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I was just wondering that, Tachyons travel faster than the speed of light. So in theory, if Tachyons exists can they escape event horizon?

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    $\begingroup$ Tachyons don't actually move faster than light, see this question and its answers. $\endgroup$ – ACuriousMind Aug 17 '16 at 19:56
  • $\begingroup$ @ACuriousMind: that's an ambiguity in terminology between field theory and relativity; relativistic tachyons travel faster than light by definition $\endgroup$ – Christoph Aug 18 '16 at 8:19
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    $\begingroup$ @Qmechanic: this is a perfectly valid question; rephrased: Are there spacelike geodesics in Schwarzschild spacetime that cross the event horizon from within? $\endgroup$ – Christoph Aug 18 '16 at 8:43
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So this problem depends on both the vacuum of field theory and the notion of the causal wedge in GR. In case of quantum mechanics, there exist particles such as tachyons which essentially travel outside of the light cone which is defined by GR and hence one would be justified in asking if whether a tachyon can escape a black hole.

However, a tachyon in a more formal field theoretic setting is essentially when the mass of some field $\phi$ $$m_\phi^2 < 0$$ in which case the field theory vacuum undergoes a spontaneous symmetry breaking and assumes a different value in terms of the expectation value of $m_\phi^2$. Now, if this field $\phi$ is what determines the vacuum structure of the black hole interior, which is unknown in a formal setting (see papers on the interior Hilbert space of the black hole and complementarity), then any tachyonic mode will lead to a phase transition and an instability in the vacuum. However, when we consider phase transition and black holes, I must point out that the way to define an instability is to construct the instability on the horizon and see if it obeys the correct thermodynamic properties at asymptotic infinity or the boundary of spacetime. So regarding tachyonic modes in the interior, I am quite in the dark.

So in a nutshell, creating a tachyon itself would lead to some form of a spontaneous phase transition in which the tachyonic mode no longer exists. So from a rigourous QFT + GR setting, I don't think tachyons exist the way it is portrayed in simpler QM models. So no, tachyons will not escape the horizon simply because the theory will not allow for them to exist.

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