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In weak lensing by large-scale structure, the thin-lens approximation may break down, and low-density extended structures may not be well approximated by multiple thin-lens planes. In this case, the deflection can be derived by instead assuming that the gravitational potential is slowly varying everywhere (for this reason, this approximation is ...
In 2009, weak gravitational lensing was used to extend the mass-X-ray-luminosity relation to older and smaller structures than was previously possible to improve measurements of distant galaxies. [29] As of 2013 the most distant gravitational lens galaxy, J1000+0221, had been found using NASA's Hubble Space Telescope.
When density and gravity are approximately constant (that is, for relatively small changes in height), simply multiplying height difference, gravity, and density will yield a good approximation of pressure difference. If the pressure at one point in a liquid with uniform density ρ is known to be P 0, then the pressure at another point is P 1:
The key difference between an embedded lens and a traditional lens is that the mass of a standard lens contributes to the mean of the cosmological density, whereas that of an embedded lens does not. Consequently, the gravitational potential of an embedded lens has a finite range, i.e., there is no lensing effect outside of the void.
TeVeS has enjoyed some success in making contact with gravitational lensing and structure formation observations, [81] but faces problems when confronted with data on the anisotropy of the cosmic microwave background, [82] the lifetime of compact objects, [83] and the relationship between the lensing and matter overdensity potentials. [84]
The air's motion is affected by the pressure differences, but the existence of the pressure differences depends on the air's motion. The relationship is thus a mutual, or reciprocal, interaction: Air flow changes speed or direction in response to pressure differences, and the pressure differences are sustained by the air's resistance to ...
This temperature inversion is the opposite of what is normally the case; air is usually warmer close to the surface, and cooler higher up. In calm weather, a layer of significantly warmer air can rest over colder dense air, forming an atmospheric duct which acts like a refracting lens, producing a series of both inverted and erect images.
Strong gravitational lensing is a gravitational lensing effect that is strong enough to produce multiple images, arcs, or Einstein rings. Generally, for strong lensing to occur, the projected lens mass density must be greater than the critical density, that is . For point-like background sources, there will be multiple images; for extended ...