scholarly journals Hyperbolic Motion in Gravitational Theories

1980 ◽  
Vol 33 (4) ◽  
pp. 757
Author(s):  
W Davidson
Keyword(s):  
General Relativity ◽  
Test Particle ◽  
High Speed ◽  
Equation Of Motion ◽  
Hyperbolic Motion ◽  
Speed Test ◽  
Gravitational Theories ◽  
Spherical Mass

The equation of motion of a high speed test particle in the field of a spherical mass is discussed for a parametric range of gravitational theories, including general relativity. It is shown how in principle such hyperbolic orbits may discriminate between these theories.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

Free Vibration Analysis for Thin Wire of Modern Wiresaw Between Sliced Wafers in Wafer Manufacturing Processes

2000 ◽  
Author(s):  
Songbin Wei ◽  
Imin Kao
Keyword(s):  
High Speed ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Manufacturing Processes ◽  
Thin Wire ◽  
Wire Vibration ◽  
The Wire ◽  
The Impact ◽  
Wafer Manufacturing ◽  
Impact Problem

Abstract In wiresaw manufacturing process where thin wire moving at high speed is pushed onto ingot to produce slices of wafer, the wire is constrained by two wafer walls as it slices into the ingot. In this paper, we investigate the vibration of such wire under the constraints of wafer walls. To address this problem, the model for wire vibration with impact to wafer walls is developed. The equation of motion is discretized using the Galerkin’s method. The principle of impulse and momentum is utilized to solve the impact problem. The results of analysis and simulation indicate that the response under a pointwise sinusoidal excitation is neither periodical nor symmetric with respect to the horizontal axis, due to the excitation from the impact. The wire vibration behavior is affected dramatically by the wafer wall constraints.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

scholarly journals Tactile Occupant Detection Sensor for Automotive Airbag

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5288
Author(s):  
Naveen Shirur ◽  
Christian Birkner ◽  
Roman Henze ◽  
Thomas M. Deserno
Keyword(s):  
High Speed ◽  
Tactile Sensors ◽  
Low Velocity ◽  
Speed Test ◽  
Multi Stage ◽  
The Matrix ◽  
Contact Data ◽  
Single Sensor ◽  
Matrix Sensor ◽  
Contact Position

Automotive airbags protect occupants from crash forces during severe vehicle collisions. They absorb energy and restrain the occupants by providing a soft cushion effect known as the restraint effect. Modern airbags offer partial restraint effect control by controlling the bag’s vent holes and providing multi-stage deployment. Full restraint effect control is still a challenge because the closed-loop restraint control system needs airbag–occupant contact and interaction feedback. In this work, we have developed novel single and matrix capacitive tactile sensors to measure the occupant’s contact data. They can be integrated with the airbag surface and folded to follow the dynamic airbag shape during the deployment. The sensors are tested under a low-velocity pendulum impact and benchmarked with high-speed test videos. The results reveal that the single sensor can successfully measure occupant–airbag contact time and estimate the area, while the contact position is additionally identified from the matrix sensor.

Rotordynamic Performance of a Shaft With Large Overhung Mass Supported by Foil Bearings

2016 ◽  
Vol 139 (4) ◽  
Author(s):  
Nguyen LaTray ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Foil Bearings ◽  
Speed Test ◽  
Foil Bearing ◽  
Stable Conditions ◽  
Bending Mode ◽  
Mode Vibration ◽  
Lift Off ◽  
Compact Design ◽  
Bearing System

This work presents the theoretical and experimental rotordynamic evaluations of a rotor–air foil bearing (AFB) system supporting a large overhung mass for high-speed application. The proposed system highlights the compact design of a single shaft rotor configuration with turbomachine components arranged on one side of the bearing span. In this work, low-speed tests up to 45 krpm are performed to measure lift-off speed and to check bearing manufacturing quality. Rotordynamic performance at high speeds is evaluated both analytically and experimentally. In the analytical approach, simulated imbalance responses are studied using both rigid and flexible shaft models with bearing forces calculated from the transient Reynolds equation along with the rotor motion. The simulation predicts that the system experiences small synchronous rigid mode vibration at 20 krpm and bending mode at 200 krpm. A high-speed test rig is designed to experimentally evaluate the rotor–air foil bearing system. The high-speed tests are operated up to 160 krpm. The vibration spectrum indicates that the rotor–air foil bearing system operates under stable conditions. The experimental waterfall plots also show very small subsynchronous vibrations with frequency locked to the system natural frequency. Overall, this work demonstrates potential capability of the air foil bearings in supporting a shaft with a large overhung mass at high speed.

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 ◽  
Vol 27 (06) ◽  
pp. 1841012 ◽  
Author(s):  
Victor Berezin ◽  
Vyacheslav Dokuchaev ◽  
Yury Eroshenko
Keyword(s):  
General Relativity ◽  
Weyl Tensor ◽  
Delta Function ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Gravitational Fields ◽  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

scholarly journals HOLLOWGRAPHY DRIVEN HOLOGRAPHY: BLACK HOLE WITH VANISHING VOLUME INTERIOR

2010 ◽  
Vol 19 (14) ◽  
pp. 2345-2351 ◽  
Author(s):  
AHARON DAVIDSON ◽  
ILYA GURWICH
Keyword(s):  
Phase Transition ◽  
General Relativity ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Schwarzschild Solution ◽  
Entropy Formula ◽  
Gravitational Theories ◽  
Hollow Interior ◽  
Spatial Volume ◽  
Self Similar

Hawking–Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one-parameter family degenerates) which takes place precisely at the would-have-been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel "hollow" interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called "hollowgraphy" driven holography.

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