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Abstract We construct an explicit model for the black hole to white hole transition (known as the black hole fireworks scenario) using the cut-and-paste technique. We model a black hole collapse using the evolution of a time-like shell in the background of the loop quantum gravity inspired metric and then the space-like shell analysis to construct the firework geometry. Our simple and well-defined analysis removes some subtle issues that were present in the previous literature [1] and makes the examination of the junction conditions easier. We further point out that the infalling and asymptotic observers, both in ours and the original scenario in ref. [1], encounter quite different physics. While the proper time of the bounce for an infalling observer can be determined without ambiguity, the bouncing time interval for the asymptotic observer can be chosen arbitrarily by changing how one cuts and pastes the spacetimes outside the event horizons. It is puzzling that the proper time of a distant (rather than infalling) observer is subject to randomness since the infalling observer is supposed to experience a stronger quantum gravity effect. This result might suggest that a black hole firework scenario does not allow for the existence of an effectively classical spacetime inside the horizon. The main message is therefore that even if we strictly follow the thin shell formalism to cut and paste spacetimes, this does not guarantee that the resulting spacetime offers a physically reasonable background. 

Abstract The Kruskal–Szekeres coordinate construction for the Schwarzschild spacetime could be interpreted simply as a squeezing of thet-line into a single point, at the event horizon $r=2M$. Starting from this perspective, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner–Nordström manifold, $M_{\text{RN}}$. We develop a new method to construct Kruskal-like coordinates through casting the metric in new null coordinates, and find two algebraically distinct ways to chart $M_{\text{RN}}$, referred to as classes: type-I and type-II within this work. We pedagogically illustrate our method by crafting two compact, conformal, and global coordinate systems labeled ${\mathrm{GK}}_{\text{I}}$and ${\mathrm{GK}}_{\text{II}}$as an example for each class respectively, and plot the corresponding Penrose diagrams. In both coordinates, the metric differentiability can be promoted to $C^{\mathrm{\infty }}$in a straightforward way. Finally, the conformal metric factor can be written explicitly in terms of thetandrfunctions for both types of charts. We also argued that the chart recently reported in Soltani (2023 arXiv:2307.11026) could be viewed as another example for the type-II classification, similar to ${\mathrm{GK}}_{\text{II}}$. 

Abstract We demonstrate that a model with extra dimensions formulated in Csaki et al. (Phys Rev D 62:045015, 2000), which fatefully reproduces Friedmann–Robertson–Walker (FRW) equations on the brane, allows for an apparent superluminal propagation of massless signals. Namely, a massive brane curves the spacetime and affects the trajectory of a signal in a way that allows a signal sent from the brane through the bulk to arrive (upon returning) to a distant point on the brane faster than the light can propagate along the brane. In particular, the signal sent along the brane suffers a greater gravitational time delay than the bulk signal due to the presence of matter on the brane. While the bulk signal never moves with the speed greater than the speed of light in its own locality, this effect still enables one to send signals faster than light from the brane observer’s perspective. For example, this effect might be used to resolve the cosmological horizon problem. In addition, one of the striking observational signatures would be arrival of the same gravitational wave signal at two different times, where the first signals arrives before its electromagnetic counterpart. We used GW170104 gravitational wave event to impose a strong limit on the model with extra dimensions in question. 

Abstract We investigate the Teukolsky equation in horizon-penetrating coordinates to study the behavior of perturbation waves crossing the outer horizon. For this purpose, we use the null ingoing/outgoing Eddington–Finkelstein coordinates. The first derivative of the radial equation is a Fuchsian differential equation with an additional regular singularity to the ones the radial one has. The radial functions satisfy the physical boundary conditions without imposing any regularity conditions. We also observe that the Hertz-Weyl scalar equations preserve their angular and radial signatures in these coordinates. Using the angular equation, we construct the metric perturbation for a circularly orbiting perturber around a black hole in Kerr spacetime in a horizon-penetrating setting. Furthermore, we completed the missing metric pieces due to the massMand angular momentumJperturbations. We also provide an explicit formula for the metric perturbation as a function of the radial part, its derivative, and the angular part of the solution to the Teukolsky equation. Finally, we discuss the importance of the extra singularity in the radial derivative for the convergence of the metric expansion.