scholarly journals Curvature Tensor of the Stationary Accelerated Frame in Gravity Field

2021 ◽  
Author(s):  
Sangwha Yi

We define an accelerated frame that moves along rˆ -axis in the general relativistic curved space-time. We then calculate the curvature tensor of this accelerated frame in the stationary gravity field. The curvature tensor is divided into two parts: the curvature tensor as observed by the observer and the curvature tensor of the observer’s own planet in the gravity field.

2021 ◽  
Vol 13 (1) ◽  
pp. 43-54
Author(s):  
Horia DUMITRESCU ◽  
Vladimir CARDOS ◽  
Radu BOGATEANU

The gravity or reactive bundle energy is the outlet of the morphogenetic impact, known as “BIG BANG”, creating a bounded ordered/structured universe along with the solar system, including the EARTH-world with its human race. Post-impact, the huge kinetic energy is spread into stellar bodies associated with the light flux under strong mutual connections or gravitational bundle. Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures. Gravity according to the curved space-time theory is not seen as a gravitational force, but it manifests itself in the relativistic form of the space-time curvature needing the constancy of the light speed. But the constant light velocity makes the tidal wave/pulsating energy, a characteristic of solar energy, impossible. The Einstein’s field equation, expressed in terms of tensor formulation along with the constant light speed postulate, needs two special space-time tensors (curvature and torsion) in 4 dimensions, where for the simplicity the torsion/twist tensor is less well approximated (Bianchi identity) leading to a constant/frozen gravity (twist-free gravity).The non-zero torsion tensor plays a significant physical role in the planetary dynamics as a finest gear of a planet, where its spinning rotation is directly connected to the own work and space-time structure (or clock), controlled by light fluctuations (or tidal effect of gravity). The spin correction of Einstein’s gravitational field refers to the curvature-torsion effect coupled with fluctuating light speed. The mutual curvature-torsion bundle self-sustained by the quantum fluctuations of light speed engenders helical gravitational wave fields of a quantum nature where bodies orbit freely in the light speed field (cosmic wind). In contrast to the Einstein’s field equation describing a gravitational frozen field, a quantum tidal gravity model is proposed in the paper.


2019 ◽  
Vol 32 (3) ◽  
pp. 282-291 ◽  
Author(s):  
Ole Keller ◽  
Lee M. Hively

Jiménez and Maroto [Phys. Rev. D 83, 023514 (2011)] predicted free-space, longitudinal electrodynamic waves in curved space-time, if the Lorenz condition is relaxed. A general-relativistic extension of Woodside’s electrodynamics [Am. J. Phys. 77, 438 (2009)] includes a dynamical, scalar field in both the potential- and electric/magnetic-field formulations without mixing the two. We formulate a longitudinal-wave theory, eliminating curvature polarization, magnetization density, and scalar field in favor of the electric/magnetic fields and the metric tensor. We obtain a wave equation for the longitudinal electric field for a spatially flat, expanding universe with a scale factor. This work is important, because: (i) the scalar- and longitudinal-fields do not cancel, as in classical quantum electrodynamics; and (ii) this new approach provides a first-principles path to an extended quantum theory that includes acceleration and gravity.


2019 ◽  
Vol 491 (4) ◽  
pp. 4807-4815
Author(s):  
M Mościbrodzka

ABSTRACT We present radpol – a numerical scheme for integrating multifrequency polarized radiative transfer equations along rays propagating in a curved space–time. The scheme includes radiative processes such as synchrotron emission, absorption, Faraday rotation, and conversion, and, for the first time, relativistic Compton scatterings including effects of light polarization. The scheme is fully covariant and is applicable to model radio-γ-ray emission and its polarization from, e.g. relativistic jets and accretion flows on to black holes and other exotic objects described in alternative metric theories and modelled semi-analytically or with time-dependent magnetohydrodynamical simulations. We perform a few tests to validate the implemented numerical algorithms that handle light polarization in curved space–time. We demonstrate application of the scheme to model broad-band emission spectra from a relativistically hot, geometrically thick coronal-like inflow around a supermassive black hole where the disc model is realized in a general relativistic magnetohydrodynamical simulation.


1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.


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