In this hypothetical universe, the speed of light $$c$$ is proportional to the local gravitational field strength $$g$$, defined as $$c = c_{\infty} + \kappa g$$, where $$c_{\infty}$$ is the baseline speed in weak gravity, $$\kappa$$ is a constant, and $$g = GM / r^2$$ (Newtonian approximation). A laser pulse sent radially from a weak-gravity region toward a massive black hole experiences the following:

### **Speed**
- **Initial Region (Weak Gravity)**: The speed of light is approximately $$c_{\infty}$$ (e.g., 300,000 km/s).  
- **Approach to Black Hole**: As gravitational field strength $$g \propto 1/r^2$$ increases, $$c$$ increases proportionally. For example, near the event horizon where $$g$$ is extreme, $$c$$ may become significantly higher than $$c_{\infty}$$.  
- **Inside Event Horizon**: The pulse accelerates further due to immense $$g$$, but no information escapes beyond this point.  

### **Frequency and Wavelength**
- **Frequency**: Hypothesizing that the laser's emitted frequency $$\nu_0$$ remains **locally invariant** (no gravitational redshift assumed), an observer at infinity would detect a **redshift** due to energy conservation:  
  - The photon gains kinetic energy as it falls into the gravity well, decreasing its frequency.  
  - **Observed Effect**: $$\nu_{\text{observed}} = \nu_0 \sqrt{1 - \frac{2GM}{rc^2}}$$ (analogous to GR gravitational redshift, but modified by variable $$c$$).  
- **Wavelength**: Given $$\lambda = c / \nu$$, as $$c$$ increases and $$\nu$$ decreases, the wavelength $$\lambda$$ **increases dramatically**. For example:  
  - Weak gravity: $$\lambda \approx c_{\infty} / \nu_0$$.  
  - Near black hole: $$\lambda$$ expands as the pulse stretches spatially.  

### **Trajectory**
- **Radial Path**: If aimed directly at the black hole, the trajectory remains **radial and straight** due to symmetry.  
- **Near-Miss Path**: If the pulse has a transverse component:  
  - **Bending**: Light bends **away** from the black hole, opposite to GR. Here, the refractive index $$n \propto 1/c$$ decreases near the hole, causing deflection toward regions of **lower** $$n$$ (like a mirage).  
  - **Magnitude**: Deflection angle is small without transverse velocity, but increases with proximity and impact parameter.  
- **At Event Horizon**: Radial light paths converge inward; escape is impossible beyond this radius.  

### **Key Physics Summary**
| Property          | Weak Gravity (Large $$r$$)          | Near Black Hole (Small $$r$$)          |
|-------------------|-------------------------------------|----------------------------------------|
| **Speed ($$c$$)** | Baseline $$c_{\infty}$$             | Increases $$\propto 1/r^2$$            |
| **Frequency ($$\nu$$)** | Emitted $$\nu_0$$                | Redshifted (decreases)                 |
| **Wavelength ($$\lambda$$)** | $$\lambda_0 = c_{\infty}/\nu_0$$  | Significantly increases                |
| **Trajectory**    | Radial/straight                    | Radial or deflected away if non-radial |  

### **Journey Synopsis**
1. **Launch**: Pulse departs at $$c_{\infty}$$ with $$\nu_0$$ and $$\lambda_0$$.  
2. **Transit**: Accelerates; $$\nu$$ drops, $$\lambda$$ grows. If not radial, path curves away.  
3. **Event Horizon**: Crosses threshold, $$c$$ peaks, and the pulse is captured forever.  

This behavior starkly contrasts with GR, where constant $$c$$ causes blueshift during infall and light bends **toward** masses. Here, accelerating light redshifts and repels, driven by gravity-dependent $$c$$.