We consider a spherically symmetric line element which admits either a black hole geometry or a wormhole geometry and show that in both cases the apparent horizon or the wormhole throat is partially characterized by the zero set of a single curvature invariant. The detection of the apparent horizon by this invariant is consistent with the geometric horizon detection conjectures and implies that it is a geometric horizon of the black hole, while the detection of the wormhole throat presents a conceptual problem for the conjectures. To distinguish between these surfaces, we determine a set of curvature invariants that fully characterize the apparent horizon and wormhole throat. Motivated by this result, we introduce the concept of a geometric surface as a generalization of a geometric horizon and extend the geometric horizon detection conjectures to geometric surfaces. As an application, we employ curvature invariants to characterize three important surfaces of the line element introduced by Simpson, Martin-Moruno, and Visser, which describes transitions between regular Vaidya black holes, traversable wormholes, and black bounces.

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.

Erasing a black hole leaves spacetime flat, so light passing through the region before any star forms and after the black hole’s evaporation shows no time delay, just like a flying mirror that returns to its initial starting point. Quantum radiation from a round-trip flying mirror has not been solved despite the model’s mathematical simplicity and physical clarity. Here, we solve the particle creation from worldlines that asymptotically start and stop at the same spot, resulting in interesting spectra and symmetries, including the time dependence of thermal radiance associated with Bose-Einstein and Fermi-Dirac Bogoliubov coefficients. Fourier analysis, intrinsically linked to the Bogoliubov mechanism, shows that a thermal Bogoliubov distribution does not describe the spin-statistics of the quantum field.

A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar, $r_1$, $r_2$, and $w_2$. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natário warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble.

A mirror with time-dependent boundary conditions will interact with the quantum vacuum to produce real particles via a phenomenon called the dynamical Casimir effect (DCE). When asymmetric boundary conditions are imposed on the fluctuating mirror, the DCE produces an asymmetric spectrum of particles. We call this the asymmetric dynamical Casimir effect (ADCE). Here, we investigate the necessary conditions and general structure of the ADCE through both a waves-based and a particles-based perspective. We review the current state of the ADCE literature and expand upon previous studies to generate new asymmetric solutions. The physical consequences of the ADCE are examined, as the imbalance of particles produced must be balanced with the subsequent motion of the mirror. The transfer of momentum from the vacuum to macroscopic objects is discussed.