Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polymer Schwarzschild black hole: An effective metric   We consider the modified Einstein equations obtained in the framework of
effective spherically symmetric polymer models inspired by Loop Quantum
Gravity. When one takes into account the anomaly free point-wise holonomy
quantum corrections, the modification of Einstein equations is parametrized by
a function $f(x)$ of one phase space variable. We solve explicitly these
equations for a static interior black hole geometry and find the effective
metric describing the trapped region, inside the black hole, for any $f(x)$.
This general resolution allows to take into account a standard ambiguity
inherent to the polymer regularization: namely the choice of the spin $j$
labelling the SU$(2)$-representation of the holonomy corrections. When $j=1/2$,
the function $f(x)$ is the usual sine function used in the polymer litterature.
For this simple case, the effective exterior metric remains the classical
Schwarzschild's one but acquires modifications inside the hole. The interior
metric describes a regular trapped region and presents strong similarities with
the Reissner-Nordstr\"om metric, with a new inner horizon generated by quantum
effects. We discuss the gluing of our interior solution to the exterior
Schwarzschild metric and the challenge to extend the solution outside the
trapped region due to covariance requirement. By starting from the anomaly free
polymer regularization for inhomogeneous spherically symmetric geometry, and
then reducing to the homogeneous interior problem, we provide an alternative
treatment to existing polymer interior black hole models which focus directly
on the interior geometry, ignoring covariance issue when introducing the
polymer regularization.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin