# Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars

Keir, J

3 June 2016

## Journal:

Classical and Quantum Gravity

## Last Updated:

2020-11-27T08:46:37.657+00:00

13

33

## DOI:

10.1088/0264-9381/33/13/135009

135009-135009

## abstract:

We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, this slow decay is highly suggestive of nonlinear instability. We also prove that, in a large class of asymptotically flat, spherically symmetric spacetimes, logarithmic decay actually holds as a uniform upper bound. In the presence of stable trapping, this result is therefore the best one can obtain. In addition, we provide an application of these results to ultracompact neutron stars, suggesting that all stars with $r\lt 3M$ might be unstable.

1081366

Submitted

Journal Article