### Journey of the Laser Pulse in This Hypothetical Universe

In this hypothetical universe, the speed of light \(c\) is not constant but varies proportionally to the local gravitational field strength \(g\) (i.e., \(c \propto g\)). Stronger gravity (higher \(g\)) means a higher local speed of light. For a massive black hole, \(g\) increases as the distance \(r\) to the black hole decreases (in a Newtonian approximation, \(g \propto 1/r^2\), so \(c \propto 1/r^2\)). The spaceship is in a region of very weak gravity (large \(r\), low \(g\), slow \(c\)), and it sends a laser pulse toward the black hole.

I'll describe the changes to the pulse's speed, frequency, and trajectory based on this rule, treating the situation analogously to light propagating in a medium with a spatially varying speed (similar to optics in a graded-index material). I assume flat space and no gravitational time dilation unless otherwise noted (as the problem doesn't specify GR-like effects beyond the varying \(c\)). The pulse behaves like a wave packet with local properties determined by the local \(c\).

#### Speed
- **Initial speed**: In the weak-gravity region near the spaceship, \(g\) is small, so the pulse starts with a relatively low speed, \(c_\text{weak}\).
- **As it approaches the black hole**: The pulse enters regions of stronger gravity (higher \(g\)), so the local speed of light increases. The pulse therefore **speeds up** continuously. 
  - Near the black hole (small \(r\)), \(g\) becomes very large, so \(c\) becomes very high (approaching infinity as \(r \to 0\) in a point-mass model).
  - The front of the pulse (closer to the black hole) is always in a slightly stronger gravity field than the back, so the front travels faster than the back. This causes the pulse to **stretch** in length over time.
- **Overall effect**: The pulse accelerates toward the black hole, reaching extremely high speeds near it. If it reaches the black hole's "surface" or singularity, its speed would theoretically become infinite (though the black hole's actual structure isn't specified in this hypothetical).

#### Frequency
- **Definition**: Here, frequency \(f\) refers to the oscillation frequency of the laser light (number of wave cycles per unit time), as measured by the rate at which wave crests pass a local observer using a global time coordinate.
- **Change during journey**: The frequency **remains constant** throughout the journey, equal to the frequency at emission.
  - This is because the time interval between consecutive wave crests (as measured in a global time frame) does not change—the travel time offset from the emission point to any given location is the same for all crests.
  - However, the wavelength \(\lambda\) (spatial distance between crests) **increases** proportionally to the local \(c\) (since \(\lambda = c / f\), and \(f\) is constant while \(c\) increases). This matches the stretching of the pulse described above: the same number of wave cycles spreads over a longer physical distance.
- **No redshift or blueshift in the standard sense**: Unlike in general relativity (where infalling light blueshifts due to time dilation), the frequency here doesn't change because no time dilation is specified. If the universe includes GR-like time dilation (clocks running slower near the black hole), the locally measured frequency would **blueshift** (increase), as the observer's proper time slows relative to the emission point. However, based on the problem's statement, I'll stick with constant frequency.

#### Trajectory
- **General behavior**: The varying speed of light acts like a varying refractive index \(n \propto 1/c\) (lower \(n\) near the black hole where \(c\) is high). Light rays follow paths that minimize travel time (Fermat's principle), which means they **bend toward regions of higher speed** (stronger gravity, toward the black hole).
  - This is analogous to gravitational lensing in normal physics, but here it's due to the speed variation rather than spacetime curvature.
  - The pulse is "attracted" to the high-speed region around the black hole, so its path curves inward.
- **Specific changes**:
  - If the pulse is aimed **directly at the black hole** (radial path), it travels in a straight line toward the center, with no bending due to symmetry, but still speeding up as described.
  - If aimed slightly off-center (e.g., a grazing path), the trajectory **bends toward the black hole**, potentially orbiting or spiraling in if the deflection is strong enough. This could lead to capture if the bending exceeds a critical angle, similar to a photon sphere in GR.
  - The bending increases as the pulse gets closer, where the gradient in \(c\) (and thus the "index" variation) is steeper.
- **Overall effect**: The path is not a straight line in general; it curves as if gravity "pulls" the light by making it prefer high-speed regions. This could result in the pulse being captured by the black hole even if not perfectly aimed.

### Additional Notes
- **Comparison to real physics**: In our universe, light speed is constant, and infalling light blueshifts with a straight-line trajectory in flat space or bending due to curved spacetime in GR. Here, the varying \(c\) introduces acceleration and bending purely from the speed gradient, without needing curved space.
- **What happens at the black hole?**: As \(r \to 0\), \(c \to \infty\), so the pulse would reach the center in finite time but with infinite speed. There's no event horizon mentioned, but if one exists, the pulse might cross it at very high speed.
- **Assumptions**: This description assumes a point-mass black hole, radial symmetry, and no dispersion (light of all frequencies behaves the same). If time dilation is present (as in GR), add blueshift to the frequency change.

This hypothetical setup leads to intriguing differences from real physics, emphasizing how a variable speed of light could mimic gravitational effects on light.