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(b,v)-Type Variables for Effective Polymer Black Holes

Dec 11
Group Seminar
2:00 pm o'clock to 3:30 pm o'clock
Fabio Mele (Universität Regensburg)
SR 02.729

Quantum gravity effects in effective models of loop quantum gravity, such as loop quantum cosmology, are encoded in the choice of so-called polymerisation schemes. Physical viability of the models, such as an onset of quantum effects at curvature scales near the Planck curvature, severely restrict the possible choices. An alternative point of view on the choice of polymerisation scheme is to choose adapted variables so that the scheme is the simplest possible one, known as $\\mu_0$-scheme in loop quantum cosmology. There, physically viable models with $\\mu_0$-scheme polymerise the Hubble rate $b$ that is directly related to the Ricci scalar and the matter energy density on-shell. Consequently, the onset of quantum effects depends precisely on those parameters. Following this second viewpoint, in this talk I will introduce similar variables for black-to-white hole transitions modelled using the description of the Schwarzschild interior as a Kantowski-Sachs cosmology. The resulting model uses the $\\mu_0$-scheme and features sensible physics (sensible onset of quantum effects, unique curvature upper bound) for a broad range of initial conditions (choices of black and white hole masses). The resulting Hamiltonian is remarkably simple and at most quadratic in its arguments, allowing for a straightforward quantisation.