Massless Majorana spinors in the Kerr spacetime
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918240927612928 |
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| author | Cai, Tianyuan Zhang, Xiao |
| author_facet | Cai, Tianyuan Zhang, Xiao |
| contents | In this paper, we show that massive Majorana spinors \eqref{1.2} do not exist if they are $t$-dependent or $ϕ$-dependent in Kerr, or Kerr-(A)dS spacetimes. For massless Majorana spinors in the non-extreme Kerr spacetime, the Dirac equation can be separated into radial and angular equations, parameterized by two complex constants $ε_1$, $ε_2$. If at least one of $ε_1$, $ε_2$ is zero, massless Majorana spinors can be solved explicitly. If $ε_1$, $ε_2$ are nonzero, we prove the nonexistence of massless time-periodic Majorana spinors in the non-extreme Kerr spacetime which are $L^p$ outside the event horizon for $ 0<p\le\frac{6}{|ε_1|+|ε_2| +2}$. We then provide the Hamiltonian formulation for massless Majorana spinors and prove that the self-adjointness of the Hamiltonian leads to the angular momentum $a=0$ and spacetime reduces to the Schwarzschild spacetime, moreover, the massless Majorana spinor must be $ϕ$-independent. Finally, we show that, in the Schwarzschild spacetime, for initial data with $L^2$ decay at infinity, the probability of the massless Majorana spinors to be in any compact region of space tends to zero as time tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09253 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Massless Majorana spinors in the Kerr spacetime Cai, Tianyuan Zhang, Xiao General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry In this paper, we show that massive Majorana spinors \eqref{1.2} do not exist if they are $t$-dependent or $ϕ$-dependent in Kerr, or Kerr-(A)dS spacetimes. For massless Majorana spinors in the non-extreme Kerr spacetime, the Dirac equation can be separated into radial and angular equations, parameterized by two complex constants $ε_1$, $ε_2$. If at least one of $ε_1$, $ε_2$ is zero, massless Majorana spinors can be solved explicitly. If $ε_1$, $ε_2$ are nonzero, we prove the nonexistence of massless time-periodic Majorana spinors in the non-extreme Kerr spacetime which are $L^p$ outside the event horizon for $ 0<p\le\frac{6}{|ε_1|+|ε_2| +2}$. We then provide the Hamiltonian formulation for massless Majorana spinors and prove that the self-adjointness of the Hamiltonian leads to the angular momentum $a=0$ and spacetime reduces to the Schwarzschild spacetime, moreover, the massless Majorana spinor must be $ϕ$-independent. Finally, we show that, in the Schwarzschild spacetime, for initial data with $L^2$ decay at infinity, the probability of the massless Majorana spinors to be in any compact region of space tends to zero as time tends to infinity. |
| title | Massless Majorana spinors in the Kerr spacetime |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2512.09253 |