scholarly journals From bending of light to positive mass: A non-PDE perspective

2021 ◽  
Vol 62 (6) ◽  
pp. 062503
Author(s):  
Xiaokai He ◽  
Xiaoning Wu ◽  
Naqing Xie
Keyword(s):  
Positive Mass ◽  
Bending Of Light

scholarly journals Gamma Astrometric Measurement Experiment: testing General Relativity with a small mission

2007 ◽  
Vol 3 (S248) ◽  
pp. 290-291 ◽  
Author(s):  
A. Vecchiato ◽  
M. G. Lattanzi ◽  
M. Gai ◽  
R. Morbidelli
Keyword(s):  
General Relativity ◽  
Solar Eclipse ◽  
Galactic Center ◽  
The Sun ◽  
Measurement Experiment ◽  
The One ◽  
First Time ◽  
Bending Of Light

AbstractGAME (Gamma Astrometric Measurement Experiment) is a concept for an experiment whose goal is to measure from space the γ parameter of the Parameterized Post-Newtonian formalism, by means of a satellite orbiting at 1 AU from the Sun and looking as close as possible to its limb. This technique resembles the one used during the solar eclipse of 1919, when Dyson, Eddington and collaborators measured for the first time the gravitational bending of light. Simple estimations suggest that, possibly within the budget of a small mission, one could reach the 10−6level of accuracy with ~106observations of relatively bright stars at about 2° apart from the Sun. Further simulations show that this result could be reached with only 20 days of measurements on stars ofV≤ 17 uniformly distributed. A quick look at real star densities suggests that this result could be greatly improved by observing particularly crowded regions near the galactic center.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

scholarly journals The Jang Equation and the Positive Mass Theorem in the Asymptotically Hyperbolic Setting

2021 ◽  
Author(s):  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Spatial Dimension ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic ◽  
Jang Equation

AbstractWe solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

The history of the core dynamos of Mars and the Moon inferred from their crustal magnetization: a brief review

2019 ◽  
Vol 56 (9) ◽  
pp. 917-931
Author(s):  
Jafar Arkani-Hamed
Keyword(s):  
The Moon ◽  
Positive Mass ◽  
Polar Wander ◽  
The Core ◽  
True Polar Wander ◽  
History Of ◽  
Giant Impacts ◽  
Crustal Magnetization ◽  
Multiple Impact ◽  
Thermochemical Convection

The core dynamos of Mars and the Moon have distinctly different histories. Mars had no core dynamo at the end of accretion. It took ∼100 Myr for the core to create a strong dynamo that magnetized the martian crust. Giant impacts during 4.2–4.0 Ga crippled the core dynamo intermittently until a thick stagnant lithosphere developed on the surface and reduced the heat flux at the core–mantle boundary, killing the dynamo at ∼3.8 Ga. On the other hand, the Moon had a strong core dynamo at the end of accretion that lasted ∼100 Myr and magnetized its primordial crust. Either precession of the core or thermochemical convection in the mantle or chemical convection in the core created a strong core dynamo that magnetized the sources of the isolated magnetic anomalies in later times. Mars and the Moon indicate dynamo reversals and true polar wander. The polar wander of the Moon is easier to explain compared to that of Mars. It was initiated by the mass deficiency at South Pole Aitken basin, which moved the basin southward by ∼68° relative to the dipole axis of the core field. The formation of mascon maria at later times introduced positive mass anomalies at the surface, forcing the Moon to make an additional ∼52° degree polar wander. Interaction of multiple impact shock waves with the dynamo, the abrupt angular momentum transfer to the mantle by the impactors, and the global overturn of the core after each impact were probably the factors causing the dynamo reversal.

scholarly journals Ocean-driven thinning enhances iceberg calving and retreat of Antarctic ice shelves

2015 ◽  
Vol 112 (11) ◽  
pp. 3263-3268 ◽  
Author(s):  
Yan Liu ◽  
John C. Moore ◽  
Xiao Cheng ◽  
Rupert M. Gladstone ◽  
Jeremy N. Bassis ◽  
...  
Keyword(s):  
Mass Loss ◽  
Mass Balance ◽  
Climate Forcing ◽  
Empirical Estimate ◽  
Positive Mass ◽  
Ice Shelves ◽  
Total Mass Loss ◽  
Rapid Changes ◽  
Iceberg Calving ◽  
Ice Sheet Mass Balance

Iceberg calving from all Antarctic ice shelves has never been directly measured, despite playing a crucial role in ice sheet mass balance. Rapid changes to iceberg calving naturally arise from the sporadic detachment of large tabular bergs but can also be triggered by climate forcing. Here we provide a direct empirical estimate of mass loss due to iceberg calving and melting from Antarctic ice shelves. We find that between 2005 and 2011, the total mass loss due to iceberg calving of 755 ± 24 gigatonnes per year (Gt/y) is only half the total loss due to basal melt of 1516 ± 106 Gt/y. However, we observe widespread retreat of ice shelves that are currently thinning. Net mass loss due to iceberg calving for these ice shelves (302 ± 27 Gt/y) is comparable in magnitude to net mass loss due to basal melt (312 ± 14 Gt/y). Moreover, we find that iceberg calving from these decaying ice shelves is dominated by frequent calving events, which are distinct from the less frequent detachment of isolated tabular icebergs associated with ice shelves in neutral or positive mass balance regimes. Our results suggest that thinning associated with ocean-driven increased basal melt can trigger increased iceberg calving, implying that iceberg calving may play an overlooked role in the demise of shrinking ice shelves, and is more sensitive to ocean forcing than expected from steady state calving estimates.

NUMERICAL STUDY OF THE INTERACTION BETWEEN POSITIVE AND NEGATIVE MASS OBJECTS IN GENERAL RELATIVITY

2012 ◽  
Vol 21 (07) ◽  
pp. 1250061 ◽  
Author(s):  
ZHOUJIAN CAO
Keyword(s):  
Boundary Condition ◽  
General Relativity ◽  
Numerical Study ◽  
Naked Singularity ◽  
Newtonian Limit ◽  
Computational Domain ◽  
Positive Mass ◽  
Negative Mass ◽  
Mass Particle ◽  
Causal Property

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

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