We present stable solution of static spherically symmetric Einstein-Yang-Mills equations with the SU(2) gauge group. This solution is asymptotically flat and regular at r = 0 and with nontrivial Yang-Mills(YM) connection. With quantized values of the Arnowitt-Deser-Misner (ADM) mass, the solutions asymptotically approach the Schwarzschild solution and have zero global YM charges. Numerical evidences suggest that this solution is both linearly and nonlinearly stable and has a ring of generic curvature singularities along the horizon. An effective counterexample to the no-hair conjecture is provided by this stable solution. Moreover, the stable black hole solution suggests that the coupling of gauge field to gravity in early Universe will generate a new type of black holes. Their stability means that these might be a possible new source of primordial black holes left over from the early Universe and serves as a possible new candidate for dark matter.
We present a new class of the black hole solutions of Einstein-Maxwell-Yang-Mills theory. These solutions have both U(1) charge and Yang-Mills hair. We also investigate the thermodynamic properties.
We investigate dyonic black hole and dyon solutions of four-dimensional $SU(N)$ Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer $N$, with $2N-2$ gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asympto…
We consider $d\geqslant 4$ Einstein--(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearizing the (extended) Yang-Mills equations on the background of the electric Reissner-Nordström (RN) black hole, we show the existence of normalizable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realization of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically prefer…
In the Bogomol'nyi-Prasad-Sommerfield (BPS) limit of Einstein-Yang-Mills-Higgs theory, we construct numerically a non-Abelian wormhole supported by a phantom field. The probe limit is the Yang-Mills-Higgs field in the background of Ellis wormhole when the gravity is switched off. The wormhole solutions possess the Yang-Mills-Higgs hair in the presence of gravity; Thus a branch of hairy wormhole solutions emerge from the Ellis wormhole when the gravitational coupling constant increases. We find that the mass of wormholes and scalar charge of phantom field increase monotonically when the gravita…
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $Λ$. These solutions are described by $N-1$ magnetic gauge field functions $ω_{j}$. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any $N$, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions $ω_{j}$ have no zeros,…
Aspects of hairy black holes in spontaneously-broken Einstein-Yang-Mills systems: Stability analysis and Entropy considerations
我们在自发破缺的杨-米尔斯规范理论中分析了（3+1）维黑洞时空，这些规范理论最近被提出来作为逃避标量无毛定理的候选理论。虽然我们表明，在原则上的无毛定理的条件不适用于这种情况下，然而，我们证明了“精神”的定理是不违反的，在这个意义上说，存在不稳定性，在sphaleron和引力部门。本文用变分法对由于拓扑原因而不稳定的弧翼扇进行了不稳定性分析。如图所示，在该扇区中存在对线性扰动不稳定的模式。不稳定性也存在于引力领域。提出了一种利用灾变理论计算引力不稳定模的方法。灾变泛函的作用是由黑洞的质量泛函起的。希格斯真空期望值（v. e. v.）作为一个控制参数，有一个临界值，超过这个临界值就会出现不稳定性。（稳定的）史瓦西解就是从这个角度理解的。灾变论方法极大地促进了非阿贝尔黑洞的普适稳定性研究，它超越了线性扰动。一些基本的熵的考虑也提出.
We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called "regular" case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS $\mathfrak{su}(N)$ system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for $Λ<0$, solutions are much less constrained as $r\rightarrow\inft…
We present solutions to classical field equations for purely magnetic $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory in asymptotically Anti-de Sitter space. These solutions are found to be stable under linear, time-dependent perturbations. Recent work has also shown that these solutions may in general be uniquely characterized by a countably infinite set of asymptotically measured, gauge-invariant charges. In light of this discovery, we revisit Bizon's `modified No-Hair conjecture', and suggest a new version that accommodates these solutions.
In this paper we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian along with the restriction to homogeneity allows for an anomaly free effective quantization. In particular we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fiel…
We here investigate static, spherically symmetric solutions to $\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory with a negative cosmological constant $Λ$ in the case of dyonic solutions, which possess a non-trivial electric sector of the gauge field. We are able to find non-trivial solutions to this system, and show that some may be uniquely characterised by a countably infinite set of global charges, which may have implications for Bizon's modified `No Hair' theorem.
We compute the holographic stress tensor of colored Lifshitz spacetimes following the proposal by Ross-Saremi for gravity duals of non-relativistic theories. For a well-defined variational principle, we first construct a finite on-shell action for the Einstein-Yang-Mills model in four dimensions with Lifshitz spacetime as a solution. We then solve the linearised equations of motion and identify the modes that preserve the asymptotically Lifshitz condition. Employing these modes, we also show that the stress tensor is finite, obeying the scaling and the diffeomorphism Ward identities, i.e., con…
This is a brief summary of the most important hairy black hole solutions in 3+1 spacetime dimensions discovered over the last 25 years. These were first of all the Einstein-Yang-Mills black holes and their various generalizations including the Higgs field, the dilaton and the curvature corrections, and also the Skyrme black holes. More recently, these were black holes supporting a scalar field violating the energy conditions or non-minimally coupled to gravity, and also spinning black holes with massive complex scalar hair. Finally, these were black holes with massive graviton hair.
We construct numerically the symmetric non-Abelian wormholes which are supported by a phantom field in the Einstein-Yang-Mills-Higgs theory beyond Bogomol'nyi-Prasad-Sommerfield (BPS) limit where the Higgs self-interaction constant $λ$ is non-vanishing. Analogous to the BPS limit, the probe limit is the Yang-Mills-Higgs field in the background of the Ellis wormhole when the gravity is switched off. In the presence of gravity, the wormhole solutions possess the Yang-Mills-Higgs hair where families of hairy wormholes solutions emerge from the Ellis wormhole when the gravitational coupling consta…
We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr…
The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves $c_T$ to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the universe. In this work, we investigate the presence of black hole hair in the remaining viable cosmological theories of modified gravity that respect the constraint $c_T=1$. We focus mainly on scalar-tensor theories of gravity, analyzing static, asymptotically flat black holes in Horndeski, Beyond Horndeski, Einstein-Scalar-Gauss-Bonnet, and Chern-Simons theories. We fi…
In this letter, we find the first dynamically stable non-singular solution spherically symmetric SU(2) Einstein-Yang-Mills equation. This solutions is regular at r=0 and asymptotically flat. Since the Yang-Mills field strength decay exponentially, the Einstein-Yang-Mills particle perhaps can be used to be a candidate for dark matter.
The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions that are solutions of the Yang-Mills-Einstein-Dirac coupled field equations, on fluid membranes with finite tension. Their solutions characterize MGD Yang-Mills-Dirac stars, whose mass has order of the Chandrasekhar mass, once the range of both the fermionic self-interaction and the Yang-Mills coupling constants is suitably chosen. Physical features of MGD Yang-Mills-Dirac stars are then discussed, and their ADM mass are derived, as a function o…
