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### Can a Gravitational Lens Magnify Gravity? Theoretical Considerations and a Possible Solar System Test

Robert J. Nemiroff

Can Gravity Magnify Gravity?

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.

Can Gravity Magnify Gravity?

- Yes
- Reasons that gravity might be able to magnify gravity
- Gravity can magnify light (called “gravitational lensing”)
- General Relativistic (GR) gravity is known to be self-interacting
- PPN beta parameter measured to be not zero
- First order effect is very small -- might have gone unnoticed
- Speed of gravity not uniquely determined -- might be c
- String theory (M-theory, etc.) background not uniquely determined -- might not be “flat”
- If spacetime is truly curved -- shouldn’t everything including virtual particles have to negotiate that curvature?

Can Gravity Magnify Gravity?

- No
- Reasons that gravity might not be able to magnify gravity
- Newtonian gravity has infinite speed
- Some general relativity (GR) advocates think GR says “no”, but the calculation is difficult and, so far, no one has proven it.
- If yes, some believe that perpetual motion machines might be allowed, although this also has not been proven.
- Many particle physics calculations are done on a “flat background” meaning that virtual particles feel no gravity.
- If yes, there might be some sign of this out in the universe, although so far no one has been able to think of a visible effect.

Can Gravity Magnify Gravity?

Pick One

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.

Can Gravity Magnify Gravity?

Our Sun as a Gravitational Lens

Focal length of transparent Sun: ~25 AU

Focal length of opaque Sun : ~550 AU

Can Gravity Magnify Gravity?

Gravitational Hollows

* 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.

Can Gravity Magnify Gravity?

How to see our Sun’s gravitational hollows at 25 AU:

Place a satellite at 25 AU opposite a nearby star and look for:

- Slightly high gravitational acceleration for satellites in a hollow toward the Sun: a/a.
- Slightly high gravitational redshift of light emitted from a hollow: /.
- Slight time delay tdrift for signals traversing a hollow.

For nearby stars, the magnitude of all of these effects is now within the realm of present day Earth-laboratory experiments.

Can Gravity Magnify Gravity?

* 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.

Can Gravity Magnify Gravity?

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 .

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