Reply to "Comment on `Quantum versus classical instability of scalar fields in curved backgrounds'"

TL;DR

This paper refutes a previous claim about scalar field instability in curved backgrounds, reaffirming that no tachyonic modes exist in certain static spacetimes without horizons, based on correct criteria.

Contribution

The authors clarify and correct the criterion for normalizable bound solutions, reaffirming the stability result for scalar fields in specific curved spacetimes.

Findings

Incorrect criterion used in the comment paper

Reaffirmation of no tachyonic modes in the specified spacetimes

Correction of the stability analysis methodology

Abstract

We show that the reasoning which led the author of arXiv:1310.6252 to reach his conclusions relies on an incorrect criterion for the existence of normalizable bound solutions. We reinforce that the general result derived in the Appendix of our paper (arXiv:1310.2185), namely, that "there are no tachyonic (i.e., unstable) modes for minimally coupled scalar fields in asymptotically flat spherically symmetric static spacetimes containing no horizons" is indeed correct.