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Exploration of a singular fluid spacetime.

Grant N Remmen1

  • 1Department of Physics, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 USA.

General Relativity and Gravitation
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Summary

Researchers explored singular isothermal spheres in general relativity, finding solutions with a fixed mass-to-radius ratio. These objects, unlike black holes, have naked singularities and connections to dark matter profiles.

Keywords:
Dilaton solutionsNaked singularitiesPerfect fluid solutionsTidal Love numbers

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Area of Science:

  • General Relativity
  • Astrophysics
  • Cosmology

Background:

  • Investigating singular solutions in self-gravitating perfect fluids is crucial for understanding extreme astrophysical objects.
  • Singular isothermal spheres offer a unique class of solutions within general relativity.

Purpose of the Study:

  • To analyze the properties of singular isothermal spheres, a special class of singular solutions in general relativity.
  • To explore their mass-to-radius ratio, singularity structure, and connections to other physics concepts.

Main Methods:

  • Analytical investigation of static, spherically-symmetric solutions for a perfect fluid with an arbitrary equation-of-state parameter.
  • Perturbative analysis to determine radial modes and tidal Love numbers.
  • Examination of geodesic structure and connections to theoretical frameworks like the double copy and swampland distance conjecture.

Main Results:

  • Static, spherically-symmetric solutions (singular isothermal spheres) exist for arbitrary equation-of-state parameters.
  • These solutions exhibit a fixed mass-to-radius ratio, similar to black holes, but possess a naked singularity.
  • For specific parameters, solutions arise from a homogeneous dilaton background, breaking spatial homogeneity.

Conclusions:

  • Singular isothermal spheres present a distinct class of relativistic objects with unique properties.
  • Their characteristics offer insights into dark matter profiles, holographic entropy, and the behavior of singularities.
  • The study highlights potential connections between general relativity solutions and fundamental physics principles.