Observing Objects with Escape Velocities Near Light Speed: Possibilities and Challenges

Introduction

Israel posed a fascinating question regarding objects with escape velocities extremely close to the speed of light. This discussion delves into the theoretical and practical challenges of observing such objects, utilizing the laws of physics and astronomical observations.

What Does It Mean to Have an Escape Velocity Close to Light Speed?

Israel's initial query was whether it would be possible to observe an object capable of escaping at a velocity just shy of the speed of light (1 nm/s less than the speed of light, or 0.99999999999999999666435904801847950424423c). This question is intriguing due to the profound implications for both astrophysics and relativity.

Theoretical Considerations

Technically, it is theoretically possible to observe such an object, although the practical challenges are immense. If an object had an escape velocity just below light speed, the emitted light would experience extreme gravitational redshift, shifting to longer wavelengths before reaching Earth (observed as radio waves). For instance, a green photon emitted by the object would be observed as radio waves with a wavelength of approximately 425 meters and a frequency around 705.39 kHz. (Equation: lambda;2.34lambda;e [/itex]).

The energy of the photon can be calculated, and for an object with an initial temperature of 2,616,000 K, the emitted photon’s energy would be negligible compared to the cosmic background radiation (CMBR) of 2.7 K, meaning it would be impossible to detect the object's light against the cosmic noise.

Practical Detection Methods

However, practical detection can still be achieved in certain scenarios. Suppose we are dealing with a neutron star that is just below the critical mass needed for collapse into a black hole. Neutron stars are known to have extreme magnetic fields and can act as powerful radio beacons. Even if the emitted light from the surface is redshifted to the point of radio frequencies, the intense magnetic fields would cause the neutron star to emit powerful radio emissions. These emissions can be detected using sensitive radio telescopes, even when the light itself is invisible to the naked eye.

The gravitational redshift effect would cause the emitted light to stretch, making it difficult to detect. For example, the observed wavelength of the emitted light (λ0) would be 2.34 times the emitted wavelength (λe) for a 10000 K object.

Theoretical Calculations and Observational Limits

Israel’s next query was about an object with a surface escape velocity extremely close to the speed of light. The equation used to calculate λ0 is given by:

lambda;gamma;lambda;e [/itex]

where γ (gamma) is the Lorentz factor for the escape velocity. In practical terms, gamma values extremely close to light speed indicate that the object's light would be observed in the ELF (Extremely Low Frequency) band, with wavelengths less than 100,000 kilometers. This implies that objects with surface escape velocities just shy of light speed would emit light in a range that might not be directly observable by current telescopes, but theoretically detectable.

Conclusion

In summary, while the concept of observing an object with an escape velocity just below the speed of light poses significant challenges, it is theoretically possible. Practical methods involve the detection of gravitational redshift and the emission of radio frequencies, which can be picked up by sensitive instruments. The key factors are the instrument sensitivity, the object's temperature, and the specific characteristics of the emitted radiation.