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The effect of Hawking radiation on the redistribution of the entanglement and mutual information in the Schwarzschild spacetime is investigated. Our analysis shows that the physically accessible correlations degrade while the unaccessible correlations increase as the Hawking temperature increases because the initial correlations described by inertial observers are redistributed between all the bipartite modes. It is interesting to note that, in the limit case that the temperature tends to infinity, the accessible mutual information equals to just half of its initial value, and the unaccessible mutual information between mode $A$ and $II$ also equals to the same value.
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We study the evolution of the two scalar fields entangled via a mutual interaction in an expanding spacetime. We compute the logarithmic negativity to leading order in perturbation theory and show that for lowest order in the coupling constants, the mutual interaction will give rise to the survival of the quantum correlations in the limit of the smooth expansion. The results suggest that interacting fields can codify more information about the underlying expansion spacetime and lead to interesting observable effects.
In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of a solution to null infinity and to the event horizon. In the process, we establish some regularity properties of solutions of the wave equation on the spacetime. In particular, we prove that the regularity of the solution across the event horizon and across null infinity is determined by the regularity and decay rate of the initial data at the event horizon and at infinity. We also show that the radiation field is unitary with respect to the conserved energy and prove support theorems for each piece of the radiation field.
We provide expansions of the Detweiler-Whiting singular field for motion along arbitrary, planar accelerated trajectories in Schwarzschild spacetime. We transcribe these results into mode-sum regularization parameters, computing previously unknown terms that increase the convergence rate of the mode-sum. We test our results by computing the self-force along a variety of accelerated trajectories. For non-uniformly accelerated circular orbits we present results from a new 1+1D discontinuous Galerkin time-domain code which employs an effective-source. We also present results for uniformly accelerated circular orbits and accelerated bound eccentric orbits computed within a frequency-domain treatment. Our regularization results will be useful for computing self-consistent self-force inspirals where the particles worldline is accelerated with respect to the background spacetime.
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
The retarded Green function for linear field perturbations of black hole spacetimes is notoriously difficult to calculate. One of the difficulties is due to a Dirac-$delta$ divergence that the Green function possesses when the two spacetime points are connected by a direct null geodesic. We present a procedure which notably aids its calculation in the case of Schwarzschild spacetime by separating this direct $delta$-divergence from the remainder of the retarded Green function. More precisely, the method consists of calculating the multipolar $ell$-modes of the direct $delta$-divergence and subtracting them from the corresponding modes of the retarded Green function. We illustrate the usefulness of the method with some specific calculations in the case of the scalar Green function and self-field for a point scalar charge in Schwarzschild spacetime.
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