A black hole with a mass of one trillion times that of the Sun, often referred to as a "trillion-solar-mass black hole," would be an incredibly massive object. The size of a black hole is typically described by its Schwarzschild radius, which represents the radius of the event horizon—the boundary beyond which nothing, not even light, can escape the black hole's gravitational pull.
To calculate the Schwarzschild radius of a black hole, we can use the formula:
R = 2GM/c^2,
where R is the Schwarzschild radius, G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.
For a trillion-solar-mass black hole, we would have M = 1 trillion (1,000,000,000,000) times the mass of the Sun, which is approximately 2 × 10^36 kilograms.
Plugging these values into the formula, we find:
R ≈ 2 × (6.674 × 10^(-11) m^3 kg^(-1) s^(-2)) × (2 × 10^36 kg) / (9 × 10^16 m^2 s^(-2)),
Simplifying the expression:
R ≈ 8.89 × 10^14 meters.
To put this into perspective, the Schwarzschild radius of a trillion-solar-mass black hole would be approximately 889 billion kilometers or about 552 billion miles.
It is worth noting that such an enormous black hole has not been observed in the universe thus far. The most massive known black holes are in the range of tens of billions to a few tens of billions of solar masses. The formation and existence of a trillion-solar-mass black hole would require specific conditions and mechanisms that are not yet fully understood. Therefore, while it is theoretically possible, the existence of a trillion-solar-mass black hole remains hypothetical until further observational evidence or theoretical models provide more insight.