scholarly journals SPIN-3/2 FERMIONS IN TWISTOR FORMALISM

2001 ◽  
Vol 16 (32) ◽  
pp. 2103-2113 ◽  
Author(s):  
MITSUO J. HAYASHI
Keyword(s):  
Twistor Space ◽  
Integrability Condition ◽  
Local Existence ◽  
Flat Space ◽  
Space Time ◽  
Necessary Condition ◽  
Field Equations ◽  
Weyl Spinor ◽  
Cartan Theory ◽  
The Right

Consistency conditions for the local existence of massless spin-3/2 fields have been explored to find the facts that the field equations for massless helicity-3/2 particles are consistent if the space–time is Ricci-flat, and that in Minkowski space–time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity-3/2 fields, we show in flat space–time that the charges of spin-3/2 fields, defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space–time that the (anti-)self-duality of the space–time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space–time to that with torsion (Einstein–Cartan theory), and investigate the consistency of existence of spin-3/2 fields in this theory. A simple solution to this consistency problem is found: The space–time has to be conformally (anti-)self-dual, left-(or right-) torsion-free. The integrability condition on α-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed torsion.

SOME NONCONFORMAL ACCELERATING PERFECT FLUID PLATES OF EMBEDDING CLASS 1 USING SIMILARITY TRANSFORMATIONS

2010 ◽  
Vol 25 (09) ◽  
pp. 1863-1879 ◽  
Author(s):  
Y. K. GUPTA ◽  
PRATIBHA ◽  
SACHIN KUMAR
Keyword(s):  
Perfect Fluid ◽  
Flat Space ◽  
Space Time ◽  
Explicit Solutions ◽  
Field Equations ◽  
Similarity Transformations ◽  
Higher Dimensional ◽  
Class 1 ◽  
Brane Theory ◽  
Respective Category

In view of renewed interest in the space–time embedded in higher-dimensional flat space which are useful in extrinsic gravity, string and brane theory, a set of six explicit solutions to Einstein's field equations for nonconformally flat accelerating and shearing perfect fluid plates is obtained using similarity transformations method by considering a five-dimensional flat metric. All the solutions thus obtained are analyzed physically. All the solutions are new in their respective category as far as authors are aware.

scholarly journals TACHYON MONOPOLE

2005 ◽  
Vol 20 (23) ◽  
pp. 5491-5499 ◽  
Author(s):  
XIN-ZHOU LI ◽  
DAO-JUN LIU
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Flat Space ◽  
Space Time ◽  
Global Monopole ◽  
Tachyon Field ◽  
Field Equations ◽  
Monopole Solution ◽  
Static Space

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.

Symmetries and conservation laws of some asymptotically symmetric spacetimes of interest in gravitational waves

2019 ◽  
Vol 16 (10) ◽  
pp. 1950152 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
B. B. I. Gadjagboui ◽  
Ghulam Shabbir
Keyword(s):  
Conservation Laws ◽  
Gravitational Waves ◽  
Flat Space ◽  
Einstein Equations ◽  
Necessary Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Symmetric Spacetimes ◽  
Flat Spacetimes

In this paper, we discuss symmetries and the corresponding conservation laws of certain exact solutions of the Einstein field equations (EFEs) representing a Schwarzschild black hole and gravitational waves in asymptotically flat space times. Of particular interest are symmetries of asymptotically flat spacetimes because they admit a property that identifies them for the existence of gravitational waves there. In the light of this fact, we discuss symmetry algebras of a few recently published solutions of Einstein equations in asymptotically flat metrics. Given the fact that gravitational waves are of great interest in relativity, we focus in this paper on finding the type of symmetries they admit and their corresponding conservation laws. We also show how these symmetries are radically different from the other well-known symmetries and present necessary condition that distinguishes them.

NON-MINIMAL COUPLING, VARIABLE SPEED OF LIGHT AND COSMOLOGY

2002 ◽  
Vol 17 (20) ◽  
pp. 2777-2777
Author(s):  
P. TEYSSANDIER
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Space Time ◽  
Variable Speed ◽  
Speed Of Light ◽  
Field Equations ◽  
Minimal Coupling ◽  
Structural Constant ◽  
Dimensional Space Time ◽  
Photon Gas

Presently, there exists some renewed interest in time varying speed of light theories as possible solutions of the major cosmological problems1. It is often believed that the local Lorentzian invariance is broken if the speed of light in a vacuum is not a constant. We point out that this belief is not necessarily founded and that a variable speed of light is perfectly consistent with general relativity under the assumption of non-minimal coupling between electromagnetism and curvature. Two kinds of arguments may be invoked in favour of such an assumption. First, a theorem due to Horndeski2 shows that in a four-dimensional space-time the Einstein-Maxwell field equations are not the only second-order vector potential field equations which stem from a Lagrangian scalar density, are consistent with the charge conservation and reduce to Maxwell's equations in a flat space-time (see also3). Second, according to QED4,5, vacuum polarization induces tidal gravitational effects which imply that photons propagating in a curved space-time have velocities exceeding the value of the "Lorentzian structural constant" c. The modified electromagnetic field equations given by Horndeski2 are studied here in the geometrical optics limit. Considering the case of Friedmann-Robertson-Walker cosmological models, we find the value of the speed of light as a function of the energetic content of the universe. We deduce from this result a new equation of state for a photon gas and we discuss the consequences of this equation on the evolution of the scale factor during the radiation-dominated era.

ON THE QUARTIC HIGHER-DERIVATIVE GRAVITATIONAL TERMS IN THE HETEROTIC SUPERSTRING THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 373-404 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Einstein Equations ◽  
Quadratic Term ◽  
Additional Contribution ◽  
Superstring Theory ◽  
Weyl Spinor ◽  
Higher Derivative

The quartic higher-derivative gravitational terms [Formula: see text] in the heterotic-superstring effective Lagrangian [Formula: see text], defined from the Riemann ten-tensor [Formula: see text], are expanded, after reduction to the conformally-flat physical D-space gij, in terms of the Ricci tensor Rij and scalar R. The resulting quadratic term [Formula: see text] is tachyon-free and agrees exactly with the prediction from global supersymmetry in the nonlinear realization of Volkov and Akulov of the flat-space, quadratic fermionic Lagrangian [Formula: see text] for a massless Dirac or Weyl spinor, only when D = 4, assuming the Einstein equation [Formula: see text] for the energy–momentum tensor. This proves that the heterotic superstring has to be reduced from ten to four dimensions if supersymmetry is to be correctly incorporated into the theory, and it rules out the bosonic string and type-II superstring, for which [Formula: see text] has the different a priori forms ±(R2-4RijRij) derived from [Formula: see text], which also contain tachyons (that seem to remain after the inclusion of a further contribution to [Formula: see text] from [Formula: see text]). The curvature of space–time introduces a mass into the Dirac equation, [Formula: see text], while quadratic, higher-derivative terms [Formula: see text] make an additional contribution to the Einstein equations, these two effects causing a difference between [Formula: see text] and [Formula: see text] on the one hand, and the predictions from [Formula: see text] and [Formula: see text] on the other. The quartic terms [Formula: see text] still possess some residual symmetry, however, enabling us to estimate the radius-squared of the internal six-dimensional space [Formula: see text] in units of the Regge slope-parameter α′ as B r ≈ 1.75, indicating that compactification occurs essentially at the Planck era, due to quantum mechanical processes, when the action evaluated within the causal horizon is S h ~ 1. This symmetry is also discussed with regard to the zero-action hypothesis. The dimensionality D = 4 of space–time is rederived from the Wheeler–DeWitt equation (Schrödinger equation) of quantum cosmology in the mini-superspace approximation, by demanding invariance and positive-semi-definiteness of the potential [Formula: see text] under Wick rotation of the time coordinate, which also determines the three-space to be flat, so that K = 0, and again involves the nonlinearity of gravitation.

Self-conjugate gravitational fields. I

1963 ◽  
Vol 275 (1361) ◽  
pp. 245-256 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Flat Space ◽  
Space Time ◽  
Second Order ◽  
Necessary Condition ◽  
Tensor Form ◽  
Gravitational Fields ◽  
Null Electromagnetic Field ◽  
Scalar Invariants

By splitting the curvature tensor R hijk into three 3-tensors of the second rank in a normal co-ordinate system, self-conjugate empty gravitational fields are defined in a manner analogous to that of the electromagnetic field. This formalism leads to three different types of self-conjugate gravitational fields, herein termed as types A, B and C . The condition that the gravitational field be self-conjugate of type A is expressed in a tensor form. It is shown that in such a field R hijk is propagated with the fundamental velocity and all the fourteen scalar invariants of the second order vanish. The structure of R hijk defines a null vector which can be identified as the vector defining the propagation of gravitational waves. It is found that a necessary condition for an empty gravitational field to be continued with a flat space-time across a null 3-space is that the field be self-conjugate of type A. The concept of the self-conjugate gravitational field is extended to the case when R ij # 0 but the scalar curvature R is zero. The condition in this case is also expressed in a tensor form. The necessary conditions that the space-time of an electromagnetic field be continued with an empty gravitational field or a flat space-time across a 3-space have been obtained. It is shown that for a null electromagnetic field whose gravitational field is self-conjugate of type A , all the fourteen scalar invariants of the second order vanish.

Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time

1962 ◽  
Vol 270 (1340) ◽  
pp. 103-126 ◽  
Keyword(s):  
Boundary Conditions ◽  
Gravitational Waves ◽  
Superposition Principle ◽  
Flat Space ◽  
Space Time ◽  
Axially Symmetric ◽  
Field Equations ◽  
Spatial Infinity ◽  
Metric Tensor ◽  
Gravitational Fields

Gravitational fields containing bounded sources and gravitational radiation are examined by analyzing their properties at spatial infinity. A convenient way of splitting the metric tensor and the Einstein field equations, applicable in any space-time, is first introduced. Then suitable boundary conditions are set. The group of co-ordinate transformations that preserves the boundary conditions is analyzed. Different possible gravitational fields are characterized intrinsically by a combination of (i) characteristic initial data, and (ii) Dirichlet data at spatial infinity. To determine a particular solution one must specify four functions of three variables and three functions of two variables; these functions are not subject to constraints. A method for integrating the field equations is given; the asymptotic behaviour of the metric and Riemann tensors for large spatial distances is analyzed in detail; the dynamical variables of the radiation modes are exhibited; and a superposition principle for the radiation modes of the gravitational field is suggested. Among the results are: (i) the group of allowed co-ordinate transformations contains the inhomogeneous orthochronous Lorentz group as a subgroup; (ii) each of the five leading terms in an asymptotic expansion of the Riemann tensor has the algebraic structure previously predicted from analyzing the Petrov classification; (iii) gravitational waves appear to carry mass away from the interior; (iv) time-dependent periodic solutions of the field equations which obey the stated boundary conditions do not exist. It was found that the general fields studied in the present work are in many ways very similar to the axially symmetric fields recently studied by Bondi, van der Burg & Metzner.

scholarly journals Agency and the Successive Structure of Time-Consciousness

Erkenntnis ◽  
2021 ◽  
Author(s):  
Camden Alexander McKenna
Keyword(s):  
Temporal Structure ◽  
Basic Structure ◽  
The Self ◽  
Necessary Condition ◽  
Epistemic Status ◽  
Mental Attitude ◽  
Time Consciousness ◽  
Possibility Space ◽  
The Right ◽  
Wrong Sort

AbstractI argue for constraining the nomological possibility space of temporal experiences and endorsing the Succession Requirement for agents. The Succession Requirement holds that the basic structure of temporal experience must be successive for agentive subjects, at least in worlds that are law-like in the same way as ours. I aim to establish the Succession Requirement by showing non-successively experiencing agents are not possible for three main reasons, namely that they (1) fail to stand in the right sort of causal relationship to the outcomes of their actions, (2) exhibit the wrong sort of epistemic status for agency, and (3) lack the requisite agentive mental attitude of intentionality. I conclude that agency is incompatible with non-successive experience and therefore we should view the successive temporal structure of experience as a necessary condition for agency. I also suggest that the Succession Requirement may actually extend beyond my main focus on agency, offering preliminary considerations in favor of seeing successive experience as a precondition for selfhood as well. The consequences of the Succession Requirement are wide-ranging, and I discuss various implications for our understanding of agency, the self, time consciousness, and theology, among other things.

Tail asymptotics of an infinitely divisible space-time model with convolution equivalent Lévy measure

2021 ◽  
Vol 58 (1) ◽  
pp. 42-67 ◽  
Author(s):  
Mads Stehr ◽  
Anders Rønn-Nielsen
Keyword(s):  
Space Time ◽  
Time Interval ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Time Model ◽  
Spatial Object ◽  
Tail Behaviour ◽  
Fixed Radius ◽  
The Right ◽  
Space Time Model

AbstractWe consider a space-time random field on ${{\mathbb{R}^d} \times {\mathbb{R}}}$ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.

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