Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal
  Tendexes II. Stationary Black Holes   When one splits spacetime into space plus time, the Weyl curvature tensor
(which equals the Riemann tensor in vacuum) splits into two spatial, symmetric,
traceless tensors: the tidal field $E$, which produces tidal forces, and the
frame-drag field $B$, which produces differential frame dragging. In recent
papers, we and colleagues have introduced ways to visualize these two fields:
tidal tendex lines (integral curves of the three eigenvector fields of $E$) and
their tendicities (eigenvalues of these eigenvector fields); and the
corresponding entities for the frame-drag field: frame-drag vortex lines and
their vorticities. These entities fully characterize the vacuum Riemann tensor.
In this paper, we compute and depict the tendex and vortex lines, and their
tendicities and vorticities, outside the horizons of stationary (Schwarzschild
and Kerr) black holes; and we introduce and depict the black holes' horizon
tendicity and vorticity (the normal-normal components of $E$ and $B$ on the
horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is
proportional to the horizon's intrinsic scalar curvature, and the horizon
vorticity is proportional to an extrinsic scalar curvature. We show that, for
horizon-penetrating time slices, all these entities ($E$, $B$, the tendex lines
and vortex lines, the lines' tendicities and vorticities, and the horizon
tendicities and vorticities) are affected only weakly by changes of slicing and
changes of spatial coordinates, within those slicing and coordinate choices
that are commonly used for black holes. [Abstract is abbreviated.]

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th