In this hypothetical universe where the speed of light (\(c'\)) is proportional to the local gravitational field strength (\(g\)), the journey of the laser pulse toward the black hole unfolds as follows:

### **Speed**
- **Increasing Velocity**: As the laser pulse approaches the black hole, the gravitational field strength (\(g = GM/r^2\)) intensifies, causing \(c'\) to rise. The pulse accelerates continuously, moving faster as it nears the black hole.

### **Trajectory**
- **Bending Toward the Black Hole**: The spatial variation in \(c'\) creates a refractive index gradient. Analogous to light bending in a medium with a refractive index gradient, the portion of the wavefront closer to the black hole moves faster, causing the pulse to refract toward the region of higher \(c'\). This results in a curved trajectory, mimicking gravitational lensing but driven by variable light speed rather than spacetime curvature.

### **Frequency**
- **Redshift Due to Gravitational Time Dilation**: Clocks in stronger gravitational fields (closer to the black hole) run slower relative to those in weaker fields. An observer near the black hole would measure the laser pulse's frequency as lower (**redshift**) compared to its emitted frequency. While the wavelength increases (\(\lambda = c'/f\)), the dominant effect is the time dilation-induced reduction in observed frequency, akin to gravitational redshift in general relativity.

### **Summary**
The laser pulse **accelerates** as it descends into the black hole’s gravitational well, follows a **curved path** due to the gradient in light speed, and undergoes **redshift** as a consequence of time dilation in the stronger gravitational field. These effects collectively highlight how a variable speed of light could alter light’s behavior in a gravitational field compared to our universe.