# First quantization light ray in Schwarzschild's black hole

• Andre' Quanta
In summary, the dynamics of a light ray in a Schwarzschild's metric is described by the geodesic equation, not a Lagrangian. First quantization is not applicable to a light ray in this metric, but can be applied to a particle with mass. The eigenvalues of the Hamiltonian for this system would depend on the specific values of the constants a and b in the potential.
Andre' Quanta
The dinamic of a light ray in a Schwarzschild' s metric is governed by a lagrangian where the potential is V(x)= a*(1/r)^2-b*(1/r)^3 with a and b positive costants.
The presence of a Lagrangian it means that is possible to apply a first quantization of this sistem; if so which are the eigenvalues of the Hamiltonian of this sistem?

I would like to clarify that the dynamic of a light ray in a Schwarzschild's metric is governed by the geodesic equation, not a Lagrangian. The presence of a potential in the Lagrangian may suggest the possibility of a particle with mass moving in this metric, but it is not applicable to a massless particle such as light.

In terms of first quantization, it is not possible to apply it to a light ray in a Schwarzschild's metric as it violates the principle of equivalence in general relativity. However, if we consider a particle with mass moving in this metric, then we can apply first quantization and obtain the eigenvalues of the Hamiltonian.

The eigenvalues of the Hamiltonian for this system would depend on the specific values of the constants a and b. Without knowing their values, it is not possible to determine the exact eigenvalues. However, we can make some general observations.

Since both a and b are positive constants, the potential V(x) would always be positive. This suggests that the eigenvalues of the Hamiltonian would also be positive. The specific values of the eigenvalues would depend on the specific values of a and b, and would require further analysis and calculations.

In conclusion, it is not possible to apply first quantization to a light ray in a Schwarzschild's metric. However, if we consider a particle with mass moving in this metric, we can apply first quantization and determine the eigenvalues of the Hamiltonian. The specific values of the eigenvalues would depend on the specific values of the constants a and b in the potential.

## 1. What is the concept of first quantization in relation to light rays in a Schwarzschild's black hole?

First quantization refers to the process of applying quantum mechanics to a single particle, such as a light ray, in a given system. In the case of a Schwarzschild's black hole, this means treating the light ray as a quantum particle and accounting for its wave-particle duality and probabilistic behavior.

## 2. How does the first quantization of light rays in a Schwarzschild's black hole differ from classical physics?

In classical physics, light rays are treated as classical particles with well-defined trajectories. However, in first quantization, light rays are described by a wave function that represents the probability of finding the particle at a certain location. This approach is necessary in the extreme gravitational field of a black hole where classical physics breaks down.

## 3. What is the significance of first quantization in understanding the properties of a Schwarzschild's black hole?

First quantization allows us to study the behavior of light rays in the extreme gravitational field of a Schwarzschild's black hole. By treating light as a quantum particle, we can better understand its interaction with the black hole and how it is affected by the curvature of spacetime. This is crucial in understanding the properties of black holes and their role in the universe.

## 4. Can first quantization be applied to other types of black holes?

Yes, first quantization can be applied to any type of black hole, as long as it is described by the general theory of relativity. This includes rotating black holes, charged black holes, and even hypothetical black holes such as primordial black holes.

## 5. Are there any practical applications of first quantization of light rays in a Schwarzschild's black hole?

While first quantization of light rays in a Schwarzschild's black hole is primarily a theoretical concept, it has potential applications in fields such as astrophysics and cosmology. By understanding how light behaves in the extreme conditions of a black hole, we can gain insights into the nature of spacetime and the behavior of matter and energy in the universe.

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