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Eugen Radu - One of the best experts on this subject based on the ideXlab platform.
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Boson and Dirac stars in D ≥ 4 dimensions
Physics Letters B, 2019Co-Authors: Jose Luis Blázquez-salcedo, Christian Knoll, Eugen RaduAbstract:Abstract We present a comparative study of spherically symmetric, localized, particle-like solutions for spin s = 0 , 1 / 2 and 1 gravitating fields in a D-dimensional, asymptotically flat spaceTime. These fields are massive, possessing a Harmonic Time Dependence and no self-interaction. Special attention is paid to the mathematical similarities and physical differences between the bosonic and fermionic cases. We find that the generic pattern of solutions is similar for any value of the spin s, depending only on the dimensionality of spaceTime, the cases D = 4 , 5 being special.
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Asymptotically flat spinning scalar, Dirac and Proca stars
Physics Letters B, 2019Co-Authors: Carlos A R Herdeiro, Eugen Radu, I. Perapechka, Ya. ShnirAbstract:Abstract Einstein's gravity minimally coupled to free, massive, classical fundamental fields admits particle-like solutions. These are asymptotically flat, everywhere non-singular configurations that realise Wheeler's concept of a geon: a localised lump of self-gravitating energy whose existence is anchored on the non-linearities of general relativity, trivialising in the flat spaceTime limit. In [1] the key properties for the existence of these solutions (also referred to as stars or self-gravitating solitons) were discussed – which include a Harmonic Time Dependence in the matter field –, and a comparative analysis of the stars arising in the Einstein-Klein-Gordon, Einstein-Dirac and Einstein-Proca models was performed, for the particular case of static, spherically symmetric spaceTimes. In the present work we generalise this analysis for spinning solutions. In particular, the spinning Einstein-Dirac stars are reported here for the first Time. Our analysis shows that the high degree of universality observed in the spherical case remains when angular momentum is allowed. Thus, as classical field theory solutions, these self-gravitating solitons are rather insensitive to the fundamental fermionic or bosonic nature of the corresponding field, displaying similar features. We describe some physical properties and, in particular, we observe that the angular momentum of the spinning stars satisfies the quantisation condition J = m N , for all models, where N is the particle number and m is an integer for the bosonic fields and a half-integer for the Dirac field. The way in which this quantisation condition arises, however, is more subtle for the non-zero spin fields.
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Kerr black holes with Proca hair
Classical and Quantum Gravity, 2016Co-Authors: Carlos A R Herdeiro, Eugen Radu, Helgi F. RunarssonAbstract:Bekenstein proved that in Einstein’s gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein’s assumption that matter inherits spaceTime symmetries, we show this model admits asymptotically flat, stationary, axisymmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spaceTime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a Harmonic Time Dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field. ∗herdeiro@ua.pt †eugen.radu@ua.pt ‡helgi.runarsson@gmail.com 1 ar X iv :1 60 3. 02 68 7v 1 [ gr -q c] 8 M ar 2 01 6
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proca stars gravitating bose einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
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Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
Betti Hartmann - One of the best experts on this subject based on the ideXlab platform.
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Spontaneous scalarization of boson stars
Journal of High Energy Physics, 2019Co-Authors: Yves Brihaye, Betti HartmannAbstract:We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the $(\alpha {\cal R} + \gamma {\cal G}) \phi^2$ scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has Harmonic Time Dependence, while their space-Time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling $\alpha$ and $\gamma$, respectively. This is, in particular, true for boson stars that are {\it a priori} stable with respect to decay into individual bosonic particles. A fundamental difference between the $\alpha$- and $\gamma$-scalarization exists, though: while we find an interval in $\alpha > 0$ for which boson stars can {\it never} be scalarized when $\gamma=0$, there is no restriction on $\gamma\neq 0$ when $\alpha=0$. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
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Spontaneous scalarization of boson stars
Journal of High Energy Physics, 2019Co-Authors: Yves Brihaye, Betti HartmannAbstract:We study the spontaneous scalarization of spherically symmetric, asymptoically flat boson stars in the ( α ℛ + γ G $$ \mathcal{G} $$ ) ϕ ^2 scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has Harmonic Time Dependence, while their space-Time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling α and γ , respectively. This is, in particular, true for boson stars that are a priori stable with respect to decay into individual bosonic particles. A fundamental difference between the α - and γ -scalarization exists, though: while we find an interval in α > 0 for which boson stars can never be scalarized when γ = 0, there is no restriction on γ ≠ 0 when α = 0. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
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Critical phenomena of charged Einstein-Gauss-Bonnet black holes with charged scalar hair
Classical and Quantum Gravity, 2018Co-Authors: Yves Brihaye, Betti HartmannAbstract:Einstein-Gauss-Bonnet-gravity (EGB) coupled minimally to a $U(1)$ gauged, massive scalar field possesses -- for appropriate choices of the $U(1)$ charge -- black hole solutions that carry charged scalar hair if the frequency of the Harmonic Time-Dependence of the scalar field is equal to the upper bound on the superradiant frequency. The existence of these solutions has first been discussed in \cite{Grandi:2017zgz}. In this paper, we demonstrate that the critical value of the scalar charge results from the requirement of non-extremality of the charged black hole solutions and the fact that the scalar field should not escape to infinity. Moreover, we investigate the hairy black holes in more detail and demonstrate that the branch of these solutions joins the branch of the corresponding charged EGB black hole for vanishing scalar field, but is {\it not} connected to the branch of boson stars in the limit of vanishing horizon radius. This indicates that it is unlikely that these black holes appear from the collapse of the corresponding boson stars. Finally, we prove a No-hair theorem for charged scalar fields with Harmonic Time-Dependence for static, spherically symmetric, asymptotically flat electro-vacuum black holes in $d$ space-Time dimensions and hence demonstrate that the GB term is crucial for the existence of the hairy black holes discussed in this paper.
Carlos A R Herdeiro - One of the best experts on this subject based on the ideXlab platform.
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Asymptotically flat spinning scalar, Dirac and Proca stars
Physics Letters B, 2019Co-Authors: Carlos A R Herdeiro, Eugen Radu, I. Perapechka, Ya. ShnirAbstract:Abstract Einstein's gravity minimally coupled to free, massive, classical fundamental fields admits particle-like solutions. These are asymptotically flat, everywhere non-singular configurations that realise Wheeler's concept of a geon: a localised lump of self-gravitating energy whose existence is anchored on the non-linearities of general relativity, trivialising in the flat spaceTime limit. In [1] the key properties for the existence of these solutions (also referred to as stars or self-gravitating solitons) were discussed – which include a Harmonic Time Dependence in the matter field –, and a comparative analysis of the stars arising in the Einstein-Klein-Gordon, Einstein-Dirac and Einstein-Proca models was performed, for the particular case of static, spherically symmetric spaceTimes. In the present work we generalise this analysis for spinning solutions. In particular, the spinning Einstein-Dirac stars are reported here for the first Time. Our analysis shows that the high degree of universality observed in the spherical case remains when angular momentum is allowed. Thus, as classical field theory solutions, these self-gravitating solitons are rather insensitive to the fundamental fermionic or bosonic nature of the corresponding field, displaying similar features. We describe some physical properties and, in particular, we observe that the angular momentum of the spinning stars satisfies the quantisation condition J = m N , for all models, where N is the particle number and m is an integer for the bosonic fields and a half-integer for the Dirac field. The way in which this quantisation condition arises, however, is more subtle for the non-zero spin fields.
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Kerr black holes with Proca hair
Classical and Quantum Gravity, 2016Co-Authors: Carlos A R Herdeiro, Eugen Radu, Helgi F. RunarssonAbstract:Bekenstein proved that in Einstein’s gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein’s assumption that matter inherits spaceTime symmetries, we show this model admits asymptotically flat, stationary, axisymmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spaceTime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a Harmonic Time Dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field. ∗herdeiro@ua.pt †eugen.radu@ua.pt ‡helgi.runarsson@gmail.com 1 ar X iv :1 60 3. 02 68 7v 1 [ gr -q c] 8 M ar 2 01 6
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proca stars gravitating bose einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
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Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
Yves Brihaye - One of the best experts on this subject based on the ideXlab platform.
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Spontaneous scalarization of boson stars
Journal of High Energy Physics, 2019Co-Authors: Yves Brihaye, Betti HartmannAbstract:We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the $(\alpha {\cal R} + \gamma {\cal G}) \phi^2$ scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has Harmonic Time Dependence, while their space-Time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling $\alpha$ and $\gamma$, respectively. This is, in particular, true for boson stars that are {\it a priori} stable with respect to decay into individual bosonic particles. A fundamental difference between the $\alpha$- and $\gamma$-scalarization exists, though: while we find an interval in $\alpha > 0$ for which boson stars can {\it never} be scalarized when $\gamma=0$, there is no restriction on $\gamma\neq 0$ when $\alpha=0$. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
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Spontaneous scalarization of boson stars
Journal of High Energy Physics, 2019Co-Authors: Yves Brihaye, Betti HartmannAbstract:We study the spontaneous scalarization of spherically symmetric, asymptoically flat boson stars in the ( α ℛ + γ G $$ \mathcal{G} $$ ) ϕ ^2 scalar-tensor gravity model. These compact objects are made of a complex valued scalar field that has Harmonic Time Dependence, while their space-Time is static and they can reach densities and masses similar to that of supermassive black holes. We find that boson stars can be scalarized for both signs of the scalar-tensor coupling α and γ , respectively. This is, in particular, true for boson stars that are a priori stable with respect to decay into individual bosonic particles. A fundamental difference between the α - and γ -scalarization exists, though: while we find an interval in α > 0 for which boson stars can never be scalarized when γ = 0, there is no restriction on γ ≠ 0 when α = 0. Typically, two branches of solutions exist that differ in the way the boson star gets scalarized: either the scalar field is maximal at the center of the star, or on a shell with finite radius which roughly corresponds to the outer radius of the boson star. We also demonstrate that the former solutions can be radially excited.
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Critical phenomena of charged Einstein-Gauss-Bonnet black holes with charged scalar hair
Classical and Quantum Gravity, 2018Co-Authors: Yves Brihaye, Betti HartmannAbstract:Einstein-Gauss-Bonnet-gravity (EGB) coupled minimally to a $U(1)$ gauged, massive scalar field possesses -- for appropriate choices of the $U(1)$ charge -- black hole solutions that carry charged scalar hair if the frequency of the Harmonic Time-Dependence of the scalar field is equal to the upper bound on the superradiant frequency. The existence of these solutions has first been discussed in \cite{Grandi:2017zgz}. In this paper, we demonstrate that the critical value of the scalar charge results from the requirement of non-extremality of the charged black hole solutions and the fact that the scalar field should not escape to infinity. Moreover, we investigate the hairy black holes in more detail and demonstrate that the branch of these solutions joins the branch of the corresponding charged EGB black hole for vanishing scalar field, but is {\it not} connected to the branch of boson stars in the limit of vanishing horizon radius. This indicates that it is unlikely that these black holes appear from the collapse of the corresponding boson stars. Finally, we prove a No-hair theorem for charged scalar fields with Harmonic Time-Dependence for static, spherically symmetric, asymptotically flat electro-vacuum black holes in $d$ space-Time dimensions and hence demonstrate that the GB term is crucial for the existence of the hairy black holes discussed in this paper.
Vitor Cardoso - One of the best experts on this subject based on the ideXlab platform.
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proca stars gravitating bose einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
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Proca stars: Gravitating Bose–Einstein condensates of massive spin 1 particles
Physics Letters B, 2016Co-Authors: Richard Brito, Vitor Cardoso, Carlos A R Herdeiro, Eugen RaduAbstract:Abstract We establish that massive complex Abelian vector fields (mass μ) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a Harmonic Time Dependence (frequency w), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer m ∈ Z + . PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, M max , attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with m = 1 , 2 , 3 ), M max ≃ 1.058 M Pl 2 / μ ( M max ≃ 1.568 , 2.337 , 3.247 M Pl 2 / μ ), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.
