Electrically-charged Lifshitz spacetimes, and hyperscaling violations

Electrically-charged Lifshitz spacetimes are hard to come by. In this paper, we construct a class of such solutions in five dimensional Einstein gravity coupled to Maxwell and SU(2) Yang-Mills fields. The solutions are electrically-charged under the Maxwell field, whose equation is sourced by the Yang-Mills instanton(-like) configuration living in the hyperbolic four-space of the Lifshitz spacetime. We then introduce a dilaton and construct charged and colored Lifshitz spacetimes with hyperscaling violations. We obtain a class of exact Lifshitz black holes. We also perform similar constructions in four dimensions

Exact black hole formation in asymptotically (A)dS and flat spacetimes

We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a static scalar-hairy black hole. The solution can be asymptotically AdS, flat or dS depending on the value of the cosmological constant parameter Λ in the potential. As the advanced time u increases, the metric approaches the static limit in an exponential fashion, i.e., e−u/u0 with u0∼1/(α4M0)1/3 , where M0 is the mass of the final black hole and α is the second parameter in the potential. Similarly to the Vaidya solution, at u=0 , the spacetime can be matched to an (A)dS or flat vacuum except that at the origin a naked singularity may occur. Moreover, a limiting case of our solution with α=0 gives rise to an (A)dS generalization of the Roberts solution. Our results provide a new model for investigating formation of real life black holes with Λ≥0 . For Λ<0 , it can be instead used to study non-equilibrium thermalization of certain strongly-coupled field theory

Non-abelian (hyperscaling violating) Lifshitz black holes in general dimensions

We consider Einstein gravities coupled to a cosmological constant and multiple SU(2) Yang–Mills fields in general dimensions and find that the theories admit colored Lifshitz solutions with dynamic exponents z>1 . We also introduce a Maxwell field and construct exact electric charged black holes that asymptote to the z=D−1 colored Lifshitz spacetimes and analyze their thermodynamical first law. Furthermore, we introduce a dilaton to the system and construct Lifshitz spacetimes with hyperscaling violations. After turning on the Maxwell field, we obtain a class of hyperscaling violating Lifshitz black holes when θ=2D−2[z−(D−1)]

SU(2)-colored (A)dS black holes in conformal gravity

We consider four-dimensional conformal gravity coupled to the U(1) Maxwell and SU(2) Yang-Mills fields. We study the structure of general black hole solutions carrying five independent parameters: the mass, the electric U(1) and magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical pressure associated with the cosmological constant, which is an integration constant in conformal gravity. We derive the thermodynamical first law of the black holes. We obtain some exact solutions including an extremal black hole with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges. We derive the remainder of the first law for this special solution. We also reexamine the colored black holes and derive their first law in Einstein-Yang-Mills gravity with or without a cosmological constant

Charged black holes in colored Lifshitz spacetimes

We consider Einstein gravities coupled to a cosmological constant and SU(2) Yang–Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents z>1 . We study the wave equations of the SU(2) scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that approach the D=4 , z=3 and D=5 , z=4 colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes

Direct CP violation in τ±→K±ρ0(ω)ντ→K±π+π-ντ

We study the direct CP violation in the τ±→K±ρ0(ω)ντ→K±π+π-ντ decay process in the standard model. An interesting mechanism involving the charge symmetry violating mixing between ρ0 and ω is applied to enlarge the CP asymmetry. We find that the CP-violating asymmetry can be enhanced greatly via this ρ – ω mixing mechanism when the invariant mass of the π+π- pair is in the vicinity of the ω resonance. With this mechanism, the maximum differential and localized integrated CP asymmetries can reach -(5.6-1.7+2.9)×10-12 and 6.3-3.3+2.4×10-11 , respectively, which is still negligible

Non-extended phase space thermodynamics of Lovelock AdS black holes in the grand canonical ensemble

Recently, extended phase space thermodynamics of Lovelock AdS black holes has been of great interest. To provide insight from a different perspective and gain a unified phase transition picture, the non-extended phase space thermodynamics of (n+1) -dimensional charged topological Lovelock AdS black holes is investigated in detail in the grand canonical ensemble. Specifically, the specific heat at constant electric potential is calculated and the phase transition in the grand canonical ensemble is discussed. To probe the impact of the various parameters, we utilize the control variate method and solve the phase transition condition equation numerically for the cases k=1,-1 . There are two critical points for the case n=6,k=1 , while there is only one for the other cases. For k=0 , there exists no phase transition point. To figure out the nature of the phase transition in the grand canonical ensemble, we carry out an analytic check of the analog form of the Ehrenfest equations proposed by Banerjee et al. It is shown that Lovelock AdS black holes in the grand canonical ensemble undergo a second-order phase transition. To examine the phase structure in the grand canonical ensemble, we utilize the thermodynamic geometry method and calculate both the Weinhold metric and the Ruppeiner metric. It is shown that for both analytic and graphical results that the divergence structure of the Ruppeiner scalar curvature coincides with that of the specific heat. Our research provides one more example that Ruppeiner metric serves as a wonderful tool to probe the phase structures of black holes

A note on Maxwell’s equal area law for black hole phase transition

The state equation of the charged AdS black hole is reviewed in the T – r+ plane. With a view on the the phase transition, the T – S , P – V , P – ν graphs are plotted and then the equal area law is used in the three cases to get the phase transition point ( P ,  T ). The analytical phase transition point relations for P – T of a charged AdS black hole has been obtained successfully. By comparing the three results, we find that the equal area law possibly cannot be used directly for the P – ν plane. According to the T – S , P – V results, we plot the P – T – Q graph and find that for a highly charged black hole a very low temperature condition is required for the phase transition

Observational constraint on the interacting dark energy models including the Sandage–Loeb test

Two types of interacting dark energy models are investigated using the type Ia supernova (SNIa), observational <math><mrow><mi>H</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></math> data (OHD), cosmic microwave background shift parameter, and the secular Sandage–Loeb (SL) test. In the investigation, we have used two sets of parameter priors including WMAP-9 and Planck 2013. They have shown some interesting differences. We find that the inclusion of SL test can obviously provide a more stringent constraint on the parameters in both models. For the constant coupling model, the interaction term has been improved to be only a half of the original scale on corresponding errors. Comparing with only SNIa and OHD, we find that the inclusion of the SL test almost reduces the best-fit interaction to zero, which indicates that the higher-redshift observation including the SL test is necessary to track the evolution of the interaction. For the varying coupling model, data with the inclusion of the SL test show that the parameter <math><mi mathvariant="italic">ξ</mi></math> at <math><mrow><mn>1</mn><mi mathvariant="italic">σ</mi></mrow></math> C.L. in Planck priors is <math><mrow><mi mathvariant="italic">ξ</mi><mo>&gt;</mo><mn>3</mn></mrow></math> , where the constant <math><mi mathvariant="italic">ξ</mi></math> is characteristic for the severity of the coincidence problem. This indicates that the coincidence problem will be less severe. We then reconstruct the interaction <math><mrow><mi mathvariant="italic">δ</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo></mrow></math> , and we find that the best-fit interaction is also negative, similar to the constant coupling model. However, for a high redshift, the interaction generally vanishes at infinity. We also find that the phantom-like dark energy with <math><mrow><msub><mi>w</mi><mi>X</mi></msub><mo>&lt;</mo><mo>-</mo><mn>1</mn></mrow></math> is favored over the <math><mi mathvariant="italic">Λ</mi></math> CDM model

Phase Transitions, Geometrothermodynamics, and Critical Exponents of Black Holes with Conformal Anomaly

We investigate the phase transitions of black holes with conformal anomaly in canonical ensemble. Some interesting and novel phase transition phenomena have been discovered. It is shown that there are striking differences in both Hawking temperature and phase structure between black holes with conformal anomaly and those without it. Moreover, we probe in detail the dependence of phase transitions on the choice of parameters. The results show that black holes with conformal anomaly have much richer phase structure than those without it. There would be two, only one, or no phase transition points depending on the parameters. The corresponding parameter regions are derived both numerically and graphically. Geometrothermodynamics are built up to examine the phase structure we have discovered. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges. Furthermore, critical behaviors are investigated by calculating the relevant critical exponents. And we prove that these critical exponents satisfy the thermodynamic scaling laws