RESEARCH GROUP

MATHEMATICAL STRUCTURES OF THE UNIVERSE

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61. 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.

62. M. Heller, L. Pysiak, W. Sasin
Inner Geometry of Random Operators
Demonstratio Mathematica, vol. 39, pp. 971-978 (2006).

Abstract:
Abstract

63. 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.

64. Leszek M. Sokołowski
Physical interpretation and viability of various metric nonlinear gravity theories
Proceedings of MG11 Meeting, Berlin, July 23-29, 2006 (2006).

Abstract:

65. L. Pysiak, M. Heller, Z. Odrzygóźdź, W. Sasin
Observables in a Noncommutative Approach to the Unification of Quanta and Gravity: A Finite Model
General Relativity and Gravitation, vol. 37, pp. 541-555 (2005).

Abstract:

66. Marek Demianski, Zdzislaw A. Golda, Andrzej Woszczyna
Evolution of density perturbations in a realistic universe
Gen. Rel. Grav., vol. 37, pp. 2063-2082 (2005).
[abstract] [preprint] [journal]

Abstract:
Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.

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