Gravity

AbstractThis chapter discusses the Einstein theory of gravity, which consists of two main elements: (1) gravity is related to a curvature of space-time in which particles move along geodesic curves; and (2) dynamics of the metric field is determined by Einstein equations. Sakharov theory of gravity, in which gravity is induced by vacuum fluctuations, reproduces Einstein theory. The effective gravity emerging in quantum liquids is similar to Sakharov gravity, but in quantum liquids only the first element of Einstein theory is present — the effective metric for quasiparticles, while the metric field obeys hydrodynamic type equations instead of Einstein equations. The chapter also introduces the cosmological constant problem. In particle physics, field quantization allows a zero-point energy, the constant vacuum energy when all fields are in their ground states. In the absence of gravity the constant energy can be ignored, since only the difference between the energies of the field in the excited and ground states is meaningful. In the Einstein theory of gravity, however, the gravitational field reacts to the total value of the energy momentum tensor of the matter fields, and thus the absolute value of the vacuum energy becomes meaningful. If the energy momentum tensor of the vacuum is non-zero it must be added to the Einstein equations. The corresponding contribution to the action is given by the cosmological term, which was introduced by Einstein.