Backdraft: String Creation in an Old Schwarzschild Black Hole

Abstract

We analyze string production in the background of a Schwarzschild black hole, after developing first quantized methods which capture string-theoretic nonadiabatic effects which can exceed naive extrapolations of effective field theory. Late-time infalling observers are strongly boosted in the near horizon region relative to early observers and formation matter. In the presence of large boosts in flat spacetime, known string and D-brane scattering processes exhibit enhanced string production, even for large impact parameter. This suggests the possibility that the nonadiabatic dynamics required to realize the firewall proposal of AMPS occurs for old black holes, with the late-time observer catalyzing the effect. After setting up this dynamical thought experiment, we focus on a specific case: the production of open strings stretched D-particles, at least one of which falls in late (playing the role of a late time observer). For relatively boosted D-branes, we precisely recover earlier results of Bachas, McAllister and Mitra which we generalize to brane trajectories in the black hole geometry. For two classes of late-time probes, we find a regime of significant non-adiabaticity by horizon crossing, assessing its dependence on the boost in each case. Closed string probes, as well as additional effects in D-brane scattering, may produce other significant non-adiabatic effects depending on the boost, something we leave for further work.

Figures (4)

• Figure 1: The relatively boosted trajectories 1 and 2 described in the text. Near the horizon, the spacetime reduces to a patch of Minkowski space. This raises the question of whether the strong boost-induced non-adiabatic effects described in BachasRelDbranesVeneziano might arise for probes of black holes, providing a dynamical mechanism for the breakdown of effective field theory.
• Figure 2: A Kruskal diagram of the setup for $E<m$. Starting from a constant radial position $r=R$ outside the black hole, two D-branes are dropped in at very different times $t=0$ and $t=\Delta t$. As we increase $\Delta t$, the intersection point between the solid and dashed purple lines approaches the horizon as in (\ref{['meeting']}).
• Figure 3: The integration contour corresponding to the particle-production saddle point of the worldline path integral. Here $t_*$ is a branch point at which the frequency vanishes, taking the value $ia/b$ in the simple example described in the text.
• Figure 4: The contour of integration going around the branch point where $\omega(T)=0$. The imaginary part of the action gets a contribution from the integral around the branch cut.