The equations of motion in a conformally invariant theory of gravitation and electromagnetism

1982 ◽  
Vol 70 (2) ◽  
pp. 259-267 ◽  
Author(s):  
D. Gregorash ◽  
G. Papini
Keyword(s):  
Invariant Theory ◽  
Equations Of Motion ◽  
Conformally Invariant ◽  
Theory Of Gravitation

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals Einstein gravity as a 3D conformally invariant theory

2011 ◽  
Vol 28 (4) ◽  
pp. 045005 ◽  
Author(s):  
Henrique Gomes ◽  
Sean Gryb ◽  
Tim Koslowski
Keyword(s):  
Invariant Theory ◽  
Einstein Gravity ◽  
Conformally Invariant

scholarly journals WIGGLY STRINGS IN LINEARIZED BRANS–DICKE GRAVITY

2000 ◽  
Vol 15 (21) ◽  
pp. 1369-1375 ◽  
Author(s):  
ANDRÉS ARAZI ◽  
CLAUDIO SIMEONE
Keyword(s):  
Linear Approximation ◽  
Cosmic String ◽  
Light Propagation ◽  
Equations Of Motion ◽  
Theory Of Gravitation

The metric around a wiggly cosmic string is calculated in the linear approximation of Brans–Dicke theory of gravitation. The equations of motion for relativistic and nonrelativistic particles in this metric are obtained. Light propagation is also studied and it is shown that photon trajectories can be bounded.

CONFORMALLY INVARIANT FIELD THEORY IN TWO DIMENSIONS AND STRINGS IN CURVED SPACETIME

1988 ◽  
Vol 03 (08) ◽  
pp. 1759-1846 ◽  
Author(s):  
SANJAY JAIN
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Virasoro Algebra ◽  
Functional Integral ◽  
Two Dimensions ◽  
Intrinsic Metric ◽  
Existence Of A Solution ◽  
Conformally Invariant ◽  
Brst Charge ◽  
Spacetime Metric

The formalism of conformally invariant field theory on a 2-dimensional real manifold with an intrinsic metric is developed in the functional integral framework. This formalism is used to study the relationships between reparametrization, Weyl, conformal and BRST invariances for strings in generic backgrounds. Conformal invariance of string amplitudes in the presence of backgrounds is formulated in terms of the Virasoro conditions, i.e., that physical vertex operators generate (1,1) representations of the Virasoro algebra, or, equivalently, the condition Q|Ψ〉=0 on physical states |Ψ〉, where Q is the BRST charge. The consequences of these conditions are investigated in the case of specific backgrounds. Strings in group manifolds are discussed exactly. For a generic slowly varying spacetime metric and dilaton field, a perturbatively renormalized vertex operator solution to the Virasoro conditions is constructed. It is shown that the existence of a solution to the Virasoro conditions or the equation Q|Ψ〉=0 requires the spacetime metric to satisfy Einstein’s equations. These conditions therefore constitute equations of motion for both the spectrum and backgrounds of string theory.

CRITICAL BEHAVIOR IN TWO-DIMENSIONAL QUANTUM GRAVITY AND EQUATIONS OF MOTION OF THE STRING

1990 ◽  
Vol 05 (11) ◽  
pp. 799-813 ◽  
Author(s):  
SUMIT R. DAS ◽  
AVINASH DHAR ◽  
SPENTA R. WADIA
Keyword(s):  
Equations Of Motion ◽  
Two Dimensions ◽  
Target Space ◽  
Two Dimensional ◽  
Minimal Models ◽  
Conformally Invariant ◽  
Motion Time ◽  
Dynamical Degree ◽  
Renormalization Group Equations

We show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. We discuss an example of such a trajectory in the space containing the c < 1 minimal models. We also discuss the connection between this work and the recent attempts to construct non-perturbative string theories based on matrix models.

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