GRAVITY IN CURVED PHASE-SPACES, FINSLER GEOMETRY AND TWO-TIMES PHYSICS

2012 ◽  
Vol 27 (12) ◽  
pp. 1250069 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Phase Space ◽  
Tangent Bundle ◽  
Finsler Geometry ◽  
Space Time ◽  
Vacuum Field ◽  
Field Equations ◽  
Problem Of Time ◽  
Gravitational Field Equations ◽  
Cotangent Space ◽  
Kaluza Klein

The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TMd-1, 1(T*Md-1, 1) of a d-dim space–time Md-1, 1 are investigated following the strict distinguished d-connection formalism of Lagrange–Finsler and Hamilton–Cartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in space–times of 2d dimensions, with two times, after a d+d Kaluza–Klein-like decomposition of the 2d-dim scalar curvature R is performed and involving the introduction of a nonlinear connection [Formula: see text]. The physical applications of the 4-dim phase space metric solutions found in this work, corresponding to the cotangent space of a 2-dim space–time, deserve further investigation. The physics of two times may be relevant in the solution to the problem of time in quantum gravity and in the explanation of dark matter. Finding nontrivial solutions of the generalized gravitational field equations corresponding to the 8-dim cotangent bundle (phase space) of the 4-dim space–time remains a challenging task.

scholarly journals THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

2010 ◽  
Vol 25 (08) ◽  
pp. 1661-1698 ◽  
Author(s):  
ANZHONG WANG ◽  
N. O. SANTOS
Keyword(s):  
String Theory ◽  
Matter Field ◽  
Newtonian Potential ◽  
Field Equations ◽  
Hierarchy Problem ◽  
Large Extra Dimension ◽  
Gravitational Field Equations ◽  
Spatial Dimensions ◽  
Derivatives Of ◽  
Kaluza Klein

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

scholarly journals Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Sanjay Oli
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Space Time ◽  
Time Dependent ◽  
Field Equations ◽  
Current Observation ◽  
Kinematical Parameters ◽  
Kaluza Klein

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

Geodesic Correspondence in the Brans-Dicke Theory

1975 ◽  
Vol 18 (1) ◽  
pp. 151-153 ◽  
Author(s):  
B. O. J. Tupper
Keyword(s):  
Ricci Tensor ◽  
Recent Article ◽  
Space Time ◽  
Vacuum Field ◽  
Field Equations ◽  
All Solutions

In a recent article [1] vacuum field solutions of the Brans-Dicke [2] field equations were found, the space-time metric in each solution being of the Friedmann type. Most of these solutions existed only for specific values of the parameter ω and, in particular, the two largest sets of solutions corresponded to the values and . Peters [3, 4] has shown that when all solutions of the Brans-Dicke vacuum equations are conformai to space-times with vanishing Ricci tensor. The purpose of this note is to investigate the possible geometric consequences of the value .

scholarly journals Quantum Theory of Gravitation

1998 ◽  
Vol 51 (3) ◽  
pp. 459
Author(s):  
H. S. Green
Keyword(s):  
Quantum Theory ◽  
Wave Equations ◽  
Algebraic Method ◽  
Empty Space ◽  
Space Time ◽  
Field Equations ◽  
Gauge Groups ◽  
Gravitational Field Equations ◽  
Non Euclidean Geometry ◽  
Curvature Tensors

It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.

scholarly journals New Solutions of Einstein Equations Representing Spinning Masses

1974 ◽  
Vol 64 ◽  
pp. 191-191
Author(s):  
Humitaka Sato ◽  
Akira Tomimatsu
Keyword(s):  
Exact Solutions ◽  
Event Horizon ◽  
Equatorial Plane ◽  
Space Time ◽  
Einstein Equations ◽  
Vacuum Field ◽  
Kerr Metric ◽  
Field Equations ◽  
Asymptotically Flat

We found new, stationary axisymmetric, asymptotically flat exact solutions to Einstein's vacuum field equations, which are classified by an integer δ and Kerr metric is the solution of δ = 1. The number of ring singularity on the equatorial plane is δ. The odd δ metrices contain the surfaces of event horizon but the even δ metrices do not. Except the Kerr metric, however, the space-time becomes singular at the poles on these surfaces.

scholarly journals KALUZA - KLEIN COSMOLOGICAL MODEL WITH QUARK AND STRANGE QUARK MATTER INF(R,T)GRAVITY

2021 ◽  
Vol 9 (04) ◽  
pp. 264-271
Author(s):  
Samadhan L. Munde ◽  
Keyword(s):  
Cosmological Model ◽  
Quark Matter ◽  
Deceleration Parameter ◽  
Strange Quark ◽  
Space Time ◽  
Strange Quark Matter ◽  
Field Equations ◽  
Constant Deceleration Parameter ◽  
General Solutions ◽  
Kaluza Klein

In this paper,Kaluza-Klein space-time with quark and strange quark matter in gravity has been considered. The general solutions of the field equations of Kaluza-Klein space-time have been obtained under the assumption of constant deceleration parameter. The physical and geometrical aspects of the model are also discussed in details.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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