arXiv subjects

Helder A. S. Costa

Publications and source records attributed to Helder A. S. Costa.

5 recordsLinked to original sources

arXiv2026

Explicit Analytical Representations for the Schwarzschild Radial Equation via Hypergeometric and Frobenius Expansions

The massive Klein-Gordon equation on the Schwarzschild exterior reduces to a radial differential equation of confluent-Heun type. We present its exact reduction by rigorously retaining a subleading centrifugal term that preserves the horizon indicial exponents but critically shifts the accessory parameters. Within the Svartholm--Schmidt hypergeometric-expansion framework, we derive the three-term recurrence relation and establish the corrected continued-fraction compatibility condition matching the minimal tail to the lower-end recurrence. Crucially, we demonstrate that the physical compactification coordinate $z=(r-1)/r$ shifts the irregular singular point to $z=1$, inherently transforming the hypergeometric expansion into a five-term recurrence that cannot degenerate to three terms. To circumvent this obstruction, we construct the horizon-normalized physical branch via a direct Frobenius series at $z=0$. This representation exhibits high-order convergence and near-precision-floor residuals against the exact radial ODE, while clarifying why quasinormal-mode spectral selection remains a connection problem at the irregular singular endpoint.

gr-qc↗

arXiv2025

Dispersive vacuum as a decoherence amplifier of an Unruh-DeWitt detector

Recently, interest has been growing in studies on discrete or "pixelated" space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a cellular structure on the order of the Planck length, and if this is true we should certainly have observable effects. In this paper, we investigated the effects caused by the dispersive vacuum on the decoherence process of an Unruh-DeWitt detector, our setup consists of a uniformly accelerated detector, initially in a qubit state, which interacts with a massless scalar field during a time interval finite. We use dispersion relations drawn from doubly special relativity and Hořava-Lifshitz gravity, with these modifications the vacuum becomes dispersive and has a corresponding refractive index. We calculate the probability transition rates, the probability of finding the detector in the ground state, and the quantum coherence variation. Our results indicate that the decoherence process occurs more quickly in cases with changes in the dispersion relation in the regime of high accelerations and interaction time. Additionally, the decoherence increases as the vacuum becomes more dispersive due to the increase in the order of modification in the dispersion relation, and this happens because the dispersive vacuum amplifies the effects of quantum fluctuations that are captured by the detector when interacting with the field.

hep-th↗

arXiv2020

Decoherence of a uniformly accelerated finite-time detector

We study a uniformly accelerated detector coupled to a massless scalar field for a finite time interval. By considering the detector initially prepared in a superposition state, qubit state, we find that the acceleration induces decoherence on the qubit. Our results suggest the dependence of loss of coherence on the polar angle of qubit state on a Bloch sphere and the time interaction. The adjust those parameters can significantly improve the conditions to estimate the degree of decoherence induced by Unruh radiation.

hep-th↗

arXiv2020

Ramsey interferometry as a witness of acceleration radiation

We adapt a typical Ramsey interferometer by inserting a linear accelerator capable of accelerating an atom inside a single-mode cavity. We demonstrate that this simple scheme allows us to estimate the effects of acceleration radiation via interferometric visibility. By using a Rydberg-like atom, our results suggest that, for the transition regime of the order of GHz and interaction time of 1 ns, acceleration radiation effects can be observable for accelerations as low as $10^{17}$ m/s$^2$.

quant-ph↗

arXiv2020

Alice and Bob in an anisotropic expanding spacetime

We investigate a quantum teleportation process between two comoving observers Alice and Bob in an anisotropic expanding spacetime. In this model, we calculate the fidelity of teleportation and we noted an oscillation of its spectrum as a function of the azimuthal angle. We found that for the polar angle $ϕ= \fracπ{2}$ and the azimuthal angle $θ\neq \frac{3π}{4} + nπ$ with $n = 0, 1, 2, ...$ the efficiency of the process decreases, i.e., the fidelity is less than one. In addition, it is shown that the anisotropic effects on the fidelity becomes more significative in the regime of smooth expansion and the limit of massless particles. On the other hand, the influence of curvature coupling becomes noticeable in the regime of fast expansion (values of $\fracρω \gg 1$).

hep-th↗