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Quasinormal Modes and Topological Characteristics of a Schwarzschild Black Hole Surrounded by the Dehnen Type Dark Matter Halo

Farokhnaz Hosseinifar, Shahin Mamedov, Filip Studnička, Hassan Hassanabadi

TL;DR

This work analyzes a Schwarzschild-like black hole embedded in a Dehnen-type dark matter halo, deriving its metric, thermodynamics, shadow, and quasinormal modes while employing a topological framework to classify photon-sphere stability and phase structure. The Dehnen halo modifies the horizon structure, Hawking temperature, and shadow, yielding an allowed BH parameter region constrained by EHT observations of Sgr A*. QNMs for scalar and electromagnetic perturbations show that increasing the halo core radius r_s lowers both the oscillation frequency and damping rate, with EM modes generally larger than scalar ones. Topologically, the black hole features a single unstable photon sphere and conventional Hawking-point transitions, with the generalized free energy revealing RN-like multizero structure, placing the solution in the RN topological class. Collectively, the results illuminate how Dehnen-type dark matter halos influence BH observables and their thermodynamic/topological character.

Abstract

In this work, we explore the critical parameters that delineate the existence of black holes, identifying the permissible ranges that facilitate their formation. A comprehensive thermodynamic analysis of black holes is conducted, leading to the calculation of black hole remnants. We investigate the trajectory of light, establishing an upper limit for the parameters based on Event Horizon Telescope (EHT) observations of Sgr A*, ensuring that the black hole's shadow resides within the allowed region. Furthermore, we derive the quasinormal modes (QNMs) for both scalar and electromagnetic perturbations. Utilizing a topological framework, we examine the stability of the photon sphere and classify the topology of the black hole in accordance with its thermodynamic potentials.

Quasinormal Modes and Topological Characteristics of a Schwarzschild Black Hole Surrounded by the Dehnen Type Dark Matter Halo

TL;DR

This work analyzes a Schwarzschild-like black hole embedded in a Dehnen-type dark matter halo, deriving its metric, thermodynamics, shadow, and quasinormal modes while employing a topological framework to classify photon-sphere stability and phase structure. The Dehnen halo modifies the horizon structure, Hawking temperature, and shadow, yielding an allowed BH parameter region constrained by EHT observations of Sgr A*. QNMs for scalar and electromagnetic perturbations show that increasing the halo core radius r_s lowers both the oscillation frequency and damping rate, with EM modes generally larger than scalar ones. Topologically, the black hole features a single unstable photon sphere and conventional Hawking-point transitions, with the generalized free energy revealing RN-like multizero structure, placing the solution in the RN topological class. Collectively, the results illuminate how Dehnen-type dark matter halos influence BH observables and their thermodynamic/topological character.

Abstract

In this work, we explore the critical parameters that delineate the existence of black holes, identifying the permissible ranges that facilitate their formation. A comprehensive thermodynamic analysis of black holes is conducted, leading to the calculation of black hole remnants. We investigate the trajectory of light, establishing an upper limit for the parameters based on Event Horizon Telescope (EHT) observations of Sgr A*, ensuring that the black hole's shadow resides within the allowed region. Furthermore, we derive the quasinormal modes (QNMs) for both scalar and electromagnetic perturbations. Utilizing a topological framework, we examine the stability of the photon sphere and classify the topology of the black hole in accordance with its thermodynamic potentials.

Paper Structure

This paper contains 9 sections, 33 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Metric and Thermodynamics properties
  3. Shadow Radius
  4. Quasi-Normal Modes by WKB method
  5. Topology and Topological Charge of Photon Sphere and Thermodynamic Potentials
  6. Photon Sphere Potential Field
  7. Temperature Potential Field
  8. Generalized Free Energy Potential Field
  9. Conclusion

Figures (10)

  • Figure 1: Density profile in terms of $r$ considering $\rho_s=0.02$.
  • Figure 2: Region that black hole does exist.
  • Figure 3: Hawking temperature as function of horizon radius for the case $\rho_s=0.01$.
  • Figure 4: Shadow radius by varying parameter $r_s$ for three cases of parameter $\rho_s$. White region is allowed for $1\sigma$ region and both white and light and light eggshell color are allowed for $2\sigma$ region.
  • Figure 5: QNMs by varying parameter $r_s$, for the case $M=1$, $\rho_s=0.01$, $s=0$ and $l=1$. Left panel: real part, right panel: imaginary part.
  • ...and 5 more figures