Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein-Maxwell-dilaton neutral black holes in strong magnetic fields:
  topological charge, shadows and lensing   The light rings (LRs) topological charge (TC) of a spacetime measures the
number of stable LRs minus the number of unstable LRs. It is invariant under
smooth spacetime deformations obeying fixed boundary conditions. Asymptotically
flat equilibrium black holes (BHs) have, generically, TC=$-1$. In
Einstein-Maxwell theory, however, the Schwarzschild-Melvin BH - describing a
neutral BH immersed in a strong magnetic field - has TC$=0$. This allows the
existence of BHs without LRs and produces remarkable phenomenological features,
like panoramic shadows. Here we investigate the generalised
Schwarzschild-Melvin solution in Einstein-Maxwell-dilaton theory, scanning the
effect of the dilaton coupling $a$. We find that the TC changes discontinuously
from TC$=0$ to TC$=-1$ precisely at the Kaluza-Klein value $a=\sqrt{3}$, when
the (empty) Melvin solution corresponds to a twisted Kaluza-Klein reduction of
five-dimensional flat spacetime, $i.e.$ the dilaton coupling $a$ induces a
topological transition in the TC. We relate this qualitative change to the
Melvin asymptotics for different $a$. We also study the shadows and lensing of
the generalised Schwarzschild-Melvin solution for different values of $a$,
relating them to the TC.

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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg