Relativistic jets comprise non-thermal emission within the AGN spectra, ranging from synchrotron sources of radio emission to higher-energy γ -ray and even cosmic ray emissions as can be seen in Figure 1. The power spectrum associated with synchrotron and self-synchrotron emission can be determined using Eq. 1 below P ν = 3 e 3 B ⁡ sin ⁡ α m e c 2 ν ν c ∫ ν / ν c ∞ K 5 / 3 η d η , (1) where the critical frequency, ν c , is given by ν c = 3 2 γ 2 ν G ⁡ sin ⁡ α , (2) with ν G as the gyrofrequency. The parameters B , α , and ν are the magnetic field strength, pitch angle, and emission frequency, respectively. The integral in the synchrotron power function here is characterized by the modified Bessel function of the second kind K 5 / 3 ( η ) , where η is defined as the ratio of the frequency to critical frequency ν c . Additionally, their spectra can be determined using various observational data analysis methods and SED correlation schemes (Homan et al., 2021). Current data analyses from observational missions have shown that the SEDs of BL Lacs and FSRQs exhibit significant continuum variability in their observed frequency bands (Harris and Krawczynski, 2006; Abdollahi et al., 2020; Valverde et al., 2020; Mohana A et al., 2023). These spectral data can be connected back to the black hole–disk system to infer the local properties of the surrounding accretion disk (i.e., matter content, dust/plasma temperature, and particle accelerations/scatterings) but are limited in describing the gravitationally induced dynamics of the relativistic jet (Gamble, 2022).

Currently, the mechanisms for relativistic jet emissions associated with AGN and other high-energy astrophysical objects like γ -ray bursts (GRBs) and microquasars are of interest in the astrophysics scientific community. Jet formation theory and emission is a major problem yet to be solved in high-energy astrophysics. One of the most widely argued models for describing this type of emission has been the Blandford–Znajek (BZ) process (Blandford and Znajek, 1977). This process describes the rotational energy extraction from black holes involving the torsion of magnetic field lines, resulting in Poynting flux-dominated outflows parallel to the rotation axis of the central object (Blandford and Znajek, 1977; Znajek, 1977). L B Z = f α H B ϕ 2 r s 2 c 8 π − 1 , (3) where Eq. 3 provides the BZ luminosity. Here, we define the parameters α H , B ϕ , a n d r s as the spin parameter of the black hole horizon, magnetic field strength in the ϕ -direction, and the corresponding Schwarzschild radius, respectively. The nature of such highly complex energetic emission mechanisms from these systems, which feature event horizons in rotating spacetimes, has been studied extensively over the last few decades (Williams, 2004; 1995; Pei et al., 2016; Toma and Takahara, 2016; King and Pringle, 2021; Gamble, 2022). Recent numerical and observational models incorporating magnetohydrodynamic (MHD) and general relativistic magnetohydrodynamic (GRMHD) methods have shown that a major contribution to jet outflows is from the poloidal magnetic field configurations from relativistic matter accreting onto the central object (Komissarov, 2005; Nathanail and Contopoulos, 2014; Koide, 2020; Akiyama et al., 2022). Unanswered questions on the relativistic nature of these jets involve figuring out how particles that make up the jet content are accelerated to ultra-relativistic speeds, of which the Lorentz factors are Γ Lorentz > 10 . What is the origin of the relativistic particles that produce non-thermal radiation that we observe? Moreover, how do these jets become matter-loaded? Focusing on the theoretical aspects of jet formation mechanisms, fundamental questions continue to remain unresolved, one of which is the causal connection of the jet to the exterior Kerr spacetime. An application of the BZ process to alternatives or extensions of general relativity by Pei et al. (2016) has shown the versatility of the decade-old theory but, again, exhibits how the BZ process needs extensions to incorporate the sources of the magnetic fields it describes (Garofalo and Singh, 2021; King and Pringle, 2021).

As mentioned, a relativistic jet is described as a beam of light that carries linear momentum and, thus, is influenced by an appreciable amount of external angular momentum in both the non-relativistic and relativistic regimes. This angular momentum would then be dependent on the origin of an associated coordinate system, owing to the intrinsic gauge dependence of angular momentum in fundamental physics descriptions. If we then proceed to describe BL Lac and FSRQ blazars as energetic point sources, we can infer the physical characteristics of the jet emission as relativistic beams transported across galactic distances. These point sources should then inherently carry rotational symmetry corresponding to rotated field lines with respect to the host black hole (Gamble, 2022). The following equations of motion described in Eq. 4, specifically under the influence of curved spacetime near the jet-launching region, illustrate the complexities of jet launching from the supermassive black holes of blazar types. Here, the potentials parameterizing particle paths in this near-horizon region are defined, yielding a set of Hamilton–Jacobi equations for each direction. It is easy to see the expected symmetries in the particle paths for the t and ϕ directions. Here, the functions R ( r ) and V ( θ ) in Eqs 6, 7 correspond to the traditional motions in the r and θ directions, respectively. Σ d r d λ = ± R r , (4a) Σ d θ d λ = ± V θ θ , (4b) Σ d ϕ d λ = − α H E − L / s i n 2 θ + α H T / Δ , (4c) Σ d t d λ = − α H α H E s i n 2 θ − L + r 2 + α H 2 T / Δ , (4d) where the functions T , R ( r ) , and V θ ( θ ) are defined as T ≡ E r 2 + α H 2 − α H L , (5) R r ≡ T 2 − Δ m 0 2 r 2 + L − α H E 2 + Q , (6) V θ θ ≡ Q − c o s 2 θ α H 2 m 0 2 − E 2 L 2 s i n 2 θ . (7) Here, E and L are the particle energy and angular momentum, respectively, m 0 is the rest mass of a test particle, and Q is identified as Carter’s constant. The functions Σ = r 2 + α H 2 c o s 2 θ and Δ = r 2 − M r + α H 2 are defined from the components of the Kerr spacetime for a rotating black hole of arbitrary mass. Within the context of this discussion on blazar jet emission, it is logical to consider not only the particle distributions in jets but also the intrinsic geometry of particle paths moving at high Lorentz factors, specifically above Γ bulk ≥ 10 − 1 0 2 . Additionally, there have been efforts to incorporate non-equatorial instabilities that contribute to the e − / e + pair production at γ -ray energies ≥ G e V around high-spin α H ≥ 0.8 black hole horizons in a description of jet launching (Williams, 1995; Williams, 2004), thus removing some of the mystery of the physical mechanisms that cause some jets to twist and carry a proportionate amount of angular momentum from the black hole. It is then intuitive to think about how one can infer the mechanisms causing such polarization in the observed spectra. Observations of blazars and radio-loud AGN have shown that polarization states exist in the spectra from these sources (Homan et al., 2021; Liodakis et al., 2021).

Observing the variability of blazars can reveal the necessary information to infer the composition of the jet emissions, the mechanisms behind the jet formation, and changes in the accretion rate of the accretion disk and can allow for the localization of the innermost emitting regions (Lawrence, 2016; Valverde et al., 2020). As the central supermassive black hole (SMBH) at the cores of blazars accretes matter and forms the surrounding accretion disk, it launches relativistic jets that emit across the electromagnetic spectrum (radio to γ -rays) (Gupta et al., 2016). Figure 2 shows such a distribution in the GeV energy flux associated with γ -ray emissions versus the very long baseline array (VLBA) flux for these radio–gamma correlated sources. This distribution shows a differentiation between high-synchrotron peak (HSP) BL Lacs that feature peaks in the range ν > 1 0 15 Hz and low-synchrotron peaked (LSP) BL Lacs that fall in the range ν < 1 0 14 Hz (Sahakyan, 2020). Refer to Giommi and Padovani (1994) and Abdo et al. (2010b) for more detailed descriptions comparing HSP and LSP signatures for BL Lacs.

Figure 3 shows that there exists a delayed variability in the radio emission for the blazar TXS 0506 + 056 (4FGL J0509.4 + 0542) compared to its higher-energy counterpart in the light curve at E p h > 1.07 GeV. This light curve, along with blazars in the MOJAVE-FERMI catalog, features this type of variability, where the radio and γ -ray emissions are correlated according to a respective time lag. There exists significant correspondence with the γ -ray flaring of TXS 0506 + 056 (4FGL J0509.4 + 0542) with neutrino incidence in the direction of this blazar (IceCubeFermi-LATMAGICAGILEASAS-SNHAWC et al., 2018). Analyzing the photo-meson production for HSP as stated above, such particle interactions within the jets of highly energetic sources like TXS 0506 + 056 (4FGL J0509.4 + 0542) and PKS 0735 + 178 (4FGL J0738.1 + 1742) (Prince et al., 2023) are a testament of the dynamic multi-messenger and multi-physics aspect of sources that feature extremely accelerated ejecta. The correlation between the radio and very high-energy (VHE) γ -ray emissions is a curious notion highlighting the new frontier of multi-messenger astrophysics in the modern era of astronomy. Additionally, HSP blazars with similar flaring characteristics are also likely to exhibit particle cascade mechanisms that produce cosmic rays (high-energy nucleons and charged particles). The 116 sources in the MOJAVE-FERMI-LAT 1FGL catalog are a prototypical example of the type of variability blazars exhibit across multiple spectral frequencies. Note that the catalog only correlates VLBI-selected 15-GHz radio-loud sources with a significant correlation to their γ -ray peaks. The catalog is sourced from the study by Kramarenko et al. (2021), a decade of joint MOJAVE-Fermi AGN monitoring: localization of the γ -ray emission region that features 331 sources with down selection to N-blazars with significantly strong radio emission ( > = 80 % ) of the 331 catalogs of sources. Both blazar classes have been reported to present strong correlations between the radio and γ -ray emissions (Max-Moerbeck et al., 2014; Mufakharov et al., 2015; Fan et al., 2016), thus indicating that the production of these jet emissions coincides with a common mechanism. A more extensive overview of radio VLBI/ γ -ray catalogs of blazars: MOJAVE-FERMI-LAT 1FGL, National Radio Astronomy Observatory (NRAO) catalogs, Atacama Large Millimeter/submillimeter Array (ALMA), and Event Horizon Telescope results and simulations will be provided in subsequent papers focusing on more details of the cross-correlation in blazars. Figure 4 shows such intra-week variability at 15 GHz in the time domain. This variability illustrates the need for time-domain follow-up for energetic sources. We can see that on a month-to-month time scale, the correlation strength peaks at ∼ 5 months. This suggests that there could be a significant observing campaign for follow-up observations. From a multi-physics perspective, improved time-dependent theoretical models and GRMHD simulations are needed to decipher such physics.

Given the nature of the high-energy emission characteristics of BL Lac and FSRQ blazars, it is additionally safe to compare them to GRBs. Both types of high-energy sources are considered to be sourced by compact objects (i.e., SMBH, X-ray binaries, neutron star mergers, core-collapse supernovae, and stellar mass black holes). Both energetic phenomena exhibit similar physical characteristics when considering their respective ejecta mechanisms. It is no coincidence that GRBs and blazar jets also feature similarities in the spectral peaks, illuminating commonalities in their respective radiation physics (Nemmen et al., 2012). A more detailed description of these physical comparisons can be found in works highlighting such comparisons (Lyu et al., 2014; Srinivasaragavan et al., 2023). An even more interesting recent inclusion in the “AGN zoo” is changing-look blazars. These are blazars that feature changes in their accretion processes, intrinsically changing from FSRQ-type to BL Lac and vice versa (Kang et al., 2024). This suggests that further investments in TDAMM science and its technological developments are needed to further elucidate the dynamical properties of AGN with blazar types, BL Lac, FSRQs, and BCUs.