# Do White Holes Exist?

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. LTB Solutions

#### How a WH Turns into a BH

## 3. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Timelike Junction

## Appendix B. The GHY Boundary Term

## Notes

1 | This is the case only if we ignore cosmic acceleration or if we consider an observer in a galaxy far away (say at $z=2$), when matter domination was an excellent approximation. |

2 | Note that both a WH and a BH require a finite total mass. If ${M}_{T}$ is infinitely large, then ${r}_{S}=\infty $ and there is no WH or BH. This in fact the standard Big Bang assumption. But this assumption is impossible to implement, even with Inflation: using local laws of gravity we have to create a uniform space of infinite extend within a finite amount of time. |

3 | Even if the exterior is not totally empty and there is some small accretion from the outside, the value of ${r}_{S}$ will slowly increase as the BH mass increases. But the ${r}_{S}$ boundary still needs to be taken into account to evaluate the action inside. |

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**Figure 1.**Relation between the Schwarszchild coordinates $(t,r)$ (in units of ${r}_{S}=1$) and the Kruskal–Szekeres coordinates $(T,X)$. The top right quadrant ($T>0$, $X>0$) is the regular BH solution (the green region is external to ${r}_{S}$). Lines of constant r are the cyan hyperbolic dashed lines. Lines of constant time t are orange dashed straight lines ($T=0$ is also $t=0$). If we radially throw a test particle at $t=0$, it will follow the continuous yellow arrow. This solution can be formally extended into the bottom right quadrant, which corresponds to a WH, and is the time reversed (horizontal flip) of the BH solution. A particle can escape the event horizon of the WH (dashed yellow arrow), but only before it is thrown! This violates causality and is therefore not a physical solution. With a vertical flip, the solution could be maximally extended to a negative radius $X<0$. But this generates a disconnected external space (yellow region), which is also not part of the original solution.

**Figure 2.**Event horizon in Equation (9) as a function of cosmic time (given by the scale factor a) for a matter-dominated FLRW metric (${\mathrm{\Omega}}_{m}=1$, ${\mathrm{\Omega}}_{\mathrm{\Lambda}}=0$, dashed red line) and for one which also has a $\mathrm{\Lambda}=3/{r}_{S}$ term (${\mathrm{\Omega}}_{m}=0.25$, ${\mathrm{\Omega}}_{\mathrm{\Lambda}}=0.75$, continuous red line).

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**MDPI and ACS Style**

Gaztanaga, E.
Do White Holes Exist? *Universe* **2023**, *9*, 194.
https://doi.org/10.3390/universe9040194

**AMA Style**

Gaztanaga E.
Do White Holes Exist? *Universe*. 2023; 9(4):194.
https://doi.org/10.3390/universe9040194

**Chicago/Turabian Style**

Gaztanaga, Enrique.
2023. "Do White Holes Exist?" *Universe* 9, no. 4: 194.
https://doi.org/10.3390/universe9040194