61. Leszek M. Sokołowski
General relativity, gravitational energy and spin-two field
Int. J. Geom. Meth. Mod. Phys. , vol. 4, pp. 1-23 (2007).
[abstract] [preprint] | Abstract:
(Lectures given at the 42 Karpacz Winter School of Theoretical Physics, Lądek Zdrój, Poland, 6-11 February 2006, "Current
Mathematical Topics in Gravitation and Cosmology"):
In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field-theory approach to gravity? and iii) can a consistent theory of a gravitationally interacting spin-two field be developed at all? The connecting link to them is the concept of a fundamental spin-2 field. A linear spin-2 field encounters insurmountable inconsistencies when coupled to gravity. After discussing the inconsistencies of any coupling of the linear spin-2 field to gravity, I exhibit the origin of the fact that a gauge invariant field has the variational metric stress tensor which is gauge dependent. I give a general theorem explaining under what conditions a symmetry of a field Lagrangian becomes also the symmetry of the stress tensor. It is a conclusion of the theorem that any attempt to define gravitational energy density in the framework of a field theory of gravity must fail. Finally I make a very brief introduction to basic concepts of how a certain kind of a necessarily nonlinear spin-2 field arises in a natural way from vacuum higher derivative gravity theories. This specific spin-2 field consistently interacts gravitationally.
| 62. Andrzej Woszczyna
Mechanika zaburzeń skalarnych w radiacyjnym wszechświecie
Prace Komisji Astrofizyki PAU, vol. 11, p. 117 (2007).
[pdf.pl] | Abstract:
Abstract | 63. Leszek M. Sokołowski, Andrzej Staruszkiewicz
On the issue of gravitons
Class. Quant. Grav. , vol. 23, pp. 5907-5918 (2006).
[abstract] [preprint] [journal] | Abstract:
We investigate the problem of whether one can anticipate any features of the graviton without a detailed knowledge of a full quantum gravity. Assuming that in linearized gravity the graviton is in a sense similar to the photon, we derive a curious large number coincidence between the number of gravitons emitted by a solar planet during its orbital period and the number of its nucleons. In Einstein's GR the analogy between the graviton and the photon is ill founded. A generic relationship between quanta of a quantum field and plane waves of the corresponding classical field is broken in the case of GR. The graviton cannot be classically approximated by a generic pp wave nor by the exact plane wave. Most important, the ADM energy is a zero frequency characteristic of any asymptotically flat spacetime and this means that any general relationship between energy and frequency is a priori impossible. In particular the formula $E=\hbar \omega$ does not hold. The graviton must have features different from those of the photon and these cannot be predicted from classical general relativity. | 64. M. Heller, L. Pysiak, W. Sasin
Inner Geometry of Random Operators
Demonstratio Mathematica, vol. 39, pp. 971-978 (2006).
| Abstract:
Abstract | 65. P. T. Chrusciel, G. M. Greuel, R. Meinel, S. J. Szybka
The Ernst equation and ergosurfaces
Class. Quantum Grav., vol. 23, pp. 4399-4414 (2006).
[abstract] [preprint] [journal] | Abstract:
We show that analytic solutions $\mcE$ of the Ernst equation with non-empty zero-level-set of $\Re \mcE$ lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a "Ernst ergosurface" $E_f$ if and only if $\mcE$ is smooth near $E_f$ and does not have zeros of infinite order there. | 66. Leszek M. Sokołowski
Physical interpretation and viability of various metric nonlinear gravity theories
Proceedings of MG11 Meeting, Berlin, July 23-29, 2006 (2006).
| Abstract:
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