No, scientists do not believe that the Earth will fall into a black hole that is close to the Milky Way's center. There is no scientific evidence or basis to support such a scenario.
The supermassive black hole located at the center of the Milky Way, known as Sagittarius A* (Sgr A*), has a mass of about 4 million times that of our Sun. While Sgr A* exerts a strong gravitational pull on nearby stars and gas clouds, it does not pose a threat to the Earth or the stability of the solar system.
The reason for this is that the Earth and the other planets in our solar system are in orbit around the Sun, which itself is orbiting around the galactic center. The gravitational interaction between the Earth, the Sun, and the black hole is governed by the laws of gravity. As long as the Earth maintains its current orbit around the Sun, it will not be drawn into the black hole.
Additionally, the distance between the Earth and the black hole at the center of the Milky Way is immense. Sgr A* is located approximately 26,000 light-years away from us, which means it would take light 26,000 years to travel from the black hole to the Earth. The vast distance and the orbital dynamics of the Earth ensure that it will remain in its current orbit and not be captured by the black hole.
In summary, there is no scientific belief or evidence to support the notion that the Earth will fall into the black hole at the center of the Milky Way. The Earth's orbit around the Sun and the immense distance between us and the black hole ensure the stability of our planet within the solar system.