Can a Gravitational Lens Magnify Gravity? Theoretical Considerations and a Possible Solar System Test. Robert J. Nemiroff. Can Gravity Magnify Gravity?.
Can a Gravitational Lens Magnify Gravity? Theoretical Considerations and a Possible Solar System Test
Robert J. Nemiroff
Abstract: Can a gravitational lens magnify gravity? The possibility has interesting theoretical implications on everything from string theories (is the background metric flat?) to the nature of spacetime near black holes (can virtual particles just ignore a black hole?). Leading theories of gravity likely indicate no magnification, but the effect might be testable by using our Sun as a gravitational lens and carefully aligning a satellite past the minimum transparent focal distance of about 25 AU. Here the magnitude of a maximal effect is estimated and found potentially observable.
In Press: ApJ 1 August 2005, v628.
Yes, GR is a non-linear theory and the two body problem is notoriously complex. Nevertheless, which is the better approximation?
* A mass near a black hole has a cloud of associated virtual particles that effectively ignore the black hole. Virtual particle trajectories are straight lines that can go right through the event horizon -- both in and out -- no problem. This is the extreme case of gravity not being able to magnify gravity.
* A mass near a black hole has a cloud of virtual particles that travel only on null geodesics (like photons), creating a region on the far side of the black hole where geodesics not only cross but converge, resulting in a region of relatively high “magnified” gravity.
Our Sun as a Gravitational Lens
Focal length of transparent Sun: ~25 AU
Focal length of opaque Sun : ~550 AU
* If gravity can magnify gravity, then gravitational hollows should exist where gravity is magnified proportionally to gravitationally lensed light. This is called a “hollow” because it might seem to some additional gravitation mass is there, but the area is actually empty -- hollow.
* Gravitational hollows would exist from the minimal focal point of a transparent object all the way to infinity.
* Each massive object creates a long thin gravitational hollow on the far side of every other massive object.
How to see our Sun’s gravitational hollows at 25 AU:
Place a satellite at 25 AU opposite a nearby star and look for:
For nearby stars, the magnitude of all of these effects is now within the realm of present day Earth-laboratory experiments.
* A gravitational hollow should not be considered a created region of new gravity, but rather an angular redistribution of already existing gravity. In other words, the excess gravity felt by a mass inside a gravitational hollow is made up for by a very slightly decreased gravity felt by all other masses outside the hollow.
* Four spacecraft are already outside 25 AU, the minimum focal length of the transparent Sun. These are the two Pioneer and two Voyager spacecraft launched by NASA last century. The existence of these spacecraft may be taken as demonstrations that it is already technologically possible to reach the minimum focal distance of the transparent Sun.
Acknowledgements: I would like to acknowledge useful comments from Kenneth Nordtvedt, Amos Ori, Christ Ftaclas, Kent Wood, John Wallin, Bijunath Patla, and an anonymous ApJ referee.
A paper similar to this poster will appear in an August 2005 edition of the Astrophysical Journal, and is currently downloadable from this web address: http://arxiv.org/abs/astro-ph/0502360 .