Generalized no-hair theorems without horizons

Carlos Barcel\'o; Ra\'ul Carballo-Rubio; Stefano Liberati

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Generalized no-hair theorems without horizons

Carlos Barceló, Raúl Carballo-Rubio, Stefano Liberati

General Relativity and Quantum Cosmology · Submitted 18 Jan 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.75 · states limitation 0.67 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	background 1.00	0.04	0.02	asserted 1.00
s1	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?	gap 0.84	0.04	0.03	unclear 0.95
s2	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.	contribution 0.62	0.95	0.92	asserted 1.00
s3	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.	result 0.99	0.95	0.51	asserted 1.00
s4	Israel's theorem is recovered continuously in the limit of infinite redshift.	result 0.72	0.81	0.11	asserted 1.00
s5	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.	interpretation 0.77	0.70	0.15	asserted 0.88

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original 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.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Listening to the Horizon: Probing Near-Horizon Reflectivity with GW250114
gr-qc 2026-10 conditional novelty 7.0 of 10

An echo search in GW250114, calibrated by the observed Direct Wave, finds no delayed echo and limits near-horizon surface reflectivity to |Rs| < 0.059 at 90 percent credibility.
Analytical model for gravitational-wave echoes from spinning remnants
gr-qc 2019-07 conditional novelty 6.0 of 10

An analytical low-frequency gravitational-wave template for the ringdown and echoes of a spinning horizonless compact object, parametrized by reflectivity and compactness, with projected detectability for current and ...
Tidal heating as a discriminator for horizons in extreme mass ratio inspirals
gr-qc 2019-10 conditional novelty 5.0 of 10

Absence of a black-hole horizon in an extreme-mass-ratio inspiral shifts the gravitational-wave phase by 10^2 to 10^4 radians, enough for LISA to bound the central object's reflectivity below 0.01 percent.

How the literature uses it

6 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Compares with it 1 paper

In the domains of validity where our analyses intersect with thosein [ref] and [ref] , we find essentially the same results: that deviations from sphericity have to die off with powers of the compactness parameter.

No-hair and almost-no-hair results for static axisymmetric black holes and ultracompact objects in astrophysical environments · Discussion and conclusions · 0.99

Cites it as background 2 papers

ECOs may potentially exhibit deviations from the Kerr metric [ref] .

Tidal heating as a discriminator for horizons in equatorial eccentric extreme mass ratio inspirals · Discussion · 0.80
The uniqueness theorem [ref] tells us that curved spacetime described by Kerr-Newman(KN) metric in the Einstein-Maxwell gravitational theory can hold at most three global conserved quantities, which are named as mass, electric charge and angular momentum.

The fastest relaxation rate of higher-dimensional Reissner--Nordstr\"{o}m black hole · Introduction · 0.98

What it cites · 17 sentences without a confident label

Compares with 2 papers

During the last stages of the preparation of this manuscript, we noticed the existence of the recent work [ref] that deals with the same problem but from a different perspective, and using a different approach (namely, constructing explicitly a family of geometries that include perturbative deviations from the Schwarzschild solution).

Exotic compact objects with soft hair · Implications and conclusions · 0.92
Also, the paper [ref] is related to some of the ideas discussed here, focusing its discussion instead on some of the possible implications that a different multipolar structure would have for gravitational waves.

How well can ultracompact bodies imitate black hole ringdowns? · Implications and conclusions · 0.85

Cites as background 8 papers

There are still many aspects to be understood regarding these theorems, from mathematical technicalities [ref] to the study of their interplay with observations [ref] .

Testing the No-Hair Theorem with Observations of Black Holes in the Electromagnetic Spectrum · Introduction · 0.99
There are still many aspects to be understood regarding these theorems, from mathematical technicalities [ref] to the study of their interplay with observations [ref] .

Testing the no-hair theorem with the continuum-fitting and the iron line methods: a short review · Introduction · 0.99
There are still many aspects to be understood regarding these theorems, from mathematical technicalities [ref] to the study of their interplay with observations [ref] .

Challenges testing the no-hair theorem with gravitational waves · Introduction · 0.99

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