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Compact astrophysical objects in modified gravity
General Relativity and Quantum Cosmology · Submitted 10 Oct 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In a third part, we establish an important stability criterion for these solutions, based on their causal structure.
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The abstract, sentence by sentence
Twenty years have passed since the discovery of the accelerated expansion of the Universe, reviving the interest for alternative theories of gravity. Adding a scalar degree of freedom to the usual metric of general relativity is one of the simplest ways to modify our gravitational theory. In parallel, our knowledge about black holes and neutron stars is booming, notably thanks to the advent of gravitational wave astronomy. This thesis is at the crossroads between the two fields, investigating the properties of compact objects in extended scalar-tensor theories. We start by reviewing essential no-hair results established since the seventies. After discussing the no-hair theorem proposed for black holes in Horndeski theory, we present its extension to stars. The second part of the thesis investigates in detail the various ways to circumvent this theorem. These notably include solutions with a time-dependent scalar field in order to match cosmological evolution, but also static and asymptotically flat configurations. In a third part, we establish an important stability criterion for these solutions, based on their causal structure. It is also the occasion to study the propagation of gravitational waves in black hole environments, and to select the theories where gravitational waves travel at the same speed as light.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Twenty years have passed since the discovery of the accelerated expansion of the Universe, reviving the interest for alternative theories of gravity. | background 1.00 | 0.03 | 0.02 | asserted 0.99 |
| s1 | Adding a scalar degree of freedom to the usual metric of general relativity is one of the simplest ways to modify our gravitational theory. | background 0.99 | 0.05 | 0.02 | asserted 0.95 |
| s2 | In parallel, our knowledge about black holes and neutron stars is booming, notably thanks to the advent of gravitational wave astronomy. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s3 | This thesis is at the crossroads between the two fields, investigating the properties of compact objects in extended scalar-tensor theories. | contribution 0.91 | 0.50 | 0.05 | asserted 0.99 |
| s4 | We start by reviewing essential no-hair results established since the seventies. | background 0.48 | 0.23 | 0.02 | asserted 0.93 |
| s5 | After discussing the no-hair theorem proposed for black holes in Horndeski theory, we present its extension to stars. | contribution 0.81 | 0.57 | 0.04 | asserted 0.88 |
| s6 | The second part of the thesis investigates in detail the various ways to circumvent this theorem. | contribution 0.98 | 0.58 | 0.04 | asserted 0.95 |
| s7 | These notably include solutions with a time-dependent scalar field in order to match cosmological evolution, but also static and asymptotically flat configurations. | contribution 0.93 | 0.42 | 0.05 | asserted 0.93 |
| s8 | In a third part, we establish an important stability criterion for these solutions, based on their causal structure. | contribution 0.94 | 0.90 | 0.15 | asserted 1.00 |
| s9 | It is also the occasion to study the propagation of gravitational waves in black hole environments, and to select the theories where gravitational waves travel at the same speed as light. | contribution 0.83 | 0.84 | 0.11 | asserted 0.98 |
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The paper
Original abstract
Twenty years have passed since the discovery of the accelerated expansion of the Universe, reviving the interest for alternative theories of gravity. Adding a scalar degree of freedom to the usual metric of general relativity is one of the simplest ways to modify our gravitational theory. In parallel, our knowledge about black holes and neutron stars is booming, notably thanks to the advent of gravitational wave astronomy. This thesis is at the crossroads between the two fields, investigating the properties of compact objects in extended scalar-tensor theories. We start by reviewing essential no-hair results established since the seventies. After discussing the no-hair theorem proposed for black holes in Horndeski theory, we present its extension to stars. The second part of the thesis investigates in detail the various ways to circumvent this theorem. These notably include solutions with a time-dependent scalar field in order to match cosmological evolution, but also static and asymptotically flat configurations. In a third part, we establish an important stability criterion for these solutions, based on their causal structure. It is also the occasion to study the propagation of gravitational waves in black hole environments, and to select the theories where gravitational waves travel at the same speed as light.
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References
How the literature uses it
19 arXiv papers cite this in 25 sentences
Papers citing it · 12 sentences without a confident label
Builds on it 1 paper
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This is thus a mere quadratic equation for $φ'$, generalizing to $k_5 ≠0$ the one derived for the cubic Galileon case in [ref] (see also [ref] ).
Large black-hole scalar charges induced by cosmology in Horndeski theories · Test scalar-field generated by a black hole · 0.99
Compares with it 1 paper
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This observation is even more relevant considering that in four dimensions, theories which are much less general than that studied here admit black hole solutions that are asymptotically AdS, flat or even exhibit a rather exotic asymptotic behavior [ref] .
Spinning black holes for generalized scalar tensor theories in three dimensions · Conclusions and discussions · 0.84
Cites it as background 11 papers
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A clear and precise discussion of its assumptions can be found e.g. in [ref] , which we briefly follow.
Exact black hole solutions in scalar-tensor theories · No-hair theorem for shift-symmetric scalar-tensor theories · 0.93
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For a review, see [ref] and references within.
The cosmic trimmer: Black-hole hair in scalar-Gauss-Bonnet gravity is altered by cosmology · Introduction · 1.00
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By now there is a number of analytic and numerical black hole solutions in scalar tensor theories most of which obtained upon breaking hypotheses to no hair theorems (see for example [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] ).
Compact objects of spherical symmetry in beyond Horndeski theories · Introduction · 0.82
What it cites · 216 sentences without a confident label
Contests 7 papers
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Using the above tools, we have corrected a misinterpretation [ref] in the literature about the said instability of a class of hairy black holes.
Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations · Conclusions · contest 0.91
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Using the above tools, we have corrected a misinterpretation [ref] in the literature about the said instability of a class of hairy black holes.
Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions · Conclusions · contest 0.91
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Using the above tools, we have corrected a misinterpretation [ref] in the literature about the said instability of a class of hairy black holes.
Instability of hairy black holes in shift-symmetric Horndeski theories · Conclusions · contest 0.91
Builds on 1 paper
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Again, this work was extended to slow rotation and realistic equations of state, giving some bounds on the parameters of the considered model [ref] .
Towards Strong Field Tests of Beyond Horndeski Gravity Theories · Star solutions · 0.90
Uses the method or tool of 2 papers
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The equations are more difficult to integrate in this case, and we resorted to numerical integration, based on the results of our work [ref] .
Black holes in a cubic Galileon universe · No scalar field around stars · 0.85
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The best way to write the field equations is in terms of the kinetic density $X=-(φ)^2/2$, as in [ref] .
Exact black hole solutions in shift symmetric scalar-tensor theories · Reflection-symmetric Horndeski models · 0.90
Uses data or values from 7 papers
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Requiring the theory to reproduce the heaviest known pulsar, PSR J0348+0432, which has mass $2.01 ±0.04 M_⊙$ [ref] , puts a bound on $β$ when it is positive [ref] .
A Massive Pulsar in a Compact Relativistic Binary · Star solutions · 0.92
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Requiring the theory to reproduce the heaviest known pulsar, PSR J0348+0432, which has mass $2.01 ±0.04 M_⊙$ [ref] , puts a bound on $β$ when it is positive [ref] .
Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity · Star solutions · 0.92
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On the other hand, the motion of stars near Sagittarius A$^*$, at the galactic center of Milky Way, shows that 4.3 million solar masses are compacted in a sphere of radius smaller than $2·10^-3$ light years [ref] .
Monitoring stellar orbits around the Massive Black Hole in the Galactic Center · Black holes · 0.81
Compares with 7 papers
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At this point, we would like to draw a parallel with the results of [ref] .
Galileon accretion · Test field limit · 1.00
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In particular, we arrive at the same conclusion as [ref] for the model ([ref]) with vanishing $Λ_b$: there is no stable homogeneous configuration.
The Paths of Gravity in Galileon Cosmology · Homogeneous solutions: a stability window · 0.98
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Within this subclass, no black hole solutions were found with a regular norm of the current $J^2$, although the solutions asymptotically agree with Dirac sourced star solutions found previously in this theory [ref] .
Solar System Constraints on Gauss-Bonnet Mediated Dark Energy · Conclusions · 0.82
Cites as support 8 papers
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Indeed, arbitrary $G_2$ and $G_3$ Horndeski functions do not affect the propagation of gravitational waves (this is true in an arbitrary background, as shown in [ref] ).
Speed of Gravitational Waves and the Fate of Scalar-Tensor Gravity · Cubic Lagrangian · 0.98
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Indeed, arbitrary $G_2$ and $G_3$ Horndeski functions do not affect the propagation of gravitational waves (this is true in an arbitrary background, as shown in [ref] ).
Time-dependent spherically symmetric covariant Galileons · Cubic Lagrangian · 0.98
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It can be shown that this action allows to account for an accelerated expansion of spacetime [ref] (at least as long as de Sitter metric can be viewed as a small deviation from Minkowski spacetime).
Classical and Quantum Consistency of the DGP Model · Cubic Lagrangian · 0.96
Cites as background 29 papers
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These conditions have been written several times in the literature [ref] .
Field-theoretical formulations of MOND-like gravity · Application to k-essence · 0.80
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These conditions have been written several times in the literature [ref] .
k-Essence, superluminal propagation, causality and emergent geometry · Application to k-essence · 0.80
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An important work [ref] was carried out to explore the Hamiltonian structure of the beyond Horndeski terms, Eqs. ([ref])-([ref]), together with standard Horndeski ones, Eq. ([ref]).
Healthy theories beyond Horndeski · Infrared modifications of gravity · 0.80
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