Spin effects on particle creation and evaporation in $f(R,T)$ gravity

TL;DR

The authors examine how particle spin affects black hole quantum emission in a modified gravity setup where $f(R,T)=R+\beta T$ is coupled to nonlinear electrodynamics. By analyzing scalar, vector, tensor, and spinor perturbations, they compute spin-dependent particle creation, derive greybody factors (some analytically and others via controlled expansions), and evaluate absorption, emission rates, and evaporation lifetimes, including high-frequency limits. A key finding is that higher-spin modes (notably tensor) experience stronger greybody transmission and emission, shortening the black hole lifetime, while increasing charge $Q$ or nonlinear couplings $\alpha,\beta$ generally suppresses emission and raises the remnant mass. The study also reinforces a consistent link between quasinormal modes and greybody factors across spins, highlighting the role of spin in black hole thermodynamics within modified gravity theories. These results improve understanding of quantum processes near horizons in extensions of GR and offer benchmarks for future explorations in higher-order or nonminimal gravity models.

Abstract

In this work, we study how the spin of particle modes influences particle creation, greybody factors, absorption, and evaporation of a black hole within the framework of modified electrodynamics in $f(R,T)$ gravity, recently proposed in Ref. [1]. All spin sectors -- scalar, vector, tensor, and spinorial -- are analyzed to obtain the corresponding features. For particle creation, we consider massless bosonic and fermionic perturbations to determine the respective particle densities. Analytical expressions for the greybody factors are derived, with suitable approximations for the tensor and spinorial cases. The absorption cross section is computed numerically, and using the Stefan-Boltzmann law, we estimate the black hole evaporation lifetime. The associated energy and particle emission rates are also discussed, along with the correspondence between quasinormal modes and greybody factors.

Figures (36)

• Figure 1: The particle density for fermions $n_{\psi}$ is shown against the frequency $\omega$. On the left panel, we consider the variation of $Q$ for fixed values of $\alpha = \beta = -0.001$. On the right panel, we vary $\alpha = \beta$ for a fixed value of $Q=0.9$.
• Figure 2: The greybody factors for spin--0 particle modes are presented for fixed values of $\alpha = \beta = -0.01$, considering various values of $Q$ and angular momentum number $\ell$. The top left panel corresponds to $\ell = 0$, the top right panel displays the case $\ell = 1$, and the bottom panel shows the results for $\ell = 2$.
• Figure 3: The greybody factors for spin--0 particle modes are presented for fixed values of $Q = 0.9$, considering various values of $\alpha = \beta$ and angular momentum number $\ell$. The top left panel corresponds to $\ell = 0$, the top right panel displays the case $\ell = 1$, and the bottom panel shows the results for $\ell = 2$.
• Figure 4: The greybody factors corresponding to spin--1 particle modes are shown for $\alpha = \beta = -0.01$, with different values of the charge $Q$ and the angular momentum quantum number $\ell$. The left and right panels represent the cases $\ell = 1$, and $\ell = 2$, respectively.
• Figure 5: The greybody factors for spin--1 particle modes are displayed for a fixed charge $Q = 0.9$, while varying the parameters $\alpha = \beta$ and the angular momentum number $\ell$. The left panel depicts the case where $\ell = 1$, and the right panel presents the results for $\ell = 2$.