No Arabic abstract
The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment.
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
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.
We study the free massive scalar field in de Sitter spacetime with static charts. In particular, we find positive-frequency modes for the Bunch-Davies vacuum state natural to the static charts as superpositions of the well-known positive-frequency modes in the conformally-flat chart. We discuss in detail how these modes are defined globally in the two static charts and the region in their future. The global structure of these solutions leads to the well-known description of the Bunch-Davies vacuum state as an entangled state. Our results are expected to be useful not only for studying the thermal properties in the vacuum fluctuations in de Sitter spacetime but also for understanding the nonlocal properties of the vacuum state.
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.
We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential, and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.