# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Morawetz estimate for linearized gravity in Schwarzschild

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

1708.06943.pdf

(Preprint), 812KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Andersson, L., Blue, P., & Wang, J. (2020). Morawetz estimate for linearized gravity
in Schwarzschild.* Annales Henri Poincaré,* *21*(3), 761-813.
doi:10.1007/s00023-020-00886-5.

Cite as: https://hdl.handle.net/21.11116/0000-0003-587F-D

##### Abstract

The equations governing the perturbations of the Schwarzschild metric satisfy

the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in

[2], we prove an integrated local energy decay estimate for both the

Regge-Wheeler and Zerilli equations. In these proofs, we use some constants

that are computed numerically. Furthermore, we make use of the $r^p$ hierarchy

estimates [13, 32] to prove that both the Regge-Wheeler and Zerilli variables

decay as $t^{-\frac{3}{2}}$ in fixed regions of $r$.

the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in

[2], we prove an integrated local energy decay estimate for both the

Regge-Wheeler and Zerilli equations. In these proofs, we use some constants

that are computed numerically. Furthermore, we make use of the $r^p$ hierarchy

estimates [13, 32] to prove that both the Regge-Wheeler and Zerilli variables

decay as $t^{-\frac{3}{2}}$ in fixed regions of $r$.