##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Jacob Sterbenz

#### UCSD

## Energy propagation for scalr radiation outside of a spherically symmetric black hole

##### Abstract:

Pieter Blue and myself concerning the nature of non-spherically symmetric finite energy waves outside of a Schwarzchild black hole. In particular, I will discuss our proof of the so called "Morawetz Estimate" which is a kind of monotonicity bound describing, in a unified way, the strength of wavefronts which form as an arbitrary burst of radiation splits into two pieces; one piece escaping to (asymptotically flat) infinity, and the other falling across the event horizon into the black hole. The main technical obstacle one must overcome in proving this kind of estimate is to capture (in a mathematical way) how an arbitrary wave "decides to split up". I will try to discuss this aspect in detail, in particular how it relates to well established ideas in quantum potential scattering.

Host:

### January 25, 2006

### 3:00 PM

### AP&M 7218

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