Solution to Einstein's Field Equation?

[McC]

From Slashdot/PhysOrg

New antigravity solution will enable space travel near speed of light by the end of this century, he predicts.

On Tuesday, Feb. 14, noted physicist Dr. Franklin Felber will present his new exact solution of Einstein's 90-year-old gravitational field equation to the Space Technology and Applications International Forum (STAIF) in Albuquerque. The solution is the first that accounts for masses moving near the speed of light.

Felber's antigravity discovery solves the two greatest engineering challenges to space travel near the speed of light: identifying an energy source capable of producing the acceleration; and limiting stresses on humans and equipment during rapid acceleration.

"Dr. Felber's research will revolutionize space flight mechanics by offering an entirely new way to send spacecraft into flight," said Dr. Eric Davis, Institute for Advanced Studies at Austin and STAIF peer reviewer of Felber's work. "His rigorously tested and truly unique thinking has taken us a huge step forward in making near-speed-of-light space travel safe, possible, and much less costly."

The field equation of Einstein's General Theory of Relativity has never before been solved to calculate the gravitational field of a mass moving close to the speed of light. Felber's research shows that any mass moving faster than 57.7 percent of the speed of light will gravitationally repel other masses lying within a narrow 'antigravity beam' in front of it. The closer a mass gets to the speed of light, the stronger its 'antigravity beam' becomes.

Felber's calculations show how to use the repulsion of a body speeding through space to provide the enormous energy needed to accelerate massive payloads quickly with negligible stress. The new solution of Einstein's field equation shows that the payload would 'fall weightlessly' in an antigravity beam even as it was accelerated close to the speed of light.

Accelerating a 1-ton payload to 90 percent of the speed of light requires an energy of at least 30 billion tons of TNT. In the 'antigravity beam' of a speeding star, a payload would draw its energy from the antigravity force of the much more massive star. In effect, the payload would be hitching a ride on a star.

"Based on this research, I expect a mission to accelerate a massive payload to a 'good fraction of light speed' will be launched before the end of this century," said Dr. Felber. "These antigravity solutions of Einstein's theory can change our view of our ability to travel to the far reaches of our universe."

More immediately, Felber's new solution can be used to test Einstein's theory of gravity at low cost in a storage-ring laboratory facility by detecting antigravity in the unexplored regime of near-speed-of-light velocities.

During his 30-year career, Dr. Felber has led physics research and development programs for the Army, Navy, Air Force, and Marine Corps, the Defense Advanced Research Projects Agency, the Defense Threat Reduction Agency, the Department of Energy and Department of Transportation, the National Institute of Justice, National Institutes of Health, and national laboratories. Dr. Felber is Vice President and Co-founder of Starmark.

[Kuroneko]

This is quite perplexing. Solutions to the field equation are spacetimes--the fact that a test particle is relativistic relative to the source body is quite irrelevant as far as the field equation is concerned. Even in ordinary Schwarzschild spacetime (as basic it it gets), the fact that giving a particle a large Lorentz boost causes apparent antigravity is well-known. In fact, this happens naturally for freefall as acceleration is apparently negative in the region between the Schwarzschild radius R and 3/2R for a particle freefalling from rest at infininity (a nice solution for any apogee is also possible). That's actually quite sensible--no external observer will see the particle cross the event horizon, so negative acceleration should be observed.

I don't know what it is that Dr. Felber actually computed. Perhaps he genuinely found something interesting by considering more general trajectories. However, I feel very confident in saying that the press report above is at best a silly distortion.

[Molyneux]

...could someone please translate that into layman?

[sketerpot]

...could someone please translate that into layman?

"Science is cool, and something especially cool may have happened. Don't hold your breath, though."

How's that?

[Kuroneko]

This whole thing looks more and more suspicious. Under radial motion in Schwarzschild spacetime, dθ = dφ = 0, so the metric is simply dτ² = Adt² - dr²/A, where A = (r-2m)/r. A particle in freefall must also obey the equation A dt/dτ = k, where k is some parameter dictated by initial conditions. If the particle has speed v at infinity, k = (1-v²)^{-1/2}, as can be seen by substituting back into the metric. Furthermore, combing the two equations gives dr/dt = -A[1-A/k²]^{1/2}, which can be differentiated to obtain d²r/dt² = A[m/r²][3A/k²-2].

Or: d²r/dt² = A[m/r²][3A(1-v²)-2]. Note how the sign behaves at v < 1/√3 and v > 1/√3 (A→1 as r→∞), i.e., changes at about 57.7% of lightspeed at infinity--suspiciously identical to the reported result! None of the above is anything new. Calculating dr/dt in this manner is an approach to deriving the Eddington-Finkelstein coordinates commonly found in relativity textbooks. For example, much of the above are exercises in d'Inverno's Introducing General Relativity.

...could someone please translate that into layman?

The kindest interpretation of the above article would therefore be that Dr. Felber generalized a well-known result to arbitrary trajectories instead of just radial ones. This would be noteworthy (I haven't seen an arbitrary-trajectory result before), but if so, the article distorts the facts almost to the point of silliness.

[Surlethe]

...could someone please translate that into layman?

I do believe Kuroneko (if I am correct in determining the thrust of your post) is saying a particle's antigravity effects isn't a solution of the field equations, and that antigravity effects are already well-known in the classic General Relativity. Then, he goes on to say that it makes sense that a particle would seem to be acted on by antigravity as it's falling into a black hole, because an observer would never see it cross the event horizon, so he would see it slow down and seem to stop.

[Kuroneko]

Small update: I'm having a discussion elsewhere on this topic, which only solidified my initial belief that this is nowhere as revolutionary as the article implies, and that someone was getting much too imaginative. Dr. Felber's paper (gr-qc/0505099) makes the careful qualifier of an "inertial observer far away from the interaction from the source and payload". Now, Dr. Felber prefers to think of the source of the gravitating body as moving, but since only relative velocities are important, it really doesn't matter if the body is rushing towards the payload or the payload rushing towards the body.

From that perspective, let me reiterate and clarify the following:

Then, he goes on to say that it makes sense that a particle would seem to be acted on by antigravity as it's falling into a black hole, because an observer would never see it cross the event horizon, so he would see it slow down and seem to stop.

Now, there is a reason I've put the qualifier "apparent" before "antigravity" in my first post of this thread, and that's simply because it's not antigravity in any meaningful sense. Let's take an object in freefall into a Schwarzschild black hole. In Schwarzschild (t,r), dr/dt<0 because it is falling toward the black hole. As far as the object itself is concerned, it reaches crosses the singularity in finite proper time and is destroyed. Nothing counterintuitive here. What an external observer sees is that the object starts slowing down near the event horizon, increasingly redshifted. It is observed to slow down so much that an external observer never sees it actually cross the horizon, its image forever hovering just above it, ever dimmer and redshifted.

That's pretty much what is described in just about every account of black holes out there. Since the object slows down, dr/dt increases toward zero (it becomes less negative), i.e., there (t,r)-acceleration d²r/dt² is positive--what the external observer sees is that the object is apparently repulsed by the black hole. It just so happens that when its velocity at infinity is greater than √3/3, then this region of apparent repulsion is actually everywhere, not just near the event horizon.