In relativistic mechanics, the 4-velocity and the 4-momentum need not be parallel. This allows their norm to have a different sign. This possibility occurs in nonlinear electrodynamics (NED) models minimally coupled to Einstein's theory. Surprisingly, for a large class of NED models with a Maxwell limit, for weak fields, the causal (acausal) photons, as determined by their 4-velocity, have a spacelike (timelike) 4-momentum, leading to good tachyons and bad bradyons. Departing from weak fields, this possibility is determined solely by the concavity of the NED Lagrangian, which is consistent with the Dominant Energy Condition analysis. As a corollary, some popular regular black hole solutions sourced by NED, such as the Bardeen and Hayward solutions, are acausal.

Brazil

Marco A.A. de Paula

Haroldo C.D. Lima Junior

Portugal

Pedro V.P. Cunha

Carlos A.R. Herdeiro

Luís C.B. Crispino

Good tachyons, bad bradyons: Role reversal in Einstein-nonlinear-electrodynamics models

Recently, a scalar counterpart of the Schwarzschild-Melvin Universe was reported [1]. We show this solution is a special case of a Schwarzschild black hole/mass in a scalar multipolar Universe, that can be constructed algebraically combining known vacuum solutions. This builds on the generalized Weyl construction for scalar-vacuum, that admits two, fully decoupled, independent harmonic functions: one for the gravitational sector and another for the scalar sector. Harmonic solutions with growing multipoles lead to naked singularities (at spatial infinity), including for the scalar counterpart of the Schwarzschild-Melvin; harmonic solutions with decaying (scalar) multipoles are asymptotically flat, but have a singular horizon, in accordance with no-scalar-hair theorems. The scalar-vacuum model can be mapped to a five dimensional pure gravity construction via Kaluza-Klein oxidization and, in this way, to the corresponding <math><mi>D</mi><mo>=</mo><mn>5</mn></math> generalized Weyl construction.

Black holes in scalar multipolar universes

In linear perturbation theory, a static perturber in the vicinity of a Schwarzschild black hole (BH) enhances [suppresses] the Gauss-Bonnet (GB) curvature invariant, <math><msub><mrow><mi>R</mi></mrow><mrow><mi>GB</mi></mrow></msub></math>, in the high [low] tide regions. By analysing exact solutions of the vacuum Einstein field equations describing one or two BHs immersed in a multipolar gravitational field, which is locally free of pathologies, including conical singularities, we study the corresponding non-linear tides on a fiducial BH, in full General Relativity (GR). We show that the tidal field due to a far away, or close by, static BH creates high/low tides that can deviate not only quantitatively but also qualitatively from the weak field/Newtonian pattern. Remarkably, the suppression in low tide regions never makes <math><msub><mrow><mi>R</mi></mrow><mrow><mi>GB</mi></mrow></msub></math> negative on the BH, even though the horizon Gaussian curvature may become negative; but <math><msub><mrow><mi>R</mi></mrow><mrow><mi>GB</mi></mrow></msub></math> can vanish in a measure zero set, a feature qualitatively recovered in a Newtonian analogue model. Thus, purely gravitational, static, tidal interactions in GR, no matter how strong, cannot induce GB$^{−}$ scalarization. We also show that a close by BH produces noticeable asymmetric tides on another (fiducial) BH.

Lorenzo Annulli

Non-linear tides and Gauss-Bonnet scalarization

In the presence of certain non-minimal couplings between a scalar field and the Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long as they are spinning fast enough. This provides a distinctive violation of the Kerr hypothesis, occurring only for some high spin range. In this paper we assess if strong magnetic fields, that may exist in the vicinity of astrophysical black holes, could facilitate this distinctive effect, by bringing down the spin threshold for scalarization. This inquiry is motivated by the fact that self-gravitating magnetic fields, by themselves, can also promote “spin-induced” scalarization. Nonetheless, we show that in the vicinity of the horizon the effect of the magnetic field B on a BH of mass M, up to <math><mi>B</mi><mi>M</mi><mo>≲</mo><mn>1</mn></math>, works against spin-induced scalarization, requiring a larger dimensionless spin j from the black hole. A geometric interpretation for this result is suggested, in terms of the effects of rotation vs. magnetic fields on the horizon geometry.

Eugen Radu

Spin-induced scalarization and magnetic fields

The possibility of mining the rotational energy from black holes has far–reaching implications. Such energy extraction could occur even for isolated black holes, if hypothetical ultralight bosonic particles exist in Nature, leading to a new equilibrium state – a black hole with synchronised bosonic hair – whose lifetime could exceed the age of the Universe. A natural question is then: for an isolated black hole and at maximal efficiency, how large is the energy fraction ϵ that can be extracted from a Kerr black hole by the superradiant growth of the dominant mode? In other words, how hairy can the resulting black hole become? A thermodynamical bound for the total superradiance efficiency, <math><mi>ϵ</mi><mo>≲</mo><mn>0.29</mn></math> (as a fraction of the initial black hole mass), has long been known, from the area law. However, numerical simulations exhibiting the growth of the dominant mode only reached about one third of this value. We show that if the development of superradiant instabilities is approximately conservative (as suggest by the numerical evolutions), this efficiency is limited to <math><mi>ϵ</mi><mo>≲</mo><mn>0.10</mn></math>, regardless of the spin of the bosonic field. This is in agreement with the maximum energy extraction obtained in numerical simulations for a vector field and predicts the result of similar simulations with a scalar field, yet to be performed.

Nuno M. Santos

A bound on energy extraction (and hairiness) from superradiance

As the electron in the hydrogen atom, a bosonic field can bind itself to a black hole occupying a discrete infinite set of states. When (i) the spacetime is prone to superradiance and (ii) a confinement mechanism is present, some of such states are infinitely long–lived. These equilibrium configurations, known as stationary clouds, are states “synchronized” with a rotating black hole's event horizon. For most, if not all, stationary clouds studied in the literature so far, the requirements (i)–(ii) are independent of each other. However, this is not always the case. This paper shows that massless neutral scalar fields can form stationary clouds around a Reissner–Nordström black hole when both are subject to a uniform magnetic field. The latter simultaneously enacts both requirements by creating an ergoregion (thereby opening up the possibility of superradiance) and trapping the scalar field in the black hole's vicinity. This leads to some novel features, in particular, that only black holes with a subset of the possible charge to mass ratios can support stationary clouds.

Black holes, stationary clouds and magnetic fields

The minimal   ${U}(1)_{\rm{{B-L}}}$   extension of the Standard Model (B-L-SM) offers an explanation for neutrino mass generation via a seesaw mechanism; it also offers two new physics states, namely an extra Higgs boson and a new   ${U}(1)_{\rm{{B-L}}}$   gauge boson. The emergence of a second Higgs particle as well as a new   ${U}(1)_{\rm{{B-L}}}$   gauge boson, both linked to the breaking of a local   ${U}(1)_{\rm{{B-L}}}$   symmetry, makes the B-L-SM rather constrained by direct searches in Large Hadron Collider (LHC) experiments. We investigate the phenomenological status of the B-L-SM by confronting the new physics predictions with the LHC and electroweak precision data. Taking into account the current bounds from direct LHC searches, we demonstrate that the prediction for the muon   ${U}(1)_{\rm{{B-L}}}$   anomaly in the B-L-SM yields at most a contribution of approximately   ${U}(1)_{\rm{{B-L}}}$   , which represents a tension of   ${U}(1)_{\rm{{B-L}}}$   standard deviations, with the current   ${U}(1)_{\rm{{B-L}}}$   uncertainty, by means of a   ${U}(1)_{\rm{{B-L}}}$   boson if its mass is in the range of   ${U}(1)_{\rm{{B-L}}}$   to   ${U}(1)_{\rm{{B-L}}}$  , within the reach of future LHC runs. This means that the B-L-SM, with heavy yet allowed   ${U}(1)_{\rm{{B-L}}}$   boson mass range, in practice, does not resolve the tension between the observed anomaly in the muon   ${U}(1)_{\rm{{B-L}}}$   and the theoretical prediction in the Standard Model. Such a heavy   ${U}(1)_{\rm{{B-L}}}$   boson also implies that the minimal value for the new Higgs mass is of the order of 400 GeV.

Felipe F. Freitas

António P. Morais

António Onofre

Sweden

Roman Pasechnik

Nicolas Sanchis-Gual

Rui Santos

What can a heavy Boson do to the Muon anomaly and to a new Higgs boson mass?  

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function <math><mi>f</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math>, between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: <math><mi>f</mi><mo>(</mo><mi>Φ</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>+</mo><mi>α</mi><msup><mrow><mi>Φ</mi></mrow><mrow><mn>4</mn></mrow></msup></math>. The domain of existence of the scalarised BHs, for fixed α, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myers-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.

Germany

Jose Luis Blázquez-Salcedo

Jutta Kunz

Alexandre M. Pombo

Einstein-Maxwell-scalar black holes: The hot, the cold and the bald

The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu–Jona-Lasinio model. The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space, i.e. the charged pion. In this framework, 
					 are treated as bound states of quarks and not as point-like charged particles. The isospin chemical potential plays the role of a trigger for charged pion condensation. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition. The dependence of pion condensation on model parameters is investigated.
				

China

Jingyi Chao

Mei Huang

Russia

Andrey Radzhabov

Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density J.Y.C. is supported by the NSFC under Grant number: 11605254 and Major State Basic Research Development Program in China (2015CB856903). M.H. is supported by the NSFC under Grant No. 11725523, 11735007 and 11261130311(CRC 110 by DFG and NSFC). A.R. is supported by the CAS President's international fellowship initiative (2017VMA0045) and numerical calculations are performed on computing cluster "Akademik V.M. Matrosov" (http://hpc.icc.ru)

Building upon the methods used recently in [1], we establish the inexistence of self-gravitating solitonic solutions for both static and strictly stationary asymptotically flat spacetimes in generalised axion electrodynamics. This is an Einstein-Maxwell-axion model, where the axion field θ is non-minimally coupled to the electromagnetic field. Considering the standard QCD axion coupling, we first present an argument for the absence of static axionic solitons, i.e. localised energy axionic-electromagnetic configurations, yielding an everywhere regular, horizonless, asymptotically flat, static spacetime. Then, for generic couplings <math><mi>f</mi><mo>(</mo><mi>θ</mi><mo>)</mo></math> and <math><mi>g</mi><mo>(</mo><mi>θ</mi><mo>)</mo></math> (subject to mild assumptions) between the axion field and the electromagnetic field invariants, we show there are still no solitonic solutions, even when dropping the staticity assumption and merely requiring a strictly stationary spacetime, regardless of the spatial isometries.