Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars

Author: 

Keir, J

Publication Date: 

3 June 2016

Journal: 

Classical and Quantum Gravity

Last Updated: 

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

Issue: 

13

Volume: 

33

DOI: 

10.1088/0264-9381/33/13/135009

page: 

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.

Symplectic id: 

1081366

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article