  Hawking discovery that black holes can evaporate through radiation emission
has posed a number of questions that with time became fundamental hallmarks for
a quantum theory of gravity. The most famous one is likely the information
paradox, which finds an elegant explanation in the Page argument suggesting
that a black hole and its radiation can be effectively represented by a random
state of qubits. Leveraging the same assumption, we ponder the extent to which
a black hole may display emergent symmetries, employing the entanglement
asymmetry as a modern, information-based indicator of symmetry breaking. We
find that for a random state devoid of any symmetry, a $U(1)$ symmetry emerges
and it is exact in the thermodynamic limit before the Page time. At the Page
time, the entanglement asymmetry shows a finite jump to a large value. Our
findings imply that the emitted radiation is symmetric up to the Page time and
then undergoes a sharp transition. Conversely the black hole is symmetric only
after the Page time.
