Crossing of Spherical Massive Shells in Vacuum Space-Time

@article{Nakao1999CrossingOS,
  title={Crossing of Spherical Massive Shells in Vacuum Space-Time},
  author={Ken-ichi Nakao and Daisuke Ida and Norimasa Sugiura},
  journal={Progress of Theoretical Physics},
  year={1999},
  volume={101},
  pages={47-71}
}
We investigate collisions between two spherical massive shells in vacuum space-time by assuming that the shells are transparent. We give an expression for the energy transfer and the change in the 3-momentum due to the collision. Compared with the Newtonian situation, the relativistic effect always increases the energy transfer. In particular, in a collision close to the singularity and the horizon defined in the region between the shells, the energy transfer can be arbitrarily large. However… 

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References

SHOWING 1-10 OF 14 REFERENCES
Dynamics and collision of massive shells in curved backgrounds
The authors analyse the dynamics of the collision of two spherical massive shells in a generally spherically symmetric background, obtaining an expression from the conservation law that imposes a
The effect of spherical shells of matter on the Schwarzschild black hole
Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless
RELATIVISTIC EQUATIONS FOR ADIABATIC, SPHERICALLY SYMMETRIC GRAVITATIONAL COLLAPSE
The Einstein equations for a spherically symmetrical distribution of matter are studied. The matter is described by the stress-energy tensor of an ideal fluid (heat flow and radiation are therefore
Shell crossings and the Tolman model
We consider the problem of shell crossings and regular maxima in the Tolman model. The necessary and sufficient conditions which guarantee no shell crossings will arise in Tolman models are derived,
Non-linear growth of cosmological density fluctuation and type of singularity
Non-linear growth of density fluctuation in one-dimensional self-gravitating system in the expanding universe is investigated. It is found that the Fourier spectrum of density fluctuation obeys a
Theory and Experiment in Gravitational Physics
New technological advances have made it feasible to conduct measurements with precision levels which are suitable for experimental tests of the theory of general relativity. This book has been
Singular hypersurfaces and thin shells in general relativity
SummaryAn approach to shock waves, boundary surfaces and thin shells in general relativity is developed in which their histories are characterized in a purely geometrical way by the extrinsic
Large-scale distribution of galaxies at the Galactic poles
GALAXIES, mapped in two or three dimensions, are not distributed randomly but are clustered on small scales (<5 h−1 Mpc, where h ≈ 0.5–1 is Hubble's constant in units of 100 km s−1Mpc−1), for reasons
The Analysis of Space-Time Singularities
1. Introductory 2. The Riemann tensor 3. Boundary constructions 4. Existence theory and differentiability 5. The analytic extension problem 6. Attributes of singularities 7. Extension theories.
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