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Register a new userThe gravity of light-waves
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Authors
Jan Willem van Holten
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Light waves carry along their own gravitational field; for simple plain electromagnetic waves the gravitational field takes the form of a pp-wave. I present the corresponding exact solution of the Einstein-Maxwell equations and discuss the dynamics of classical particles and quantum fields in this gravitational and electromagnetic background.
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A solution of the old problem raised by Tolman, Ehrenfest, Podolsky and Wheeler, concerning the lack of attraction of two light pencils moving parallel, is proposed, considering that the light can be source of nonlinear gravitational waves corresponding (in the would be quantum theory of gravity) to spin-1 massless particles.
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.
We treat a model based upon nonlinear optics for the semiclassical gravitational effects of quantum fields upon light propagation. Our model uses a nonlinear material with a nonzero third order polarizability. Here a probe light pulse satisfies a wave equation containing the expectation value of the squared electric field. This expectation value depends upon the presence of lower frequency quanta, the background field, and modifies the effective index of refraction, and hence the speed of the probe pulse. If the mean squared electric field is positive, then the pulse is slowed, which is analogous to the gravitational effects of ordinary matter. Such matter satisfies the null energy condition and produce gravitational lensing and time delay. If the mean squared field is negative, then the pulse has a higher speed than in the absence of the background field. This is analogous to the gravitational effects of exotic matter, such as stress tensor expectation values with locally negative energy densities, which lead to repulsive gravitational effects, such as defocussing and time advance. We give some estimates of the magnitude of the effects in our model, and find that they may be large enough to be observable. We also briefly discuss the possibility that the mean squared electric field could be produced by the Casimir vacuum near a reflecting boundary.
The matching between two 4-dimensional PP-waves is discussed by using Israels matching conditions. Physical consequences on the dynamics of (cosmic) strings are analyzed. The extension to space-time of arbitrary dimension is discussed and some interesting features related to the brane world scenario, BPS states in gravity and Dirac-like quantization conditions are briefly described.
Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the influence of the topological terms present in the action of this theory. Established formulas for charges resemble previously obtained ones, but we show that they are affected by the presence of the cosmological constant and topological terms. As an example we discuss the charges in the case of the AdS--Schwarzschild solution and we find that the charges give correct values.
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