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Vaidya-Reissner-Nordström Extension On the White-hole Region

Qingyao Zhang

TL;DR

This work unifies the Vaidya and Reissner–Nordström spacetimes to model a non-rotating white hole that radiates mass and loses electric charge in retarded time. Using double-null coordinates, it derives a dynamic metric with $f(u,v)=1 - \frac{2m(u)}{r} + \frac{q(u)^2}{r^2}$ and shows how $m(u)$ and $q(u)$ evolve under outgoing radiation, yielding a time-dependent Bondi mass and charge. The analysis details horizon dynamics, energy conditions, and global structure, demonstrating that radiation and EM flux reshape the apparent horizon $r_h=2m(u)$ and can avoid naked singularities while preserving cosmic censorship. The framework extends static RN to radiating charged white holes, offering a tractable platform to explore evaporation, horizon behavior, and potential implications for quantum gravity and high-energy astrophysics.

Abstract

We develop an analytic model that extends classical white hole geometry by incorporating both radiative dynamics and electric charge. Starting from a maximal analytic extension of the Schwarzschild white hole via Kruskal Szekeres coordinates, we introduce a time dependent mass function, representative of outgoing null dust to model evaporation. Building on this foundation, the study then integrates the Reissner-Nordström framework to obtain a dynamic, charged white hole solution in double null coordinates. In the resulting Vaidya Reissner Nordström metric, both the Bondi mass and the associated charge decrease monotonically with retarded time, capturing the interplay of radiation and electromagnetic effects. Detailed analysis of horizon behavior reveals how mass loss and charge shedding modify the causal structure, ensuring that energy conditions are preserved and cosmic censorship is maintained.

Vaidya-Reissner-Nordström Extension On the White-hole Region

TL;DR

This work unifies the Vaidya and Reissner–Nordström spacetimes to model a non-rotating white hole that radiates mass and loses electric charge in retarded time. Using double-null coordinates, it derives a dynamic metric with and shows how and evolve under outgoing radiation, yielding a time-dependent Bondi mass and charge. The analysis details horizon dynamics, energy conditions, and global structure, demonstrating that radiation and EM flux reshape the apparent horizon and can avoid naked singularities while preserving cosmic censorship. The framework extends static RN to radiating charged white holes, offering a tractable platform to explore evaporation, horizon behavior, and potential implications for quantum gravity and high-energy astrophysics.

Abstract

We develop an analytic model that extends classical white hole geometry by incorporating both radiative dynamics and electric charge. Starting from a maximal analytic extension of the Schwarzschild white hole via Kruskal Szekeres coordinates, we introduce a time dependent mass function, representative of outgoing null dust to model evaporation. Building on this foundation, the study then integrates the Reissner-Nordström framework to obtain a dynamic, charged white hole solution in double null coordinates. In the resulting Vaidya Reissner Nordström metric, both the Bondi mass and the associated charge decrease monotonically with retarded time, capturing the interplay of radiation and electromagnetic effects. Detailed analysis of horizon behavior reveals how mass loss and charge shedding modify the causal structure, ensuring that energy conditions are preserved and cosmic censorship is maintained.

Paper Structure

This paper contains 12 sections, 61 equations, 3 figures.

Table of Contents

  1. Schwarzschild white hole
  2. Vaidya white hole
  3. Vaidya white hole evaporation
  4. Basic Structure
  5. Mass Loss and Outgoing Energy Flux with Hiscock Model
  6. Horizon Dynamics and Spacetime Structure during Evaporation
  7. Global structure
  8. Vaidya-Reissner-Nordström white hole
  9. Vaidya-Reissner-Nordström white hole evaporation
  10. Evaporation Dynamics
  11. End of the Evaporation
  12. Conclusion

Figures (3)

  • Figure 1: The whole Schwarzschild spacetime in Kruskal–Szekeres coordinate $(T,X)$, the dash line be the event horizon ($r=2M$), two lines which asymptotically to dash lines are the singularity($r=0$), the region IV which filled with slash lines is the white hole region.
  • Figure 2: Penrose diagram
  • Figure 3: Choice for $M(v)$ for the Hiscock modelHiscockI