Macroscopic Black-Hole Remnants in a Nonlocal Field Theory: Towards Hawking Radiation in SFT

Abstract

We demonstrate that, for a large black hole of radius $a$, Hawking radiation terminates around the scrambling time $u_{\text{scr}}\equiv 2a\log (a/\ell )$ due to the nonlocal, exponential suppression of trans-Planckian interactions inherent in string field theory (SFT). Modifying a massless scalar field's interaction with a dynamical black hole background via the smearing operator $e^{{\ell }^2\square }$ (where $\ell$ denotes the string length scale), we calculate the time-dependent number expectation value $⟨\hat{N}(u)⟩$ of outgoing Hawking particles at retarded time $u$. While the standard Planck spectrum at the Hawking temperature is reproduced at early times ($u\ll u_{\text{scr}}$), the particle number approaches zero shortly after the scrambling time. This early shutoff reflects the property that the collapsing shell becomes effectively invisible to trans-Planckian modes, offering an alternative resolution to the black hole information paradox via a macroscopic remnant.

17 pages, no figure, references added