Global Existence of Smooth Solutions to Relativistic String Equations in Schwarzschild Space-Time for Small Initial Data

Cited 2|Views7

Abstract

This paper is concerned with the motion of relativistic strings in Schwarzschild space-time. In a general framework, we first analyze the basic equations for the motion of a [Formula: see text]-dimensional extended object in a general enveloping space-time [Formula: see text], which is a given Lorentzian manifold, and then we investigate some important properties enjoyed by the equations for the motion of relativistic strings in Schwarzschild space-time. In particular, the equations are shown to form a totally linearly degenerate system of first-order hyperbolic equations in [Formula: see text] dimensions. Based on this observation and under suitable assumptions, we are able to prove the global existence of smooth solutions to the Cauchy problem for the equations of motion of relativistic strings (in Schwarzschild space-time) with sufficiently small arc length.

Translated text

Key words

Schwarzschild space-time,relativistic string,nonlinear wave equation,classical solution,global existence,event horizon

求助PDF

上传PDF

Bibtex

AI Read Science

AI Summary

AI Summary is the key point extracted automatically understanding the full text of the paper, including the background, methods, results, conclusions, icons and other key content, so that you can get the outline of the paper at a glance.

Example

Background

Key content

Introduction

Methods

Results

Related work

Fund

Key content

Pretraining has recently greatly promoted the development of natural language processing (NLP)
We show that M6 outperforms the baselines in multimodal downstream tasks, and the large M6 with 10 parameters can reach a better performance
We propose a method called M6 that is able to process information of multiple modalities and perform both single-modal and cross-modal understanding and generation
The model is scaled to large model with 10 billion parameters with sophisticated deployment, and the 10 -parameter M6-large is the largest pretrained model in Chinese
Experimental results show that our proposed M6 outperforms the baseline in a number of downstream tasks concerning both single modality and multiple modalities We will continue the pretraining of extremely large models by increasing data to explore the limit of its performance

Upload PDF to Generate Summary

Must-Reading Tree

Example

Generate MRT to find the research sequence of this paper