Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conformal Rigidity from Focusing   The null curvature condition (NCC) is the requirement that the Ricci
curvature of a Lorentzian manifold be nonnegative along null directions, which
ensures the focusing of null geodesic congruences. In this note, we show that
the NCC together with the causal structure significantly constrain the metric.
In particular, we prove that any conformal rescaling of a vacuum spacetime
introduces either geodesic incompleteness or negative null curvature, provided
the conformal factor is non-constant on at least one complete null geodesic. In
the context of bulk reconstruction in AdS/CFT, our results combined with the
technique of light-cone cuts can be used in vacuum spacetimes to reconstruct
the full metric in regions probed by complete null geodesics reaching the
boundary. For non-vacuum spacetimes, our results constrain the conformal
factor, giving an approximate reconstruction of the metric.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org