The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism

Qiu Shi Wang

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The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism

Qiu Shi Wang

General Relativity and Quantum Cosmology · Submitted 19 Sep 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using the essential self-adjointness result of Finster and R\"oken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator for spinors with low masses and suitably bounded frequency spectra in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.

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arXiv ID2209.09181 (version 3)

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CitationQiu Shi Wang. "The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism." arXiv:2209.09181 (2022). https://pith.science/paper/L7SJKWW6

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.08 · mentions code or data availability 0.02.

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We analytically extend the 5D Myers-Perry metric through the event and Cauchy horizons by defining Eddington-Finkelstein-type coordinates. Then, we use the orthonormal frame formalism to formulate and perform separation of variables on the massive Dirac equation, and analyse the asymptotic behaviour at the horizons and at infinity of the solutions to the radial ordinary differential equation (ODE) thus obtained. Using the essential self-adjointness result of Finster and R\"oken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator for spinors with low masses and suitably bounded frequency spectra in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analytically extend the 5D Myers-Perry metric through the event and Cauchy horizons by defining Eddington-Finkelstein-type coordinates.	method 0.77	0.94	0.07	asserted 1.00
s1	Then, we use the orthonormal frame formalism to formulate and perform separation of variables on the massive Dirac equation, and analyse the asymptotic behaviour at the horizons and at infinity of the solutions to the radial ordinary differential equation (ODE) thus obtained.	method 0.85	0.96	0.11	asserted 1.00
s2	Using the essential self-adjointness result of Finster and R\"oken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator for spinors with low masses and suitably bounded frequency spectra in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.	result 0.84	0.91	0.51	asserted 1.00

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Original abstract

We analytically extend the 5D Myers-Perry metric through the event and Cauchy horizons by defining Eddington-Finkelstein-type coordinates. Then, we use the orthonormal frame formalism to formulate and perform separation of variables on the massive Dirac equation, and analyse the asymptotic behaviour at the horizons and at infinity of the solutions to the radial ordinary differential equation (ODE) thus obtained. Using the essential self-adjointness result of Finster and R\"oken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator for spinors with low masses and suitably bounded frequency spectra in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.

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As in [ref] , the ansatz ([ref]) allows one to make the replacements $D_ϕ→-(k_a+1/2)$ and $D_ξ→-(k_b+1/2)$, under which the Dirac equation separates into ODEs

Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator · Separation of variables · 0.96

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The asymptotic behaviour of $X̃$ at the horizons is similar to the case of the Kerr geometry in Eddington–Finkelstein-type coordinates [ref] , but different from the case of the 5D Myers-Perry geometry in Boyer-Lindquist coordinates [ref] .

Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator · Asymptotic behaviour of solutions of the radial ODE · 1.00

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