Tidally locked planet orbiting a black hole

 From copilot:

Short answer: yes—but the difference is usually tiny unless the planet is extremely close to the black hole.

Let’s unpack why.

1. Gravitational time dilation depends on distance

In general relativity, gravitational time dilation means that clocks run more slowly deeper in a gravitational well. For a (non‑rotating) black hole, the time-dilation factor depends on radius \(r\):

\[
\Delta t_{\infty} = \frac{\Delta t_{local}}{\sqrt{1 - \frac{2GM}{rc^2}}}
\]

Closer to the black hole → stronger relativistic effects.

2. A tidally locked planet is stretched across a gravitational gradient

A tidally locked planet orbiting a black hole has:

• Near side: slightly closer to the black hole
  
• Far side: slightly farther away
  

Because relativistic effects depend on distance, this means:

✅ The near side experiences slightly stronger relativistic effects
✅ The far side experiences slightly weaker relativistic effects

This includes:

• Gravitational time dilation
  
• Gravitational redshift
  
• Spacetime curvature
  

So yes, the far side really does age infinitesimally faster than the near side.

3. How big is the difference?

For most realistic scenarios: absurdly small.

Example (conceptual):

• Planet radius comparable to Earth
  
• Orbiting a stellar-mass or supermassive black hole
  
• Stable orbit well outside the event horizon
  

The fractional difference in time dilation across the planet is roughly:

\[
\Delta \left(\frac{\Delta t}{t}\right) \sim \frac{GM}{c^2} \cdot \frac{R_{planet}}{r^2}
\]

Even very close to a supermassive black hole, this difference is typically far smaller than what atomic clocks on Earth can detect—unless the planet is perilously close to the event horizon.

4. Extreme cases near the event horizon

If the planet were so close that this difference became noticeable:

• Tidal forces would likely tear the planet apart (spaghettification)
  
• Structural stresses would exceed planetary material strength
  
• Stable solid planets probably couldn’t exist there
  

Ironically, this means:

If the relativistic difference across the planet is large, the planet probably can’t survive.

5. What about rotation and frame dragging?

If the black hole is rotating (a Kerr black hole):

• Frame dragging slightly modifies spacetime
  
• The near side still experiences stronger effects
  
• The asymmetry is direction-dependent but does not reverse the conclusion
  

The near side always sits deeper in the gravitational well.

6. Summary

• ✅ A tidally locked planet orbiting a black hole does experience different relativistic effects across its surface
  
• ✅ The near side experiences stronger time dilation
  
• ✅ The far side experiences slightly weaker relativistic effects
  
• ⚠️ The difference is negligible unless the orbit is extremely close
  
• ❌ If the difference is large enough to matter, the planet likely cannot remain intact
  

If you’d like, I can:

• Estimate the effect for a specific black hole mass and orbital radius
  
• Compare this to time dilation across Earth
  
• Extend this to neutron stars or rotating black holes
  
• Explore what an observer on the planet would actually see
  

Just tell me.