Black hole with global monopole charge in self-interacting Kalb-Ramond field

TL;DR

The paper analyzes a static, spherically symmetric black hole in a theory with a self-interacting Kalb-Ramond field that spontaneously breaks Lorentz symmetry and couples to a global monopole. The authors derive modified field equations, obtain a non-Schwarzschild exterior solution with a lapse function $A(r)$ that depends on the Lorentz-violating parameter $\u03bb$ and monopole charge $\u0104$, and explore the causal structure, thermodynamics, and observational constraints. They show horizon structures vary with $\u03bb$ (single horizon for $\u03bb\le0$ vs potentially multiple horizons for $\u03bb>0$), and provide modified thermodynamic relations including entropy and Smarr corrections; solar-system tests (perihelion precession, redshift, light deflection, Shapiro delay) yield stringent bounds $|\u03bb|\lesssim 10^{-9}-10^{-4}$ and $\u0104\lesssim 10^{-6}$ to $10^{-9}\,{ m m}^{-1}$. The results offer a concrete link between KR-Lorentz-violating dynamics, global monopoles, and observable gravitational phenomena, with implications for black hole phenomenology and tests of Lorentz invariance.

Abstract

In this study, we explore a static, spherically symmetric black hole solution in the context of a self-interacting Kalb-Ramond field coupled with a global monopole. By incorporating the effects of Lorentz-violating term $\ell$ and the monopole charge $η$ in the KR field, we derive the modified gravitational field equations and analyze the resulting black hole spacetime. The obtained solution exhibits deviations from the Schwarzschild metric with topological defect, as it is influenced by the monopole charge and self-interaction potential. We investigate the thermodynamic properties of the black hole, including its Hawking temperature, entropy, and specific heat, revealing novel stability conditions. Additionally, we perform solar system tests such as perihelion precession, gravitational redshift, light deflection, and time delay of signals to impose constraints on the Lorentz-violating parameter and monopole charge. Our findings suggest that these parameters have to be significantly small, although there are different constraints imposed by individual tests, ranging from $10^{-9}\leq|\ell|\leq 10^{-4}$ and $10^{-9}\leqη\leq 10^{-6}\, \mathrm{m}^{-1}$.

Figures (11)

• Figure 1: Radial profile of $g^{rr}=A(r)$ for $\eta=0.3$, with (a) $\ell\leq0$ and an additional curve for $\eta=0$ (SBH with a topological defect), and (b) $\ell\geq0$. Unless otherwise noted, axes lengths are measured in units of the black hole mass $M$.
• Figure 2: Profiles of $r_+$ versus $\ell$ for $0\leq\eta\leq1$.
• Figure 3: Relationship between $\ell$ and $\eta$ for $\Delta>0$ (blue region), with the $\Delta=0$ curve (EBH) separating it from the naked singularity region ($\Delta<0$).
• Figure 4: The behavior of the Hawking temperature for the AdS-like black hole within $\ell \leq 0$, plotted for (a) $\eta = 0.3$, and (b) $\ell = -0.2$.
• Figure 5: Entropy behavior for the AdS-like black hole with $\ell \leq 0$ values, plotted for (a) $\eta = 0.3$, and (b) $\ell = -0.2$.