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Abstract:

We compute the effects on the temperature and precise spectrum of Hawking radiation from a Schwarzschild black hole when the emitted object is taken to be spatially extended. We find that in the low-momentum regime, the power emitted is exponentially suppressed for sufficiently large radiated objects, or sufficiently small black holes, though the temperature of emission is unchanged. We numerically determine the magnitude of this suppression as a function of the size and mass of the object and the black hole, and discuss the implications for various extended objects in nature.

Abstract:

It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland arguments. We provide such a bound for an important class of global symmetries: Those arising from a gauged $U(1)$ with the vector made massive via a Nambu-Goldstone mode. The latter is an axion which necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory. As a result, instanton-induced symmetry breaking operators with a suppression factor not smaller than $\exp(-M_{\rm P}^2/\Lambda^2)$ are present, where $\Lambda$ is a cutoff of the 4d effective theory. We provide a general argument and clarify the meaning of $\Lambda$. Simple 4d and 5d models are presented to illustrate this, and we recall that this is the standard way in which things work out in string compactifications with brane instantons. We discuss the relation of our constraint to bounds that can be derived from wormholes or gravitational instantons and to those motivated by black-hole effects at finite temperature. Finally, we discuss potential loopholes to our arguments.