Generalized no-hair theorems without horizons

DOI: 
10.1088/1361-6382/ab23b6
Publication date: 
23/07/2019
Main author: 
Barceló C.
IAA authors: 
Barceló, C.
Authors: 
Barceló C., Carballo-Rubio R., Liberati S.
Journal: 
Classical and Quantum Gravity
Refereed: 
Yes
Publication type: 
Article
Volume: 
36.0
Pages: 
13LT01
Number: 
13LT01
Abstract: 
The simplicity of black holes, as characterized by no-hair theorems, is one of the most important mathematical results in the framework of general relativity. Are these theorems unique to black hole spacetimes, or do they also constrain the geometry around regions of spacetime with arbitrarily large (although finite) redshift? This paper presents a systematic study of this question and illustrates that no-hair theorems are not restricted to spacetimes with event horizons but are instead characteristic of spacetimes with deep enough gravitational wells, extending Israel's theorem to static spacetimes without event horizons that contain small deviations from spherical symmetry. Instead of a uniqueness result, we obtain a theorem that constrains the allowed deviations from the Schwarzschild metric and guarantees that these deviations decrease with the maximum redshift of the gravitational well in the external vacuum region. Israel's theorem is recovered continuously in the limit of infinite redshift. This result provides a first extension of no-hair theorems to ultracompact stars, wormholes, and other exotic objects, and paves the way for the construction of similar results for stationary spacetimes describing rotating objects. © 2019 IOP Publishing Ltd.
Database: 
SCOPUS
ADS
URL: 
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068647343&doi=10.1088%2f1361-6382%2fab23b6&partnerID=40&md5=9da435bec005bf112c04ef02beb51e9a
ADS Bibcode: 
2019CQGra..36mLT01B
Keywords: 
black holes; general relativity; observations of black holes; quasi-black holes; tests of general relativity