No, quantum entanglement does not allow circumvention of the gravity of an event horizon or enable the transmission of information from inside a black hole. While quantum entanglement is a fascinating phenomenon where the states of two or more particles become correlated in such a way that the state of one particle is instantaneously related to the state of another, it does not violate the fundamental principles of general relativity or enable communication faster than the speed of light.
When a black hole forms and an event horizon is established, the intense gravitational pull prevents anything, including information and particles, from escaping beyond the event horizon. This is a consequence of general relativity, which describes how gravity warps spacetime. Once an object or particle crosses the event horizon, it is effectively cut off from our observable universe.
Quantum entanglement itself does not provide a means to directly observe or communicate with particles inside a black hole. Even if two entangled particles were separated by an event horizon, any measurement or observation performed on one of the entangled particles would not yield information about the other particle located inside the black hole. This is because the information about the interior of the black hole is trapped behind the event horizon and cannot be accessed from outside.
While quantum entanglement is a mysterious and non-local phenomenon, it cannot be used to bypass the constraints imposed by the event horizon of a black hole or violate the principles of general relativity. Our current understanding suggests that the information about the interior of a black hole remains inaccessible to observers outside the event horizon.