth I consider some texts in the remainder of NE VI which provide additional support for the third way of reading. In a brief concluding section, I seek to locate Aristotle’s view of practical truth, so understood, in a broader philosophical context.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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