To address the singularity problem in black hole physics, Penrose proposed the cosmic censorship conjecture . However, whether this conjecture holds in different types of black holes, especially for the Strong Cosmic Censorship Conjecture (SCCC), remains an issue worth further exploration. This study investigates the Yang-Mills field modified RN black hole, which provides new possibilities for exploring the Strong Cosmic Censorship Conjecture due to its unique nonlinear dynamical properties. In this work, the perturbation equations of two scalar fields for the Yang-Mills field modified RN black hole are derived. By combining the WKB method and the Prony method, the quasi-normal modes frequencies of the perturbations are analyzed. Additionally, constraints on the charge-to-mass ratio of the charged and massive scalar field are obtained using the Weak Gravity Conjecture (WGC), and it is shown that the Yang-Mills field modified RN black hole satisfies the SCCC conditions in the extreme state. The study reveals that the Yang-Mills field charge $q_{YM}$ significantly affects the damping effect and gravitational blueshift effect of the perturbations, causing the RN black hole in the extreme state to transition from violating the SCCC to satisfying it. Furthermore, when the charge-to-mass ratio $q/m$ of the charged and massive scalar field satisfies the WGC condition, the scalar field perturbations destabilize the Cauchy horizon of the Yang-Mills field modified RN black hole in the extreme state, thus confirming the applicability of the SCCC under extreme conditions. This study highlights the key role of nonlinear fields in singularity theory and gravitational dynamics, providing important support for the completeness of general relativity and offering new insights into the theoretical research of black holes in extreme states.
We numerically construct the stationary solutions of $SU(2)$ Einstein-Yang-Mills theory in four dimensional anti-de Sitter spacetime. When the $t$ component of $SU(2)$ gauge field is taken to the only nonzero component, we construct a class of counterexamples to the weak cosmic censorship conjecture in Einstein-Maxwell theory. However, including a nonzero $ϕ$ component of $SU(2)$ gauge field, we can argue that there is a minimum value $q_W$, when the charge carried by the $ϕ$ component is larger than this minimum value, for sufficiently large boundary electric amplitude $a$, the original count…
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.
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…
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…
