Wenting Zhou

Applying the junction conditions to the slowly rotating Kerr spacetime with a thin shell, when higher order terms in the spin parameter a can be neglected, we find that while the angular momentum L and Carter constant C of the ray remain unchanged upon crossing the shell, its energy E does not. Consequently, the impact parameters $$\eta =L/E$$ η = L / E and $$\xi =C/E^2$$ ξ = C / E 2 of the ray are discontinued at the shell. Utilizing this transformation, we study the shadow of this spacetime and the corresponding images from an equatorial thin accretion disk. The presence of the shell gives rise to distinctive features in the observed images. Notably, we observe distinct double photon rings in the images, which can gradually merge into a single ring. Moreover, the shadow boundaries and the photon rings do not exhibit a one-to-one correspondence. The abrupt changes in redshift factor and the truncated photon regions profoundly influence the image, producing distinctive features such as the step-like structures. These features in shell-equipped spacetimes can help evaluate, through future astronomical observations, the applicability of the Israel junction condition and the shell model in real astrophysical systems.

Applying the junction conditions to the slowly rotating Kerr spacetime with a thin shell, we find that while the angular momentum $L$ and Carter constant $C$ of the ray remain unchanged upon crossing the shell, its energy $E$ does not. Consequently, the impact parameters $η=L/E$ and $ξ=C/E^2$ of the ray are discontinued at the shell. Utilizing this transformation, we study the shadow of this spacetime and the corresponding images from an equatorial thin accretion disk. The presence of the shell gives rise to distinctive features in the observed images. Notably, we observe distinct double photon rings in the images, which can gradually merge into a single ring. Moreover, the shadow boundaries and the photon rings do not exhibit a one-to-one correspondence. The abrupt changes in redshift factor and the truncated photon regions profoundly influence the image, producing distinctive features such as the step-like structures. These features in shell-equipped spacetimes can help evaluate, through future astronomical observations, the applicability of the Israel junction condition and the shell model in real astrophysical systems.

The Unruh effect establishes a fundamental equivalence between acceleration and thermality by demonstrating that a uniformly accelerated ground-state detector undergoes excitation as if immersed in a thermal bath. In this paper, we investigate how acceleration influences the interaction between two ground-state atoms that are synchronously and uniformly accelerated in vacuum with proper acceleration $a$ and coupled to a fluctuating electromagnetic field. We find that the resulting interaction potential comprises both diagonal components $(δE)^{jk}$ with $j=k$, which are present in both inertial and acceleration cases, and off-diagonal components $(δE)^{jk}$ with $j\neq k$, which arise exclusively due to acceleration and vanish in the inertial case. The dependence of each component on acceleration and interatomic separation $L$ generally differs. For small accelerations, the leading-order diagonal components of the van der Waals (vdW) and Casimir-Polder (CP) interaction potentials remain unchanged from their inertial counterparts, exhibiting the standard scaling behaviors $\sim L^{-6}$ and $\sim L^{-7}$, respectively. In contrast, the off-diagonal components scale as $\sim a^2L^{-4}$ in the vdW subregions and $\sim a^2L^{-5}$ in the CP subregion. However, when the acceleration becomes sufficiently large, both diagonal and off-diagonal components of the vdW and CP interaction potentials are significantly modified, giving rise to entirely new interaction behaviors that deviate from those observed in the inertial case, whether in vacuum or thermal environments, indicating a breakdown of the acceleration-thermality equivalence established by the Unruh effect for single detectors.

Transition rates of a uniformly accelerated atom coupled to a vacuum scalar field are identical with those of one being static in a thermal bath at a temperature proportional to the proper acceleration a, i.e., $$T_U=\frac{a}{2\pi }$$T U = a 2 π . We discuss in this paper whether there exists such an equivalence in the electromagnetic field case if more atoms are involved. To be specific, we explore the similarities and distinctions between effects of a thermal bath and those of the uniformly accelerated motion by comparing the transition rates of a two-atom system initially in the symmetric or antisymmetric entangled state [ $$|\psi _{\pm }\rangle $$| ψ ± ⟩ ] in two cases, i.e., two static atoms in a thermal bath [the thermal case] and two atoms uniformly accelerated in vacuum [the acceleration case]. We discover that, for some particular orientations of atomic dipole moments, coherent radiation which happens in the acceleration case never occurs in the thermal case. The rates in the acceleration case with a low acceleration which means a low $$T_U$$T U can be smaller or larger and even equal to their counterparts in the thermal case; while the rates in the acceleration case with a high acceleration which means a high $$T_U$$T U are always much larger than their counterparts in the thermal case. Our results suggest that effects of a thermal bath and those of the uniformly accelerated motion on transition properties of a two-atom system in $$|\psi _{\pm }\rangle $$| ψ ± ⟩ are not necessarily distinctive, but can be equivalent if the acceleration is relatively low, depending on the value of the interatomic separation.