# Acceleration of a point mass

1. May 20, 2007

### MeJennifer

Can we formulate a line element that describes a free falling observer in an accelerating point mass solution?

2. May 20, 2007

### pervect

Staff Emeritus
If I understand the question correctly, the closest you can come is probably Kinnersley's photon rocket. Kinnersley, Phys Rev 186 (1969) - I don't know if it's online anywhere though.

A mass can't accelerate unless something pushes it, so you have to model the exhaust, too.

and provides more references (other than Kinnersley) in
http://www.lns.cornell.edu/spr/2004-08/msg0062833.html

3. May 21, 2007

### smallphi

There exist the so called Fermi Normal Coordinates that are the local coordinates of a free fall observer in any spacetime. The coordinate system constructed is valid locally around the world line of the observer. It is inertial to zero order (spacetime is flat locally) and has first and higher order corrections from the Riemann tensor expressed in those coordinates.

Articles that show explicitly construction of such coordinates:

Explains what Fermi N. Coord. are, how they are constructed in general and gives example of construction in Schwarzschild metric:
"Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry",
F. K. Manasse and C. W. Misner, Journal of Mathematical Physics, vol 4, num 6, 1963

Constructs Fermi N. Coord. in FRW cosmological metric:
"The Influence of the Cosmological Expansion on Local Systems", F. I. CooperStock, V. Faraoni, and D. N. Vollick, The Astrophysical Journal, 503, 61-66, 1998

Last edited: May 21, 2007
4. May 21, 2007

### MeJennifer

Thanks for replying smallphi, but I don't understand the relevance of what you write.

5. May 21, 2007

### smallphi

The Fermi normal coordinates are the physical local coordinates used by a free fall observer in arbitrary spacetime.

If you want global coordinates, one observer does not define an unique coordinate system so you will have to clarify your question.

6. May 21, 2007

### Chris Hillman

Suggest some on-line references

It's probably worth adding that the Kinnersley-Walker photon rocket is a null dust solution.

The OP is in my ignore list, but FWIW searching the arXiv on "photon rocket" in abstract field gives several papers, all of which I have read; probably the best overview is in http://www.arxiv.org/abs/gr-qc/0203064

I have extensively discussed photon rockets (and other null dust solutions) in many posts over the years to the moderated UseNet group sci.physics.research. For example, the horizons are interesting since typically one has a (nonspherical) event horizon plus a disjoint (nonplanar) Rindler horizon.

7. May 21, 2007

### MeJennifer

But this is not a question about using certain coordinates it is about a solution for an accelerating point mass, call it an "accelerating Schwarzschild solution".

8. May 21, 2007

### smallphi

OK you are asking about a solution of Einstein eq. that describes an accelerating mass. It's interesting if such a solution contains the energy source accelerating the mass.

I thought you were asking how to construct a coordinate system adapted to a free fall observer in that spacetime.

Last edited: May 21, 2007
9. May 21, 2007

### MeJennifer

Well it seems the point mass would need a non-isotropic emission of electromagnetic radiation. It seems that such an emission would reduce the mass-energy of the point mass.

My interest lies in how the acceleration of the point mass would influence the radial approach or orbit of a test particle.

Last edited: May 21, 2007