We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity’s rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.

In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy density and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it.

In this work, we study a traversable wormhole sourced by an ideal matter fluid with an antisymmetric 2-tensor background field coupled to gravity in a scenario of spontaneously broken Lorentz symmetry. Contrary to employed in the literature, we use a nonminimal curvature-coupling term $$B^{\mu \nu }B^{\kappa \lambda }R_{\mu \nu \kappa \lambda }$$B μ ν B κ λ R μ ν κ λ which incorporates all three kinds of Lorentz-violating coefficient for the pure-gravity sector of the minimal standard-model extension. We find that the wormhole is non-asymptotically globally flat and determine the allowed parameters of the theory, showing that the matter fluid must be necessarily anisotropic. We also analyze the energy conditions, checking their validity range and comparing them with those predicted by general relativity.

We investigate the quasibound states of charged massive scalar fields in the Kerr–Newman black hole spacetime by using a new approach recently developed, which uses the polynomial conditions of the Heun functions. We calculate the resonant frequencies related to the spectrum of quasibound states, as well as its corresponding angular and radial wave eigenfunctions. We also analyze the instability of the system. These results are particularized to the cases of Schwarzschild and Kerr black holes. Additionally, we compare our analytical results with the numerical ones known in the literature. Finally, we apply the obtained results to compute the characteristic times of growth and decay of bosonic particles around a supermassive black hole situated at the center of the M87 galaxy.

We consider the thermal corrections to the Casimir energy of a massless scalar field in the space-time with topology ${S}^{3}\ifmmode\times\else\texttimes\fi{}{R}^{1}$ (Einstein and Friedmann universes) containing an idealized cosmic string. The vacuum energy of the field under consideration, in this background, can be separated in two terms: one term that is simply the known vacuum energy of the massless scalar field in the Einstein and Friedmann cosmological models and the other term that formally corresponds to the vacuum energy of the electromagnetic field, also in the Einstein and Friedmann universes, multiplied by the cosmic string parameter $$\lambda${}=(1/$\alpha${})$-${}1$, where $$\alpha${}$ is a constant related to the cosmic string tension, $G$\mu${}$. The Casimir free energy and all the other thermodynamic expressions can also be separated in the same way. Thus, we use the expressions calculated in previous works for the massless scalar and electromagnetic fields in the closed Einstein and Friedmann models to investigate the low- and high-temperature limits of the Casimir free energy, internal energy, and entropy and show the role played by the presence of a cosmic string.