This question is not about tachyons entering normal matter BHs, nor is it about what would happen to tachyons in BHs. It is about a BH made of tachyons.
Tachyons on this site are considered quasi mainstream, so I will ask what would happen if we made a BH out of tachyons.
A tachyon has a spacelike worldline.
Nope, in both Newtonian physics and in general relativity, negative mass would be attracted gravitationally to positive mass, although negative mass would exert a repulsive gravitational effect on positive mass (but if the negative mass is small compared to the mass of the black hole this latter effect is negligible). In Newtonian physics this is not too difficult to derive, the Newtonian gravitational force law indicates the gravitational force vectors between a positive and negative mass would point away from each other, so the positive mass is obviously repelled, but for the negative mass the acceleration is in the opposite direction of the force due to the negative mass in F=ma, so the negative mass is attracted. In general relativity the analysis is obviously more complicated, but Hermann Bondi showed negative mass would have the same basic properties in GR, see this article. Note that if negative mass didn't fall downwards in gravity just like positive mass this would be a violation of the equivalence principle, since being in a chamber at rest in a gravitational field is supposed to be equivalent to being in a chamber accelerating in deep space, and if you let go of both a positive and negative mass in such a chamber they should naturally just move inertially while the floor of the chamber accelerates up to meet them.
So basically both Newtonian and GR would suggest that a BH made of tachyons (negative mass), should repel gravitationally.
Since in GTR there is no gravitational stress-energy tensor, the gravitational energy of a body is determined indirectly. For example, one method is when by the given mass density and body size the mass of the body is calculated, first in the absence of the metric’s influence, and then taking into account the metric’s influence and the corresponding change in the volume differential in the integral of the mass under influence of the gravitational field. The difference of the mentioned masses is equated to the mass-energy of gravitational field as to the manifestation of the metric field.
Basically, as per GR, the stress-energy of this BH would be determined indirectly, given mass density (of the tachyons) and body size the mass of the BH is calculated, first in absence of the metric's influence, and then considering the metric, with the corresponding volume differential.
Based on this, the stress-energy of this BH could be so that the BH would repel gravitationally.
In special relativity, a faster-than-light particle would have space-like four-momentum, in contrast to ordinary particles that have time-like four-momentum. Although in some theories the mass of tachyons is regarded as imaginary, in some modern formulations the mass is considered real, the formulas for the momentum and energy being redefined to this end.
The mass of the tachyon could be regarded as real, allowing compatibility with GR.
Now, the momentum 4-vector of a Tachyon is necessarily space-like and consequently, the sign of energy no longer Lorentz-invariant. Thus a Tachyon will be found to have negative energy in certain inertial frames.
If the tachyon does have negative stress-energy, it could repel gravitationally.
- Could a BH made of tachyons repel gravitationally (in case we agree they have negative mass)?