Particle Production by Tidal Forces, and the Energy - Tensor

The quantum production of spinless particles, < n_{k}(t)>, and of energy-momentum-stress, < T^{{a}{b}}(P) >, by the tidal forces of classical curved space-time are investigated in this thesis. In a first part we consider the test case of 1+1 dimensions. Our computations are finite step by step, the predicted evolution of the energy-momentum tensor < T^{ a b} > and of the spectral energy density e_{k}< n_{k }> are consistent with each other throughout curved space-time, < T^ { a b}> is covariantly conserved and has the standard trace anomaly R/24 pi for massless particles. The two chiralities, right-goers versus left-goers, are decoupled, the total < T^{{a} {b}}> is the sum of the chiral parts. We apply our methods to four problems: (1) The Rindler problem. (2) An inhomogeneous patch of curvature produces a burst of energy-momentum and of particles. (3) We compute the quantum production of energy density and pressure for a quantum field in external Friedmann-Robertson -Walker space-times in 1+1 dimensions. (4) We consider the gravitational field of a collapsing shell of classical matter in 3+1 dimensions, and we compute the production of Hawking radiation everywhere inside a linear wave guide in the radial direction. In a second part, we compute the energy density and pressures from a quantum scalar field propagating in the external field of a (3+1)-dimensional, spherically symmetric, static geometry with flat spatial sections. We consider only the (l = 0)-sector of the scalar field. The initial state of the quantum field is the gauge invariant vacuum on one of these hypersurface. Our computations are finite step by step. For the pressures we use the covariant conservation of T^{mu nu} and its four-dimensional trace. We apply our results to the case of the gravitational potential due to an homogeneous spherical body. At late times, i.e. when all switch-on effects are far away from the body, the results are that a static cloud of energy and pressure is formed inside and outside the body. In a third part we consider the quantization of a tachyon field T in the background of the two-dimensional black hole as described by the SL(2,{bf R})/U(1) coset theory proposed by E. Witten. An explicit expression for < T^2(x) > in the Hartle-Hawking state at the horizon is obtained. (Abstract shortened by UMI.).