A fully relativistic radial fall

Radial fall has historically played a momentous role. It is one of the most classical problems, the solutions of which represent the level of understanding of gravitation in a given epoch. A {\it gedankenexperiment} in a modern frame is given by a small body, like a compact star or a solar mass black hole, captured by a supermassive black hole. The mass of the small body itself and the emission of gravitational radiation cause the departure from the geodesic path due to the back-action, that is the self-force. For radial fall, as any other non-adiabatic motion, the instantaneous identity of the radiated energy and the loss of orbital energy cannot be imposed and provide the perturbed trajectory. In the first part of this letter, we present the effects due to the self-force computed on the geodesic trajectory in the background field. Compared to the latter trajectory, in the Regge-Wheeler, harmonic and all others smoothly related gauges, a far observer concludes that the self-force pushes inward (not outward) the falling body, with a strength proportional to the mass of the small body for a given large mass; further, the same observer notes an higher value of the maximal coordinate velocity, this value being reached earlier on during infall. In the second part of this letter, we implement a self-consistent approach for which the trajectory is iteratively corrected by the self-force, this time computed on osculating geodesics. Finally, we compare the motion driven by the self-force without and with self-consistent orbital evolution. Subtle differences are noticeable, even if self-force effects have hardly the time to accumulate in such a short orbit.Comment: To appear in Int. J. Geom. Meth. Mod. Phy

Conclusion: The development of the strategic state in Europe

Strategic Management in Public Organizations: European Practices and Perspectives offers the first wide-ranging survey and assessment of strategic management practices at various levels of government and public service in European countries. It shows that strategic management is much more than a management tool imported from the private sector - it has become a key element of public management reforms, and European governments at all levels are developing ‘strategic state’ characteristics. Written by leading European experts on strategic management in the public sector and in government, this book presents evaluations and analysis based on empirical investigations. The book covers strategic management at different levels of government, explore the roles of different players, and incorporate theory and practice, with opening and concluding chapters by the editors that provide an overview of strategic management in the public services and a cross-societal discussion of practices, reforms, and lessons. It reflects not only developments in strategic management practices in the European public sector, but also the increasing importance of strategic capabilities for the modernization of public governance. This book is ideal for students in postgraduate management courses (MPA, MSc, or MBA) in Europe and elsewhere.SCOPUS: bk.binfo:eu-repo/semantics/publishe

OPENING UP PUBLIC STRATEGIC MANAGEMENT: FORESIGHT’S CONTRIBUTION TO POLICY RELEVANCE, COOPERATION AND CONSISTENCY

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