Optically thick energy dominated plasma created in the source of Gamma-Ray Bursts (GRBs) expands radially with acceleration and forms a shell with constant width measured in the laboratory frame. When strong Lorentz factor gradients are present withi
n the shell it is supposed to spread at sufficiently large radii. There are two possible mechanisms of spreading: hydrodynamical and thermal ones. We consider both mechanisms evaluating the amount of spreading that occurs during expansion up to the moment when the expanding shell becomes transparent for photons. We compute the hydrodynamical spreading of an ultrarelativistically expanding shell. In the case of thermal spreading we compute the velocity spread as a function of two parameters: comoving temperature and bulk Lorentz factor of relativistic Maxwellian distribution. Based on this result we determine the value of thermal spreading of relativistically expanding shell. We found that thermal spreading is negligible for typical GRB parameters. Instead hydrodynamical spreading appears to be significant, with the shell width reaching $sim10^{10}$ cm for total energy $E=10^{54}$ erg and baryonic loading $B=10^{-2}$. Within the fireshell model such spreading will result in the duration of Proper Gamma-Ray Bursts up to several seconds.
In this paper we reexamine the optical depth of ultrarelativistic spherically symmetric outflows and reevaluate the photospheric radius for each model during both the acceleration and coasting phases. It is shown that for both the wind and the shell
models there are two asymptotic solutions for the optical depth during the coasting phase of the outflow. In particular we show that quite counterintuitively a geometrically thin shell may appear as a thick wind for photons propagating inside it. For this reason we introduce notions of photon thick and photon thin outflows, which appear more general and better physically motivated with respect to winds and shells. Photosphere of relativistic outflow is a dynamic surface. We study its geometry and find that the photosphere of photon thin outflow has always a convex shape, while in the photon thick one it is initially convex (there is always a photon thin layer in any outflow) and then it becomes concave asymptotically approaching the photosphere of an infinitely long wind. We find that both instantaneous and time integrated observed spectra are very close to the thermal one for photon thick outflows, in line with existing studies. It is our main finding that the photospheric emission from the photon thin outflow produces non thermal time integrated spectra, which may be described by the Band function well known in the GRB literature. We find that energetic GRBs should produce photon thin outflows with photospheric emission lasting less than one second for the total energy $E_0leq10^{54}$ erg and baryonic loading parameter $Bleq10^{-2}$. It means that only time integrated spectra may be observed from such GRBs.
From Doppler tracking data and data on circular motion of astronomical objects we obtain a metric of the Pioneer Anomaly. The metric resolves the issue of manifest absence of anomaly acceleration in orbits of the outer planets and extra-Pluto objects
of the Solar system. However, it turns out that the energy-momentum tensor of matter, which generates such a gravitational field in GR, violates energy dominance conditions. At the same time the equation of state derived from the energy-momentum tensor is that of dark energy with $w=-1/3$. So the model proposed must be carefully studied by Grand-Fit investigations.
