Won’t it starve in a month?
Good question. Many modern day reptiles can go a long time without food. But a t rex is many orders of magnitude bigger than anything we have now. I did do a zoology major at uni, but my physiology knowledge sucks (unsurprising given I barely passed it).
Theropods were warm blooded, like birds. They would not be able to endure without eating for weeks and months at a time like modern cold blooded reptiles.
You’re conflating how warm bloodedness works in mammals with how it would work in theropods. They were warm blooded because they could not shed heat from metabolic processes due to their volume to surface area ratio, not because their bodies needed it. We still do not understand how it actually worked. This is evidenced by us still not knowing the reason why stegosaurus had plates, Spinosaurus had their sail etc.
Also, some birds can go weeks without food during migration or injury. Further to this, theropods are many magnitudes of size larger than birds. They would have far greater fat stores than modern birds.
Disclaimer, this is based on my 16yr old zoology major, and we are in a dinosaur discovery golden age so something may have changed.