Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution

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.

Minor corrections

References in corpus (16)

• Dirac particles tunneling from BTZ black hole
• Hawking radiation of Dirac particles via tunneling from Kerr black hole
• Fermion scattering by a Schwarzschild black hole
• Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves
• Interior of a Schwarzschild black hole revisited
• Measurement of the production and lepton charge asymmetry of $\text{W}$ bosons in Pb+Pb collisions at $\sqrt{s_{\mathbf{NN}}}=$ 2.76 TeV with the ATLAS detector
• Absorption of a massive scalar field by a charged black hole
• Absorption of planar massless scalar waves by Bardeen regular black holes
• Measurement of the underlying event in the Drell-Yan process in proton-proton collisions at sqrt(s) = 7 TeV
• Is super-Planckian physics visible? -- Scattering of black holes in 5 dimensions
• The number of eigenstates: counting function and heat kernel
• Exact solution of inverse-square-root potential $V\left(r\right)=-\frac{\alpha }{\sqrt{r}}$
• Scattering theory without large-distance asymptotics
• Scattering theory without large-distance asymptotics in arbitrary dimensions
• Simplified Pure Spinor b Ghost in a Curved Heterotic Superstring Background
• Scattering of particles by deformed non-rotating black holes

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