## Ernst Mach and Machian effects in general relativity

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- Written by Jiří Bičák

I shall start with some remarks on Ernst Mach (1838-1916), who spent many years at the University in Prague and at the Vienna University. I briefly recall his and Einstein’s ideas on the origin of inertia and their influence on the construction of general relativity. I mention the direct experiment verifying relativistic dragging/gravitomagnetic effects - the Gravity Probe B; the results were summarized only recently. I shall then turn to several specific general-relativistic problems illustrating the gravitomagnetic effects: the dragging of particles and fields around a rotating black hole, dragging inside a collapsing slowly rotating spherical shell of dust, linear dragging in a static situation, and the way how Mach’s principle can be formulated in cosmology. A more detailed discussion will be devoted to the dragging effects by rotating gravitational waves.