We study several different models of extended bodies in gravitational fields. Firstly, we revisit the glider model of a dumbbell-like oscillating body. We develop an independent scheme to integrate the equations of motion. We study the radial fall of a Newtonian spring, calculate the position shifts of the spring and find the critical value of the spring constant which cannot overcome the tidal forces. We argue that the relativistic glider model is unphysical due to its behaviour in the critical regions. Secondly, we show that Dixon's theory of extended bodies predicts a geodesic motion of the centre of mass in maximally symmetric spacetimes. We prove that a system of test particles can be described by a conserved stress-energy tensor and we evaluate the position shifts of the glider model in the maximally symmetric spacetimes, showing its disagreement with Dixon's theory. We thus conclude again that the glider model must be rejected. And thirdly, we study a model of an extended body consisting of interacting particles, which is in accord with Dixon's theory. We calculate the position shifts for this model and show that the model does not predict any measurable swimming effect. Finally, we estimate the numerical error of the calculation by finding the position shifts of the model in maximally symmetric...

Gamma Ray Burst (GRB) are very bright cosmological explosions signalling the catastrophic formation of a black hole. Therefore, they act like real light beacons that could be detected through-out the Universe and be used as probes to study the contents and phases of the early Universe. However, only a handful sample is known so far. This is for two reasons: instrumental biases that may prevent their detection and the difficulty to find a near Infrared counterpart preventing their redshift measurements. The wide-field trigger camera ECLAIRs to-fly on-board the Space-based multi-band Variable Object Monitor (SVOM) mission will detect γ-/X-ray transients down to energies of 4 keV, as well as creating an alert for multi-wavelength/messenger follow-ups. My study focuses on analysing how ECLAIRs will detect GRBs, and more particularly high-redshift GRBs, based on a well-selected sample of GRBs with redshift measurement associated (see Section 2). Studying how ECLAIRs will see them may help identifying possible instrument biases as well as common observational characteristics for such GRBs that may be used in turn to recognise such special GRBs once SVOM will be launched. Using software tools developed within the ECLAIRs collaboration, I built an end-to-end simulator which I used to simulate the detection by ECLAIRs of the GRBs in the sample at their original redshift and higher redshifts (up to z = 15). I implemented a suited version of the count-rate trigger on-board ECLAIRs to assess the detectability of these bursts, and I retrieved their duration over the background when detected (see Section 2). The analysis shows good performance for detecting high-redshift GRBs in the centre of the Field of View (fully-coded), but significantly reduced, in comparison to other GRBs, for partially-coded detection. 5 of the GRBs with z > 3.83 present a successful detection up to at least z = 15 (see Section 3). The retrieved rest-frame duration of a GRB remains constant for several redshifts in the simulations if the detected burst did not present a low-flux emission in their lightcurve, which is common for high redshift GRBs. On the other hand, if the original lightcurve of a burst presents this low-flux emission, it becomes buried in noise when simulating it at higher redshifts. This confirms the tip-of-the-iceberg detection bias which depends on the lightcurve burst morphology, and it may explain why the current sample seems to present lower burst durations at higher redshifts.

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