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Register a new userMeasuring general relativity effects in a terrestrial lab by means of laser gyroscopes
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GINGER is a proposed tridimensional array of laser gyroscopes with the aim of measuring the Lense-Thirring effect, predicted by the General Relativity theory, in a terrestrial laboratory environment. We discuss the required accuracy, the methods to achieve it, and the preliminary experimental work in this direction.
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The paper discusses the optimal conguration of one or more ring lasers to be used for measuring the general relativistic effects of the rotation of the earth, as manifested on the surface of the planet. The analysis is focused on devices having their normal vector lying in the meridian plane. The crucial role of the evaluation of the angles is evidenced. Special attention is paid to the orientation at the maximum signal, minimizing the sensitivity to the orientation uncertainty. The use of rings at different latitudes is mentioned and the problem of the non-sfericity of the earth is commented.
We propose an under-ground experiment to detect the general relativistic effects due to the curvature of space-time around the Earth (de Sitter effect) and to rotation of the planet (dragging of the inertial frames or Lense-Thirring effect). It is based on the comparison between the IERS value of the Earth rotation vector and corresponding measurements obtained by a tri-axial laser detector of rotation. The proposed detector consists of six large ring-lasers arranged along three orthogonal axes. In about two years of data taking, the 1% sensitivity required for the measurement of the Lense-Thirring drag can be reached with square rings of 6 $m$ side, assuming a shot noise limited sensitivity ($ 20 prad/s/sqrt{Hz}$). The multi-gyros system, composed of rings whose planes are perpendicular to one or the other of three orthogonal axes, can be built in several ways. Here, we consider cubic and octahedron structures. The symmetries of the proposed configurations provide mathematical relations that can be used to study the stability of the scale factors, the relative orientations or the ring-laser planes, very important to get rid of systematics in long-term measurements, which are required in order to determine the relativistic effects.
Varying the gravitational Lagrangian produces a boundary contribution that has various physical applications. It determines the right boundary terms to be added to the action once boundary conditions are specified, and defines the symplectic structure of covariant phase space methods. We study general boundary variations using tetrads instead of the metric. This choice streamlines many calculations, especially in the case of null hypersurfaces with arbitrary coordinates, where we show that the spin-1 momentum coincides with the rotational 1-form of isolated horizons. The additional gauge symmetry of internal Lorentz transformations leaves however an imprint: the boundary variation differs from the metric one by an exact 3-form. On the one hand, this difference helps in the variational principle: gluing hypersurfaces to determine the action boundary terms for given boundary conditions is simpler, including the most general case of non-orthogonal corners. On the other hand, it affects the construction of Hamiltonian surface charges with covariant phase space methods, which end up being generically different from the metric ones, in both first and second-order formalisms. This situation is treated in the literature gauge-fixing the tetrad to be adapted to the hypersurface or introducing a fine-tuned internal Lorentz transformation depending non-linearly on the fields. We point out and explore the alternative approach of dressing the bare symplectic potential to recover the value of all metric charges, and not just for isometries. Surface charges can also be constructed using a cohomological prescription: in this case we find that the exact 3-form mismatch plays no role, and tetrad and metric charges are equal. This prescription leads however to different charges whether one uses a first-order or second-order Lagrangian, and only for isometries one recovers the same charges.
Electron accelerations of the order of $10^{21} g$ obtained by laser fields open up the possibility of experimentally testing one of the cornerstones of general relativity, the weak equivalence principle, which states that the local effects of a gravitational field are indistinguishable from those sensed by a properly accelerated observer in flat space-time. We illustrate how this can be done by solving the Einstein equations in vacuum and integrating the geodesic equations of motion for a uniformly accelerated particle.
We study a static, spherically symmetric wormhole model whose metric coincides with that of the so-called Ellis wormhole but the material source of gravity consists of a perfect fluid with negative density and a source-free radial electric or magnetic field. For a certain class of fluid equations of state, it has been shown that this wormhole model is linearly stable under both spherically symmetric perturbations and axial perturbations of arbitrary multipolarity. A similar behavior is predicted for polar nonspherical perturbations. It thus seems to be the first example of a stable wormhole model in the framework of general relativity (at least without invoking phantom thin shells as wormhole sources).
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