arXiv:2408.02699v1 Announce Type: new
Abstract: In this paper, we present three exact solutions to the Einstein field equations, each showing different black hole models. The first solution introduces a black hole with a variable equation of state, ( P=k(r)rho ), that can represent both singular and regular black holes based on parameters ( M_0 ) and ( w_0 ). The second solution features a black hole with Hagedorn fluid, relevant for the late stages of black hole formation, and reveals similarities to the first solution, describing both singular and regular black holes in a specific case. Furthermore, we investigate the shadow cast by these black hole solutions to constrain their parameters. Recognizing that real astrophysical black holes are dynamic, we developed a third, dynamical solution that addresses gravitational collapse and suggests the potential formation of naked singularities, indicating that a black hole can transition from regular to singular and back to regular during its evolution.

Future Roadmap for Readers

Based on the conclusions drawn from the article, there are several potential challenges and opportunities on the horizon in the field of black hole research. The following outline provides readers with a roadmap for exploring these possibilities:

1. Variable Equation of State and Singular vs. Regular Black Holes

  • Study the first exact solution which introduces a black hole with a variable equation of state, ( P=k(r)rho ).
  • Investigate the parameters ( M_0 ) and ( w_0 ) to understand their effects on the nature of the black hole (singular vs. regular).
  • Explore the implications of a variable equation of state on the behavior and properties of black holes.
  • Consider the astrophysical relevance of these findings and potential observational signatures.

2. Black Holes with Hagedorn Fluid

  • Analyze the second exact solution that features a black hole with Hagedorn fluid.
  • Explore the similarities to the first solution and their implications.
  • Investigate the specific case where both singular and regular black holes can be described.
  • Examine the late stages of black hole formation and the role of Hagedorn fluid.

3. Constraints on Black Hole Parameters through Shadow Casting

  • Study the shadow cast by the black hole solutions to gain insights into their parameters.
  • Develop techniques to infer and constrain the properties of black holes using shadow observations.
  • Consider the limitations and uncertainties associated with these constraints.
  • Explore the potential of future observational campaigns to test these predictions.

4. Dynamical Solutions and Gravitational Collapse

  • Examine the third solution that addresses gravitational collapse and the formation of naked singularities.
  • Understand the transition from regular to singular black hole and its potential reversibility.
  • Investigate the conditions under which naked singularities can form.
  • Explore the astrophysical consequences of such transitions and their observational implications.

Challenges and Opportunities

The future roadmap outlined above presents several challenges and opportunities in black hole research:

  • Challenges include understanding the physical mechanisms that give rise to variable equations of state, the nature of Hagedorn fluid, and the conditions for gravitational collapse leading to naked singularities.
  • Opportunities include the possibility of observing and distinguishing between singular and regular black holes, advancing our understanding of late-stage black hole formation, and using black hole shadows as a tool for parameter estimation.
  • Further research and observational campaigns are needed to validate and refine the conclusions presented in this paper.

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